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 ncmul::~ncmul()
  54 {
  55         debugmsg("ncmul destructor",LOGLEVEL_DESTRUCT);
  56         destroy(false);
  57 }
  58
  59 ncmul::ncmul(const ncmul & other)
  60 {
  61         debugmsg("ncmul copy constructor",LOGLEVEL_CONSTRUCT);
  62         copy(other);
  63 }
  64
  65 const ncmul & ncmul::operator=(const ncmul & other)
  66 {
  67         debugmsg("ncmul operator=",LOGLEVEL_ASSIGNMENT);
  68         if (this != &other) {
  69                 destroy(true);
  70                 copy(other);
  71         }
  72         return *this;
  73 }
  74
  75 // protected
  76
  77 void ncmul::copy(const ncmul & other)
  78 {
  79         inherited::copy(other);
  80 }
  81
  82 void ncmul::destroy(bool call_parent)
  83 {
  84         if (call_parent) inherited::destroy(call_parent);
  85 }
  86
  87 //////////
  88 // other constructors
  89 //////////
  90
  91 // public
  92
  93 ncmul::ncmul(const ex & lh, const ex & rh) : inherited(lh,rh)
  94 {
  95         debugmsg("ncmul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
  96         tinfo_key = TINFO_ncmul;
  97 }
  98
  99 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3) : inherited(f1,f2,f3)
 100 {
 101         debugmsg("ncmul constructor from 3 ex",LOGLEVEL_CONSTRUCT);
 102         tinfo_key = TINFO_ncmul;
 103 }
 104
 105 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
 106              const ex & f4) : inherited(f1,f2,f3,f4)
 107 {
 108         debugmsg("ncmul constructor from 4 ex",LOGLEVEL_CONSTRUCT);
 109         tinfo_key = TINFO_ncmul;
 110 }
 111
 112 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
 113              const ex & f4, const ex & f5) : inherited(f1,f2,f3,f4,f5)
 114 {
 115         debugmsg("ncmul constructor from 5 ex",LOGLEVEL_CONSTRUCT);
 116         tinfo_key = TINFO_ncmul;
 117 }
 118
 119 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
 120              const ex & f4, const ex & f5, const ex & f6) : inherited(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(const exvector & v, bool discardable) : inherited(v,discardable)
 127 {
 128         debugmsg("ncmul constructor from exvector,bool",LOGLEVEL_CONSTRUCT);
 129         tinfo_key = TINFO_ncmul;
 130 }
 131
 132 ncmul::ncmul(exvector * vp) : inherited(vp)
 133 {
 134         debugmsg("ncmul constructor from exvector *",LOGLEVEL_CONSTRUCT);
 135         tinfo_key = TINFO_ncmul;
 136 }
 137
 138 //////////
 139 // archiving
 140 //////////
 141
 142 /** Construct object from archive_node. */
 143 ncmul::ncmul(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 144 {
 145         debugmsg("ncmul constructor from archive_node", LOGLEVEL_CONSTRUCT);
 146 }
 147
 148 /** Unarchive the object. */
 149 ex ncmul::unarchive(const archive_node &n, const lst &sym_lst)
 150 {
 151         return (new ncmul(n, sym_lst))->setflag(status_flags::dynallocated);
 152 }
 153
 154 /** Archive the object. */
 155 void ncmul::archive(archive_node &n) const
 156 {
 157         inherited::archive(n);
 158 }
 159
 160
 161 //////////
 162 // functions overriding virtual functions from bases classes
 163 //////////
 164
 165 // public
 166
 167 basic * ncmul::duplicate() const
 168 {
 169         debugmsg("ncmul duplicate",LOGLEVEL_ASSIGNMENT);
 170         return new ncmul(*this);
 171 }
 172
 173 void ncmul::print(std::ostream & os, unsigned upper_precedence) const
 174 {
 175         debugmsg("ncmul print",LOGLEVEL_PRINT);
 176         printseq(os,'(','%',')',precedence,upper_precedence);
 177 }
 178
 179 void ncmul::printraw(std::ostream & os) const
 180 {
 181         debugmsg("ncmul printraw",LOGLEVEL_PRINT);
 182         os << "%(";
 183         for (exvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 184                 (*it).bp->printraw(os);
 185                 os << ",";
 186         }
 187         os << ",hash=" << hashvalue << ",flags=" << flags;
 188         os << ")";
 189 }
 190
 191 void ncmul::printcsrc(std::ostream & os, unsigned type, unsigned upper_precedence) const
 192 {
 193         debugmsg("ncmul print csrc",LOGLEVEL_PRINT);
 194         exvector::const_iterator it;
 195         exvector::const_iterator itend = seq.end()-1;
 196         os << "ncmul(";
 197         for (it=seq.begin(); it!=itend; ++it) {
 198                 (*it).bp->printcsrc(os,precedence);
 199                 os << ",";
 200         }
 201         (*it).bp->printcsrc(os,precedence);
 202         os << ")";
 203 }
 204
 205 bool ncmul::info(unsigned inf) const
 206 {
 207         throw(std::logic_error("which flags have to be implemented in ncmul::info()?"));
 208 }
 209
 210 typedef std::vector<int> intvector;
 211
 212 ex ncmul::expand(unsigned options) const
 213 {
 214         exvector sub_expanded_seq;
 215         intvector positions_of_adds;
 216         intvector number_of_add_operands;
 217
 218         exvector expanded_seq=expandchildren(options);
 219
 220         positions_of_adds.resize(expanded_seq.size());
 221         number_of_add_operands.resize(expanded_seq.size());
 222
 223         int number_of_adds=0;
 224         int number_of_expanded_terms=1;
 225
 226         unsigned current_position=0;
 227         exvector::const_iterator last=expanded_seq.end();
 228         for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 229                 if (is_ex_exactly_of_type((*cit),add)) {
 230                         positions_of_adds[number_of_adds]=current_position;
 231                         const add & expanded_addref=ex_to_add(*cit);
 232                         number_of_add_operands[number_of_adds]=expanded_addref.seq.size();
 233                         number_of_expanded_terms *= expanded_addref.seq.size();
 234                         number_of_adds++;
 235                 }
 236                 current_position++;
 237         }
 238
 239         if (number_of_adds==0) {
 240                 return (new ncmul(expanded_seq,1))->setflag(status_flags::dynallocated ||
 241                                                                                                         status_flags::expanded);
 242         }
 243
 244         exvector distrseq;
 245         distrseq.reserve(number_of_expanded_terms);
 246
 247         intvector k;
 248         k.resize(number_of_adds);
 249
 250         int l;
 251         for (l=0; l<number_of_adds; l++) {
 252                 k[l]=0;
 253         }
 254
 255         while (1) {
 256                 exvector term;
 257                 term=expanded_seq;
 258                 for (l=0; l<number_of_adds; l++) {
 259                         GINAC_ASSERT(is_ex_exactly_of_type(expanded_seq[positions_of_adds[l]],add));
 260                         const add & addref=ex_to_add(expanded_seq[positions_of_adds[l]]);
 261                         term[positions_of_adds[l]]=addref.recombine_pair_to_ex(addref.seq[k[l]]);
 262                 }
 263                 distrseq.push_back((new ncmul(term,1))->setflag(status_flags::dynallocated |
 264                                                                                                                 status_flags::expanded));
 265
 266                 // increment k[]
 267                 l=number_of_adds-1;
 268                 while ((l>=0)&&((++k[l])>=number_of_add_operands[l])) {
 269                         k[l]=0;
 270                         l--;
 271                 }
 272                 if (l<0) break;
 273         }
 274
 275         return (new add(distrseq))->setflag(status_flags::dynallocated |
 276                                                                                 status_flags::expanded);
 277 }
 278
 279 int ncmul::degree(const symbol & s) const
 280 {
 281         int deg_sum=0;
 282         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 283                 deg_sum+=(*cit).degree(s);
 284         }
 285         return deg_sum;
 286 }
 287
 288 int ncmul::ldegree(const symbol & s) const
 289 {
 290         int deg_sum=0;
 291         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 292                 deg_sum+=(*cit).ldegree(s);
 293         }
 294         return deg_sum;
 295 }
 296
 297 ex ncmul::coeff(const symbol & s, int n) const
 298 {
 299         exvector coeffseq;
 300         coeffseq.reserve(seq.size());
 301
 302         if (n==0) {
 303                 // product of individual coeffs
 304                 // if a non-zero power of s is found, the resulting product will be 0
 305                 exvector::const_iterator it=seq.begin();
 306                 while (it!=seq.end()) {
 307                         coeffseq.push_back((*it).coeff(s,n));
 308                         ++it;
 309                 }
 310                 return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 311         }
 312
 313         exvector::const_iterator it=seq.begin();
 314         bool coeff_found=0;
 315         while (it!=seq.end()) {
 316                 ex c=(*it).coeff(s,n);
 317                 if (!c.is_zero()) {
 318                         coeffseq.push_back(c);
 319                         coeff_found=1;
 320                 } else {
 321                         coeffseq.push_back(*it);
 322                 }
 323                 ++it;
 324         }
 325
 326         if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 327
 328         return _ex0();
 329 }
 330
 331 unsigned ncmul::count_factors(const ex & e) const
 332 {
 333         if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
 334                 (is_ex_exactly_of_type(e,ncmul))) {
 335                 unsigned factors=0;
 336                 for (unsigned i=0; i<e.nops(); i++)
 337                         factors += count_factors(e.op(i));
 338
 339                 return factors;
 340         }
 341         return 1;
 342 }
 343
 344 void ncmul::append_factors(exvector & v, const ex & e) const
 345 {
 346         if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
 347                 (is_ex_exactly_of_type(e,ncmul))) {
 348                 for (unsigned i=0; i<e.nops(); i++)
 349                         append_factors(v,e.op(i));
 350
 351                 return;
 352         }
 353         v.push_back(e);
 354 }
 355
 356 typedef std::vector<unsigned> unsignedvector;
 357 typedef std::vector<exvector> exvectorvector;
 358
 359 ex ncmul::eval(int level) const
 360 {
 361         // simplifications: ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 362         //                      ncmul(...,x1,x2,...,x3,x4,...) (associativity)
 363         //                  ncmul(x) -> x
 364         //                  ncmul() -> 1
 365         //                  ncmul(...,c1,...,c2,...)
 366         //                      *(c1,c2,ncmul(...)) (pull out commutative elements)
 367         //                  ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 368         //                      (collect elements of same type)
 369         //                  ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)
 370         // the following rule would be nice, but produces a recursion,
 371         // which must be trapped by introducing a flag that the sub-ncmuls()
 372         // are already evaluated (maybe later...)
 373         //                  ncmul(x1,x2,...,X,y1,y2,...) ->
 374         //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
 375         //                      (X noncommutative_composite)
 376
 377         if ((level==1)&&(flags & status_flags::evaluated)) {
 378                 return *this;
 379         }
 380
 381         exvector evaledseq=evalchildren(level);
 382
 383         // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 384         //     ncmul(...,x1,x2,...,x3,x4,...) (associativity)
 385         unsigned factors=0;
 386         for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit) {
 387                 factors += count_factors(*cit);
 388         }
 389
 390         exvector assocseq;
 391         assocseq.reserve(factors);
 392         for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit) {
 393                 append_factors(assocseq,*cit);
 394         }
 395
 396         // ncmul(x) -> x
 397         if (assocseq.size()==1) return *(seq.begin());
 398
 399         // ncmul() -> 1
 400         if (assocseq.size()==0) return _ex1();
 401
 402         // determine return types
 403         unsignedvector rettypes;
 404         rettypes.reserve(assocseq.size());
 405         unsigned i=0;
 406         unsigned count_commutative=0;
 407         unsigned count_noncommutative=0;
 408         unsigned count_noncommutative_composite=0;
 409         for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
 410                 switch (rettypes[i]=(*cit).return_type()) {
 411                 case return_types::commutative:
 412                         count_commutative++;
 413                         break;
 414                 case return_types::noncommutative:
 415                         count_noncommutative++;
 416                         break;
 417                 case return_types::noncommutative_composite:
 418                         count_noncommutative_composite++;
 419                         break;
 420                 default:
 421                         throw(std::logic_error("ncmul::eval(): invalid return type"));
 422                 }
 423                 ++i;
 424         }
 425         GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
 426
 427         // ncmul(...,c1,...,c2,...) ->
 428         //     *(c1,c2,ncmul(...)) (pull out commutative elements)
 429         if (count_commutative!=0) {
 430                 exvector commutativeseq;
 431                 commutativeseq.reserve(count_commutative+1);
 432                 exvector noncommutativeseq;
 433                 noncommutativeseq.reserve(assocseq.size()-count_commutative);
 434                 for (i=0; i<assocseq.size(); ++i) {
 435                         if (rettypes[i]==return_types::commutative) {
 436                                 commutativeseq.push_back(assocseq[i]);
 437                         } else {
 438                                 noncommutativeseq.push_back(assocseq[i]);
 439                         }
 440                 }
 441                 commutativeseq.push_back((new ncmul(noncommutativeseq,1))->setflag(status_flags::dynallocated));
 442                 return (new mul(commutativeseq))->setflag(status_flags::dynallocated);
 443         }
 444
 445         // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 446         //     (collect elements of same type)
 447
 448         if (count_noncommutative_composite==0) {
 449                 // there are neither commutative nor noncommutative_composite
 450                 // elements in assocseq
 451                 GINAC_ASSERT(count_commutative==0);
 452
 453                 exvectorvector evv;
 454                 unsignedvector rttinfos;
 455                 evv.reserve(assocseq.size());
 456                 rttinfos.reserve(assocseq.size());
 457
 458                 for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
 459                         unsigned ti=(*cit).return_type_tinfo();
 460                         // search type in vector of known types
 461                         for (i=0; i<rttinfos.size(); ++i) {
 462                                 if (ti==rttinfos[i]) {
 463                                         evv[i].push_back(*cit);
 464                                         break;
 465                                 }
 466                         }
 467                         if (i>=rttinfos.size()) {
 468                                 // new type
 469                                 rttinfos.push_back(ti);
 470                                 evv.push_back(exvector());
 471                                 (*(evv.end()-1)).reserve(assocseq.size());
 472                                 (*(evv.end()-1)).push_back(*cit);
 473                         }
 474                 }
 475
 476 #ifdef DO_GINAC_ASSERT
 477                 GINAC_ASSERT(evv.size()==rttinfos.size());
 478                 GINAC_ASSERT(evv.size()>0);
 479                 unsigned s=0;
 480                 for (i=0; i<evv.size(); ++i) {
 481                         s += evv[i].size();
 482                 }
 483                 GINAC_ASSERT(s==assocseq.size());
 484 #endif // def DO_GINAC_ASSERT
 485
 486                 // if all elements are of same type, simplify the string
 487                 if (evv.size()==1) {
 488                         return evv[0][0].simplify_ncmul(evv[0]);
 489                 }
 490
 491                 exvector splitseq;
 492                 splitseq.reserve(evv.size());
 493                 for (i=0; i<evv.size(); ++i) {
 494                         splitseq.push_back((new ncmul(evv[i]))->setflag(status_flags::dynallocated));
 495                 }
 496
 497                 return (new mul(splitseq))->setflag(status_flags::dynallocated);
 498         }
 499
 500         return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
 501                                                                                   status_flags::evaluated);
 502 }
 503
 504 exvector ncmul::get_indices(void) const
 505 {
 506         // return union of indices of factors
 507         exvector iv;
 508         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 509                 exvector subiv=(*cit).get_indices();
 510                 iv.reserve(iv.size()+subiv.size());
 511                 for (exvector::const_iterator cit2=subiv.begin(); cit2!=subiv.end(); ++cit2) {
 512                         iv.push_back(*cit2);
 513                 }
 514         }
 515         return iv;
 516 }
 517
 518 ex ncmul::subs(const lst & ls, const lst & lr) const
 519 {
 520         return ncmul(subschildren(ls, lr));
 521 }
 522
 523 ex ncmul::thisexprseq(const exvector & v) const
 524 {
 525         return (new ncmul(v))->setflag(status_flags::dynallocated);
 526 }
 527
 528 ex ncmul::thisexprseq(exvector * vp) const
 529 {
 530         return (new ncmul(vp))->setflag(status_flags::dynallocated);
 531 }
 532
 533 // protected
 534
 535 /** Implementation of ex::diff() for a non-commutative product. It always returns 0.
 536  *  @see ex::diff */
 537 ex ncmul::derivative(const symbol & s) const
 538 {
 539         return _ex0();
 540 }
 541
 542 int ncmul::compare_same_type(const basic & other) const
 543 {
 544         return inherited::compare_same_type(other);
 545 }
 546
 547 unsigned ncmul::return_type(void) const
 548 {
 549         if (seq.size()==0) {
 550                 // ncmul without factors: should not happen, but commutes
 551                 return return_types::commutative;
 552         }
 553
 554         bool all_commutative=1;
 555         unsigned rt;
 556         exvector::const_iterator cit_noncommutative_element; // point to first found nc element
 557
 558         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 559                 rt=(*cit).return_type();
 560                 if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
 561                 if ((rt==return_types::noncommutative)&&(all_commutative)) {
 562                         // first nc element found, remember position
 563                         cit_noncommutative_element=cit;
 564                         all_commutative=0;
 565                 }
 566                 if ((rt==return_types::noncommutative)&&(!all_commutative)) {
 567                         // another nc element found, compare type_infos
 568                         if ((*cit_noncommutative_element).return_type_tinfo()!=(*cit).return_type_tinfo()) {
 569                                 // diffent types -> mul is ncc
 570                                 return return_types::noncommutative_composite;
 571                         }
 572                 }
 573         }
 574         // all factors checked
 575         GINAC_ASSERT(!all_commutative); // not all factors should commute, because this is a ncmul();
 576         return all_commutative ? return_types::commutative : return_types::noncommutative;
 577 }
 578
 579 unsigned ncmul::return_type_tinfo(void) const
 580 {
 581         if (seq.size()==0) {
 582                 // mul without factors: should not happen
 583                 return tinfo_key;
 584         }
 585         // return type_info of first noncommutative element
 586         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 587                 if ((*cit).return_type()==return_types::noncommutative) {
 588                         return (*cit).return_type_tinfo();
 589                 }
 590         }
 591         // no noncommutative element found, should not happen
 592         return tinfo_key;
 593 }
 594
 595 //////////
 596 // new virtual functions which can be overridden by derived classes
 597 //////////
 598
 599 // none
 600
 601 //////////
 602 // non-virtual functions in this class
 603 //////////
 604
 605 exvector ncmul::expandchildren(unsigned options) const
 606 {
 607         exvector s;
 608         s.reserve(seq.size());
 609
 610         for (exvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 611                 s.push_back((*it).expand(options));
 612         }
 613         return s;
 614 }
 615
 616 const exvector & ncmul::get_factors(void) const
 617 {
 618         return seq;
 619 }
 620
 621 //////////
 622 // static member variables
 623 //////////
 624
 625 // protected
 626
 627 unsigned ncmul::precedence=50;
 628
 629 //////////
 630 // friend functions
 631 //////////
 632
 633 ex nonsimplified_ncmul(const exvector & v)
 634 {
 635         return (new ncmul(v))->setflag(status_flags::dynallocated);
 636 }
 637
 638 ex simplified_ncmul(const exvector & v)
 639 {
 640         if (v.size()==0) {
 641                 return _ex1();
 642         } else if (v.size()==1) {
 643                 return v[0];
 644         }
 645         return (new ncmul(v))->setflag(status_flags::dynallocated |
 646                                        status_flags::evaluated);
 647 }
 648
 649 #ifndef NO_NAMESPACE_GINAC
 650 } // namespace GiNaC
 651 #endif // ndef NO_NAMESPACE_GINAC