ginac/ncmul.cpp

   1 /** @file ncmul.cpp
   2  *
   3  *  Implementation of GiNaC's non-commutative products of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2000 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
 183         os << "%(";
 184         for (exvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 185                 (*it).bp->printraw(os);
 186                 os << ",";
 187         }
 188         os << ",hash=" << hashvalue << ",flags=" << flags;
 189         os << ")";
 190 }
 191
 192 void ncmul::printcsrc(std::ostream & os, unsigned upper_precedence) const
 193 {
 194         debugmsg("ncmul print csrc",LOGLEVEL_PRINT);
 195         exvector::const_iterator it;
 196         exvector::const_iterator itend = seq.end()-1;
 197         os << "ncmul(";
 198         for (it=seq.begin(); it!=itend; ++it) {
 199                 (*it).bp->printcsrc(os,precedence);
 200                 os << ",";
 201         }
 202         (*it).bp->printcsrc(os,precedence);
 203         os << ")";
 204 }
 205
 206 bool ncmul::info(unsigned inf) const
 207 {
 208         throw(std::logic_error("which flags have to be implemented in ncmul::info()?"));
 209 }
 210
 211 typedef std::vector<int> intvector;
 212
 213 ex ncmul::expand(unsigned options) const
 214 {
 215         exvector sub_expanded_seq;
 216         intvector positions_of_adds;
 217         intvector number_of_add_operands;
 218
 219         exvector expanded_seq=expandchildren(options);
 220
 221         positions_of_adds.resize(expanded_seq.size());
 222         number_of_add_operands.resize(expanded_seq.size());
 223
 224         int number_of_adds=0;
 225         int number_of_expanded_terms=1;
 226
 227         unsigned current_position=0;
 228         exvector::const_iterator last=expanded_seq.end();
 229         for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 230                 if (is_ex_exactly_of_type((*cit),add)) {
 231                         positions_of_adds[number_of_adds]=current_position;
 232                         const add & expanded_addref=ex_to_add(*cit);
 233                         number_of_add_operands[number_of_adds]=expanded_addref.seq.size();
 234                         number_of_expanded_terms *= expanded_addref.seq.size();
 235                         number_of_adds++;
 236                 }
 237                 current_position++;
 238         }
 239
 240         if (number_of_adds==0) {
 241                 return (new ncmul(expanded_seq,1))->setflag(status_flags::dynallocated ||
 242                                                                                                         status_flags::expanded);
 243         }
 244
 245         exvector distrseq;
 246         distrseq.reserve(number_of_expanded_terms);
 247
 248         intvector k;
 249         k.resize(number_of_adds);
 250
 251         int l;
 252         for (l=0; l<number_of_adds; l++) {
 253                 k[l]=0;
 254         }
 255
 256         while (1) {
 257                 exvector term;
 258                 term=expanded_seq;
 259                 for (l=0; l<number_of_adds; l++) {
 260                         GINAC_ASSERT(is_ex_exactly_of_type(expanded_seq[positions_of_adds[l]],add));
 261                         const add & addref=ex_to_add(expanded_seq[positions_of_adds[l]]);
 262                         term[positions_of_adds[l]]=addref.recombine_pair_to_ex(addref.seq[k[l]]);
 263                 }
 264                 distrseq.push_back((new ncmul(term,1))->setflag(status_flags::dynallocated |
 265                                                                                                                 status_flags::expanded));
 266
 267                 // increment k[]
 268                 l=number_of_adds-1;
 269                 while ((l>=0)&&((++k[l])>=number_of_add_operands[l])) {
 270                         k[l]=0;
 271                         l--;
 272                 }
 273                 if (l<0) break;
 274         }
 275
 276         return (new add(distrseq))->setflag(status_flags::dynallocated |
 277                                                                                 status_flags::expanded);
 278 }
 279
 280 int ncmul::degree(const symbol & s) const
 281 {
 282         int deg_sum=0;
 283         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 284                 deg_sum+=(*cit).degree(s);
 285         }
 286         return deg_sum;
 287 }
 288
 289 int ncmul::ldegree(const symbol & s) const
 290 {
 291         int deg_sum=0;
 292         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 293                 deg_sum+=(*cit).ldegree(s);
 294         }
 295         return deg_sum;
 296 }
 297
 298 ex ncmul::coeff(const symbol & s, int n) const
 299 {
 300         exvector coeffseq;
 301         coeffseq.reserve(seq.size());
 302
 303         if (n==0) {
 304                 // product of individual coeffs
 305                 // if a non-zero power of s is found, the resulting product will be 0
 306                 exvector::const_iterator it=seq.begin();
 307                 while (it!=seq.end()) {
 308                         coeffseq.push_back((*it).coeff(s,n));
 309                         ++it;
 310                 }
 311                 return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 312         }
 313
 314         exvector::const_iterator it=seq.begin();
 315         bool coeff_found=0;
 316         while (it!=seq.end()) {
 317                 ex c=(*it).coeff(s,n);
 318                 if (!c.is_zero()) {
 319                         coeffseq.push_back(c);
 320                         coeff_found=1;
 321                 } else {
 322                         coeffseq.push_back(*it);
 323                 }
 324                 ++it;
 325         }
 326
 327         if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 328
 329         return _ex0();
 330 }
 331
 332 unsigned ncmul::count_factors(const ex & e) const
 333 {
 334         if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
 335                 (is_ex_exactly_of_type(e,ncmul))) {
 336                 unsigned factors=0;
 337                 for (unsigned i=0; i<e.nops(); i++)
 338                         factors += count_factors(e.op(i));
 339
 340                 return factors;
 341         }
 342         return 1;
 343 }
 344
 345 void ncmul::append_factors(exvector & v, const ex & e) const
 346 {
 347         if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
 348                 (is_ex_exactly_of_type(e,ncmul))) {
 349                 for (unsigned i=0; i<e.nops(); i++)
 350                         append_factors(v,e.op(i));
 351
 352                 return;
 353         }
 354         v.push_back(e);
 355 }
 356
 357 typedef std::vector<unsigned> unsignedvector;
 358 typedef std::vector<exvector> exvectorvector;
 359
 360 ex ncmul::eval(int level) const
 361 {
 362         // simplifications: ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 363         //                      ncmul(...,x1,x2,...,x3,x4,...) (associativity)
 364         //                  ncmul(x) -> x
 365         //                  ncmul() -> 1
 366         //                  ncmul(...,c1,...,c2,...)
 367         //                      *(c1,c2,ncmul(...)) (pull out commutative elements)
 368         //                  ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 369         //                      (collect elements of same type)
 370         //                  ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)
 371         // the following rule would be nice, but produces a recursion,
 372         // which must be trapped by introducing a flag that the sub-ncmuls()
 373         // are already evaluated (maybe later...)
 374         //                  ncmul(x1,x2,...,X,y1,y2,...) ->
 375         //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
 376         //                      (X noncommutative_composite)
 377
 378         if ((level==1)&&(flags & status_flags::evaluated)) {
 379                 return *this;
 380         }
 381
 382         exvector evaledseq=evalchildren(level);
 383
 384         // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 385         //     ncmul(...,x1,x2,...,x3,x4,...) (associativity)
 386         unsigned factors=0;
 387         for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit) {
 388                 factors += count_factors(*cit);
 389         }
 390
 391         exvector assocseq;
 392         assocseq.reserve(factors);
 393         for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit) {
 394                 append_factors(assocseq,*cit);
 395         }
 396
 397         // ncmul(x) -> x
 398         if (assocseq.size()==1) return *(seq.begin());
 399
 400         // ncmul() -> 1
 401         if (assocseq.size()==0) return _ex1();
 402
 403         // determine return types
 404         unsignedvector rettypes;
 405         rettypes.reserve(assocseq.size());
 406         unsigned i=0;
 407         unsigned count_commutative=0;
 408         unsigned count_noncommutative=0;
 409         unsigned count_noncommutative_composite=0;
 410         for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
 411                 switch (rettypes[i]=(*cit).return_type()) {
 412                 case return_types::commutative:
 413                         count_commutative++;
 414                         break;
 415                 case return_types::noncommutative:
 416                         count_noncommutative++;
 417                         break;
 418                 case return_types::noncommutative_composite:
 419                         count_noncommutative_composite++;
 420                         break;
 421                 default:
 422                         throw(std::logic_error("ncmul::eval(): invalid return type"));
 423                 }
 424                 ++i;
 425         }
 426         GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
 427
 428         // ncmul(...,c1,...,c2,...) ->
 429         //     *(c1,c2,ncmul(...)) (pull out commutative elements)
 430         if (count_commutative!=0) {
 431                 exvector commutativeseq;
 432                 commutativeseq.reserve(count_commutative+1);
 433                 exvector noncommutativeseq;
 434                 noncommutativeseq.reserve(assocseq.size()-count_commutative);
 435                 for (i=0; i<assocseq.size(); ++i) {
 436                         if (rettypes[i]==return_types::commutative) {
 437                                 commutativeseq.push_back(assocseq[i]);
 438                         } else {
 439                                 noncommutativeseq.push_back(assocseq[i]);
 440                         }
 441                 }
 442                 commutativeseq.push_back((new ncmul(noncommutativeseq,1))->setflag(status_flags::dynallocated));
 443                 return (new mul(commutativeseq))->setflag(status_flags::dynallocated);
 444         }
 445
 446         // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 447         //     (collect elements of same type)
 448
 449         if (count_noncommutative_composite==0) {
 450                 // there are neither commutative nor noncommutative_composite
 451                 // elements in assocseq
 452                 GINAC_ASSERT(count_commutative==0);
 453
 454                 exvectorvector evv;
 455                 unsignedvector rttinfos;
 456                 evv.reserve(assocseq.size());
 457                 rttinfos.reserve(assocseq.size());
 458
 459                 for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
 460                         unsigned ti=(*cit).return_type_tinfo();
 461                         // search type in vector of known types
 462                         for (i=0; i<rttinfos.size(); ++i) {
 463                                 if (ti==rttinfos[i]) {
 464                                         evv[i].push_back(*cit);
 465                                         break;
 466                                 }
 467                         }
 468                         if (i>=rttinfos.size()) {
 469                                 // new type
 470                                 rttinfos.push_back(ti);
 471                                 evv.push_back(exvector());
 472                                 (*(evv.end()-1)).reserve(assocseq.size());
 473                                 (*(evv.end()-1)).push_back(*cit);
 474                         }
 475                 }
 476
 477 #ifdef DO_GINAC_ASSERT
 478                 GINAC_ASSERT(evv.size()==rttinfos.size());
 479                 GINAC_ASSERT(evv.size()>0);
 480                 unsigned s=0;
 481                 for (i=0; i<evv.size(); ++i) {
 482                         s += evv[i].size();
 483                 }
 484                 GINAC_ASSERT(s==assocseq.size());
 485 #endif // def DO_GINAC_ASSERT
 486
 487                 // if all elements are of same type, simplify the string
 488                 if (evv.size()==1) {
 489                         return evv[0][0].simplify_ncmul(evv[0]);
 490                 }
 491
 492                 exvector splitseq;
 493                 splitseq.reserve(evv.size());
 494                 for (i=0; i<evv.size(); ++i) {
 495                         splitseq.push_back((new ncmul(evv[i]))->setflag(status_flags::dynallocated));
 496                 }
 497
 498                 return (new mul(splitseq))->setflag(status_flags::dynallocated);
 499         }
 500
 501         return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
 502                                                                                   status_flags::evaluated);
 503 }
 504
 505 exvector ncmul::get_indices(void) const
 506 {
 507         // return union of indices of factors
 508         exvector iv;
 509         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 510                 exvector subiv=(*cit).get_indices();
 511                 iv.reserve(iv.size()+subiv.size());
 512                 for (exvector::const_iterator cit2=subiv.begin(); cit2!=subiv.end(); ++cit2) {
 513                         iv.push_back(*cit2);
 514                 }
 515         }
 516         return iv;
 517 }
 518
 519 ex ncmul::subs(const lst & ls, const lst & lr) const
 520 {
 521         return ncmul(subschildren(ls, lr));
 522 }
 523
 524 ex ncmul::thisexprseq(const exvector & v) const
 525 {
 526         return (new ncmul(v))->setflag(status_flags::dynallocated);
 527 }
 528
 529 ex ncmul::thisexprseq(exvector * vp) const
 530 {
 531         return (new ncmul(vp))->setflag(status_flags::dynallocated);
 532 }
 533
 534 // protected
 535
 536 /** Implementation of ex::diff() for a non-commutative product. It always returns 0.
 537  *  @see ex::diff */
 538 ex ncmul::derivative(const symbol & s) const
 539 {
 540         return _ex0();
 541 }
 542
 543 int ncmul::compare_same_type(const basic & other) const
 544 {
 545         return inherited::compare_same_type(other);
 546 }
 547
 548 unsigned ncmul::return_type(void) const
 549 {
 550         if (seq.size()==0) {
 551                 // ncmul without factors: should not happen, but commutes
 552                 return return_types::commutative;
 553         }
 554
 555         bool all_commutative=1;
 556         unsigned rt;
 557         exvector::const_iterator cit_noncommutative_element; // point to first found nc element
 558
 559         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 560                 rt=(*cit).return_type();
 561                 if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
 562                 if ((rt==return_types::noncommutative)&&(all_commutative)) {
 563                         // first nc element found, remember position
 564                         cit_noncommutative_element=cit;
 565                         all_commutative=0;
 566                 }
 567                 if ((rt==return_types::noncommutative)&&(!all_commutative)) {
 568                         // another nc element found, compare type_infos
 569                         if ((*cit_noncommutative_element).return_type_tinfo()!=(*cit).return_type_tinfo()) {
 570                                 // diffent types -> mul is ncc
 571                                 return return_types::noncommutative_composite;
 572                         }
 573                 }
 574         }
 575         // all factors checked
 576         GINAC_ASSERT(!all_commutative); // not all factors should commute, because this is a ncmul();
 577         return all_commutative ? return_types::commutative : return_types::noncommutative;
 578 }
 579
 580 unsigned ncmul::return_type_tinfo(void) const
 581 {
 582         if (seq.size()==0) {
 583                 // mul without factors: should not happen
 584                 return tinfo_key;
 585         }
 586         // return type_info of first noncommutative element
 587         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 588                 if ((*cit).return_type()==return_types::noncommutative) {
 589                         return (*cit).return_type_tinfo();
 590                 }
 591         }
 592         // no noncommutative element found, should not happen
 593         return tinfo_key;
 594 }
 595
 596 //////////
 597 // new virtual functions which can be overridden by derived classes
 598 //////////
 599
 600 // none
 601
 602 //////////
 603 // non-virtual functions in this class
 604 //////////
 605
 606 exvector ncmul::expandchildren(unsigned options) const
 607 {
 608         exvector s;
 609         s.reserve(seq.size());
 610
 611         for (exvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 612                 s.push_back((*it).expand(options));
 613         }
 614         return s;
 615 }
 616
 617 const exvector & ncmul::get_factors(void) const
 618 {
 619         return seq;
 620 }
 621
 622 //////////
 623 // static member variables
 624 //////////
 625
 626 // protected
 627
 628 unsigned ncmul::precedence=50;
 629
 630
 631 //////////
 632 // global constants
 633 //////////
 634
 635 const ncmul some_ncmul;
 636 const type_info & typeid_ncmul=typeid(some_ncmul);
 637
 638 //////////
 639 // friend functions
 640 //////////
 641
 642 ex nonsimplified_ncmul(const exvector & v)
 643 {
 644         return (new ncmul(v))->setflag(status_flags::dynallocated);
 645 }
 646
 647 ex simplified_ncmul(const exvector & v)
 648 {
 649         if (v.size()==0) {
 650                 return _ex1();
 651         } else if (v.size()==1) {
 652                 return v[0];
 653         }
 654         return (new ncmul(v))->setflag(status_flags::dynallocated |
 655                                        status_flags::evaluated);
 656 }
 657
 658 #ifndef NO_NAMESPACE_GINAC
 659 } // namespace GiNaC
 660 #endif // ndef NO_NAMESPACE_GINAC