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