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(0);
  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(1);
  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) :
  94         inherited(lh,rh)
  95 {
  96         debugmsg("ncmul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
  97         tinfo_key = TINFO_ncmul;
  98 }
  99
 100 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3) :
 101         inherited(f1,f2,f3)
 102 {
 103         debugmsg("ncmul constructor from 3 ex",LOGLEVEL_CONSTRUCT);
 104         tinfo_key = TINFO_ncmul;
 105 }
 106
 107 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
 108           const ex & f4) : inherited(f1,f2,f3,f4)
 109 {
 110         debugmsg("ncmul constructor from 4 ex",LOGLEVEL_CONSTRUCT);
 111         tinfo_key = TINFO_ncmul;
 112 }
 113
 114 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
 115           const ex & f4, const ex & f5) : inherited(f1,f2,f3,f4,f5)
 116 {
 117         debugmsg("ncmul constructor from 5 ex",LOGLEVEL_CONSTRUCT);
 118         tinfo_key = TINFO_ncmul;
 119 }
 120
 121 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
 122           const ex & f4, const ex & f5, const ex & f6) :
 123         inherited(f1,f2,f3,f4,f5,f6)
 124 {
 125         debugmsg("ncmul constructor from 6 ex",LOGLEVEL_CONSTRUCT);
 126         tinfo_key = TINFO_ncmul;
 127 }
 128
 129 ncmul::ncmul(const exvector & v, bool discardable) : inherited(v,discardable)
 130 {
 131         debugmsg("ncmul constructor from exvector,bool",LOGLEVEL_CONSTRUCT);
 132         tinfo_key = TINFO_ncmul;
 133 }
 134
 135 ncmul::ncmul(exvector * vp) : inherited(vp)
 136 {
 137         debugmsg("ncmul constructor from exvector *",LOGLEVEL_CONSTRUCT);
 138         tinfo_key = TINFO_ncmul;
 139 }
 140
 141 //////////
 142 // archiving
 143 //////////
 144
 145 /** Construct object from archive_node. */
 146 ncmul::ncmul(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 147 {
 148         debugmsg("ncmul constructor from archive_node", LOGLEVEL_CONSTRUCT);
 149 }
 150
 151 /** Unarchive the object. */
 152 ex ncmul::unarchive(const archive_node &n, const lst &sym_lst)
 153 {
 154         return (new ncmul(n, sym_lst))->setflag(status_flags::dynallocated);
 155 }
 156
 157 /** Archive the object. */
 158 void ncmul::archive(archive_node &n) const
 159 {
 160         inherited::archive(n);
 161 }
 162
 163
 164 //////////
 165 // functions overriding virtual functions from bases classes
 166 //////////
 167
 168 // public
 169
 170 basic * ncmul::duplicate() const
 171 {
 172         debugmsg("ncmul duplicate",LOGLEVEL_ASSIGNMENT);
 173         return new ncmul(*this);
 174 }
 175
 176 void ncmul::print(std::ostream & os, unsigned upper_precedence) const
 177 {
 178         debugmsg("ncmul print",LOGLEVEL_PRINT);
 179         printseq(os,'(','%',')',precedence,upper_precedence);
 180 }
 181
 182 void ncmul::printraw(std::ostream & os) const
 183 {
 184         debugmsg("ncmul printraw",LOGLEVEL_PRINT);
 185
 186         os << "%(";
 187         for (exvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 188                 (*it).bp->printraw(os);
 189                 os << ",";
 190         }
 191         os << ",hash=" << hashvalue << ",flags=" << flags;
 192         os << ")";
 193 }
 194
 195 void ncmul::printcsrc(std::ostream & os, unsigned upper_precedence) const
 196 {
 197         debugmsg("ncmul print csrc",LOGLEVEL_PRINT);
 198         exvector::const_iterator it;
 199         exvector::const_iterator itend = seq.end()-1;
 200         os << "ncmul(";
 201         for (it=seq.begin(); it!=itend; ++it) {
 202                 (*it).bp->printcsrc(os,precedence);
 203                 os << ",";
 204         }
 205         (*it).bp->printcsrc(os,precedence);
 206         os << ")";
 207 }
 208
 209 bool ncmul::info(unsigned inf) const
 210 {
 211         throw(std::logic_error("which flags have to be implemented in ncmul::info()?"));
 212 }
 213
 214 typedef std::vector<int> intvector;
 215
 216 ex ncmul::expand(unsigned options) const
 217 {
 218         exvector sub_expanded_seq;
 219         intvector positions_of_adds;
 220         intvector number_of_add_operands;
 221
 222         exvector expanded_seq=expandchildren(options);
 223
 224         positions_of_adds.resize(expanded_seq.size());
 225         number_of_add_operands.resize(expanded_seq.size());
 226
 227         int number_of_adds=0;
 228         int number_of_expanded_terms=1;
 229
 230         unsigned current_position=0;
 231         exvector::const_iterator last=expanded_seq.end();
 232         for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 233                 if (is_ex_exactly_of_type((*cit),add)) {
 234                         positions_of_adds[number_of_adds]=current_position;
 235                         const add & expanded_addref=ex_to_add(*cit);
 236                         number_of_add_operands[number_of_adds]=expanded_addref.seq.size();
 237                         number_of_expanded_terms *= expanded_addref.seq.size();
 238                         number_of_adds++;
 239                 }
 240                 current_position++;
 241         }
 242
 243         if (number_of_adds==0) {
 244                 return (new ncmul(expanded_seq,1))->setflag(status_flags::dynallocated ||
 245                                                                                                         status_flags::expanded);
 246         }
 247
 248         exvector distrseq;
 249         distrseq.reserve(number_of_expanded_terms);
 250
 251         intvector k;
 252         k.resize(number_of_adds);
 253
 254         int l;
 255         for (l=0; l<number_of_adds; l++) {
 256                 k[l]=0;
 257         }
 258
 259         while (1) {
 260                 exvector term;
 261                 term=expanded_seq;
 262                 for (l=0; l<number_of_adds; l++) {
 263                         GINAC_ASSERT(is_ex_exactly_of_type(expanded_seq[positions_of_adds[l]],add));
 264                         const add & addref=ex_to_add(expanded_seq[positions_of_adds[l]]);
 265                         term[positions_of_adds[l]]=addref.recombine_pair_to_ex(addref.seq[k[l]]);
 266                 }
 267                 distrseq.push_back((new ncmul(term,1))->setflag(status_flags::dynallocated |
 268                                                                                                                 status_flags::expanded));
 269
 270                 // increment k[]
 271                 l=number_of_adds-1;
 272                 while ((l>=0)&&((++k[l])>=number_of_add_operands[l])) {
 273                         k[l]=0;
 274                         l--;
 275                 }
 276                 if (l<0) break;
 277         }
 278
 279         return (new add(distrseq))->setflag(status_flags::dynallocated |
 280                                                                                 status_flags::expanded);
 281 }
 282
 283 int ncmul::degree(const symbol & s) const
 284 {
 285         int deg_sum=0;
 286         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 287                 deg_sum+=(*cit).degree(s);
 288         }
 289         return deg_sum;
 290 }
 291
 292 int ncmul::ldegree(const symbol & s) const
 293 {
 294         int deg_sum=0;
 295         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 296                 deg_sum+=(*cit).ldegree(s);
 297         }
 298         return deg_sum;
 299 }
 300
 301 ex ncmul::coeff(const symbol & s, int n) const
 302 {
 303         exvector coeffseq;
 304         coeffseq.reserve(seq.size());
 305
 306         if (n==0) {
 307                 // product of individual coeffs
 308                 // if a non-zero power of s is found, the resulting product will be 0
 309                 exvector::const_iterator it=seq.begin();
 310                 while (it!=seq.end()) {
 311                         coeffseq.push_back((*it).coeff(s,n));
 312                         ++it;
 313                 }
 314                 return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 315         }
 316
 317         exvector::const_iterator it=seq.begin();
 318         bool coeff_found=0;
 319         while (it!=seq.end()) {
 320                 ex c=(*it).coeff(s,n);
 321                 if (!c.is_zero()) {
 322                         coeffseq.push_back(c);
 323                         coeff_found=1;
 324                 } else {
 325                         coeffseq.push_back(*it);
 326                 }
 327                 ++it;
 328         }
 329
 330         if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 331
 332         return _ex0();
 333 }
 334
 335 unsigned ncmul::count_factors(const ex & e) const
 336 {
 337         if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
 338                 (is_ex_exactly_of_type(e,ncmul))) {
 339                 unsigned factors=0;
 340                 for (unsigned i=0; i<e.nops(); i++)
 341                         factors += count_factors(e.op(i));
 342
 343                 return factors;
 344         }
 345         return 1;
 346 }
 347
 348 void ncmul::append_factors(exvector & v, const ex & e) const
 349 {
 350         if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
 351                 (is_ex_exactly_of_type(e,ncmul))) {
 352                 for (unsigned i=0; i<e.nops(); i++)
 353                         append_factors(v,e.op(i));
 354
 355                 return;
 356         }
 357         v.push_back(e);
 358 }
 359
 360 typedef std::vector<unsigned> unsignedvector;
 361 typedef std::vector<exvector> exvectorvector;
 362
 363 ex ncmul::eval(int level) const
 364 {
 365         // simplifications: ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 366         //                      ncmul(...,x1,x2,...,x3,x4,...) (associativity)
 367         //                  ncmul(x) -> x
 368         //                  ncmul() -> 1
 369         //                  ncmul(...,c1,...,c2,...) ->
 370         //                      *(c1,c2,ncmul(...)) (pull out commutative elements)
 371         //                  ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 372         //                      (collect elements of same type)
 373         //                  ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)
 374         // the following rule would be nice, but produces a recursion,
 375         // which must be trapped by introducing a flag that the sub-ncmuls()
 376         // are already evaluated (maybe later...)
 377         //                  ncmul(x1,x2,...,X,y1,y2,...) ->
 378         //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
 379         //                      (X noncommutative_composite)
 380
 381         if ((level==1)&&(flags & status_flags::evaluated)) {
 382                 return *this;
 383         }
 384
 385         exvector evaledseq=evalchildren(level);
 386
 387         // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 388         //     ncmul(...,x1,x2,...,x3,x4,...) (associativity)
 389         unsigned factors=0;
 390         for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit) {
 391                 factors += count_factors(*cit);
 392         }
 393
 394         exvector assocseq;
 395         assocseq.reserve(factors);
 396         for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit) {
 397                 append_factors(assocseq,*cit);
 398         }
 399
 400         // ncmul(x) -> x
 401         if (assocseq.size()==1) return *(seq.begin());
 402
 403         // ncmul() -> 1
 404         if (assocseq.size()==0) return _ex1();
 405
 406         // determine return types
 407         unsignedvector rettypes;
 408         rettypes.reserve(assocseq.size());
 409         unsigned i=0;
 410         unsigned count_commutative=0;
 411         unsigned count_noncommutative=0;
 412         unsigned count_noncommutative_composite=0;
 413         for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
 414                 switch (rettypes[i]=(*cit).return_type()) {
 415                 case return_types::commutative:
 416                         count_commutative++;
 417                         break;
 418                 case return_types::noncommutative:
 419                         count_noncommutative++;
 420                         break;
 421                 case return_types::noncommutative_composite:
 422                         count_noncommutative_composite++;
 423                         break;
 424                 default:
 425                         throw(std::logic_error("ncmul::eval(): invalid return type"));
 426                 }
 427                 ++i;
 428         }
 429         GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
 430
 431         // ncmul(...,c1,...,c2,...) ->
 432         //     *(c1,c2,ncmul(...)) (pull out commutative elements)
 433         if (count_commutative!=0) {
 434                 exvector commutativeseq;
 435                 commutativeseq.reserve(count_commutative+1);
 436                 exvector noncommutativeseq;
 437                 noncommutativeseq.reserve(assocseq.size()-count_commutative);
 438                 for (i=0; i<assocseq.size(); ++i) {
 439                         if (rettypes[i]==return_types::commutative) {
 440                                 commutativeseq.push_back(assocseq[i]);
 441                         } else {
 442                                 noncommutativeseq.push_back(assocseq[i]);
 443                         }
 444                 }
 445                 commutativeseq.push_back((new ncmul(noncommutativeseq,1))->
 446                                                                   setflag(status_flags::dynallocated));
 447                 return (new mul(commutativeseq))->setflag(status_flags::dynallocated);
 448         }
 449
 450         // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 451         //     (collect elements of same type)
 452
 453         if (count_noncommutative_composite==0) {
 454                 // there are neither commutative nor noncommutative_composite
 455                 // elements in assocseq
 456                 GINAC_ASSERT(count_commutative==0);
 457
 458                 exvectorvector evv;
 459                 unsignedvector rttinfos;
 460                 evv.reserve(assocseq.size());
 461                 rttinfos.reserve(assocseq.size());
 462
 463                 for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
 464                         unsigned ti=(*cit).return_type_tinfo();
 465                         // search type in vector of known types
 466                         for (i=0; i<rttinfos.size(); ++i) {
 467                                 if (ti==rttinfos[i]) {
 468                                         evv[i].push_back(*cit);
 469                                         break;
 470                                 }
 471                         }
 472                         if (i>=rttinfos.size()) {
 473                                 // new type
 474                                 rttinfos.push_back(ti);
 475                                 evv.push_back(exvector());
 476                                 (*(evv.end()-1)).reserve(assocseq.size());
 477                                 (*(evv.end()-1)).push_back(*cit);
 478                         }
 479                 }
 480
 481 #ifdef DO_GINAC_ASSERT
 482                 GINAC_ASSERT(evv.size()==rttinfos.size());
 483                 GINAC_ASSERT(evv.size()>0);
 484                 unsigned s=0;
 485                 for (i=0; i<evv.size(); ++i) {
 486                         s += evv[i].size();
 487                 }
 488                 GINAC_ASSERT(s==assocseq.size());
 489 #endif // def DO_GINAC_ASSERT
 490
 491                 // if all elements are of same type, simplify the string
 492                 if (evv.size()==1) {
 493                         return evv[0][0].simplify_ncmul(evv[0]);
 494                 }
 495
 496                 exvector splitseq;
 497                 splitseq.reserve(evv.size());
 498                 for (i=0; i<evv.size(); ++i) {
 499                         splitseq.push_back((new ncmul(evv[i]))->
 500                                                            setflag(status_flags::dynallocated));
 501                 }
 502
 503                 return (new mul(splitseq))->setflag(status_flags::dynallocated);
 504         }
 505
 506         return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
 507                                                                                   status_flags::evaluated);
 508 }
 509
 510 exvector ncmul::get_indices(void) const
 511 {
 512         // return union of indices of factors
 513         exvector iv;
 514         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 515                 exvector subiv=(*cit).get_indices();
 516                 iv.reserve(iv.size()+subiv.size());
 517                 for (exvector::const_iterator cit2=subiv.begin(); cit2!=subiv.end(); ++cit2) {
 518                         iv.push_back(*cit2);
 519                 }
 520         }
 521         return iv;
 522 }
 523
 524 ex ncmul::subs(const lst & ls, const lst & lr) const
 525 {
 526         return ncmul(subschildren(ls, lr));
 527 }
 528
 529 ex ncmul::thisexprseq(const exvector & v) const
 530 {
 531         return (new ncmul(v))->setflag(status_flags::dynallocated);
 532 }
 533
 534 ex ncmul::thisexprseq(exvector * vp) const
 535 {
 536         return (new ncmul(vp))->setflag(status_flags::dynallocated);
 537 }
 538
 539 // protected
 540
 541 /** Implementation of ex::diff() for a non-commutative product. It always returns 0.
 542  *  @see ex::diff */
 543 ex ncmul::derivative(const symbol & s) const
 544 {
 545         return _ex0();
 546 }
 547
 548 int ncmul::compare_same_type(const basic & other) const
 549 {
 550         return inherited::compare_same_type(other);
 551 }
 552
 553 unsigned ncmul::return_type(void) const
 554 {
 555         if (seq.size()==0) {
 556                 // ncmul without factors: should not happen, but commutes
 557                 return return_types::commutative;
 558         }
 559
 560         bool all_commutative=1;
 561         unsigned rt;
 562         exvector::const_iterator cit_noncommutative_element; // point to first found nc element
 563
 564         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 565                 rt=(*cit).return_type();
 566                 if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
 567                 if ((rt==return_types::noncommutative)&&(all_commutative)) {
 568                         // first nc element found, remember position
 569                         cit_noncommutative_element=cit;
 570                         all_commutative=0;
 571                 }
 572                 if ((rt==return_types::noncommutative)&&(!all_commutative)) {
 573                 // another nc element found, compare type_infos
 574                         if ((*cit_noncommutative_element).return_type_tinfo()!=(*cit).return_type_tinfo()) {
 575                         // diffent types -> mul is ncc
 576                         return return_types::noncommutative_composite;
 577                         }
 578                 }
 579         }
 580         // all factors checked
 581         GINAC_ASSERT(!all_commutative); // not all factors should commute, because this is a ncmul();
 582         return all_commutative ? return_types::commutative : return_types::noncommutative;
 583 }
 584
 585 unsigned ncmul::return_type_tinfo(void) const
 586 {
 587         if (seq.size()==0) {
 588                 // mul without factors: should not happen
 589                 return tinfo_key;
 590         }
 591         // return type_info of first noncommutative element
 592         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 593                 if ((*cit).return_type()==return_types::noncommutative) {
 594                         return (*cit).return_type_tinfo();
 595                 }
 596         }
 597         // no noncommutative element found, should not happen
 598         return tinfo_key;
 599 }
 600
 601 //////////
 602 // new virtual functions which can be overridden by derived classes
 603 //////////
 604
 605 // none
 606
 607 //////////
 608 // non-virtual functions in this class
 609 //////////
 610
 611 exvector ncmul::expandchildren(unsigned options) const
 612 {
 613         exvector s;
 614         s.reserve(seq.size());
 615
 616         for (exvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 617                 s.push_back((*it).expand(options));
 618         }
 619         return s;
 620 }
 621
 622 const exvector & ncmul::get_factors(void) const
 623 {
 624         return seq;
 625 }
 626
 627 //////////
 628 // static member variables
 629 //////////
 630
 631 // protected
 632
 633 unsigned ncmul::precedence=50;
 634
 635
 636 //////////
 637 // global constants
 638 //////////
 639
 640 const ncmul some_ncmul;
 641 const type_info & typeid_ncmul=typeid(some_ncmul);
 642
 643 //////////
 644 // friend functions
 645 //////////
 646
 647 ex nonsimplified_ncmul(const exvector & v)
 648 {
 649         return (new ncmul(v))->setflag(status_flags::dynallocated);
 650 }
 651
 652 ex simplified_ncmul(const exvector & v)
 653 {
 654         if (v.size()==0) {
 655                 return _ex1();
 656         } else if (v.size()==1) {
 657                 return v[0];
 658         }
 659         return (new ncmul(v))->setflag(status_flags::dynallocated |
 660                                                                    status_flags::evaluated);
 661 }
 662
 663 #ifndef NO_NAMESPACE_GINAC
 664 } // namespace GiNaC
 665 #endif // ndef NO_NAMESPACE_GINAC