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 namespace GiNaC {
  36
  37 GINAC_IMPLEMENT_REGISTERED_CLASS(ncmul, exprseq)
  38
  39 //////////
  40 // default constructor, destructor, copy constructor assignment operator and helpers
  41 //////////
  42
  43 // public
  44
  45 ncmul::ncmul()
  46 {
  47         debugmsg("ncmul default constructor",LOGLEVEL_CONSTRUCT);
  48         tinfo_key = TINFO_ncmul;
  49 }
  50
  51 // protected
  52
  53 void ncmul::copy(const ncmul & other)
  54 {
  55         inherited::copy(other);
  56 }
  57
  58 void ncmul::destroy(bool call_parent)
  59 {
  60         if (call_parent) inherited::destroy(call_parent);
  61 }
  62
  63 //////////
  64 // other constructors
  65 //////////
  66
  67 // public
  68
  69 ncmul::ncmul(const ex & lh, const ex & rh) : inherited(lh,rh)
  70 {
  71         debugmsg("ncmul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
  72         tinfo_key = TINFO_ncmul;
  73 }
  74
  75 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3) : inherited(f1,f2,f3)
  76 {
  77         debugmsg("ncmul constructor from 3 ex",LOGLEVEL_CONSTRUCT);
  78         tinfo_key = TINFO_ncmul;
  79 }
  80
  81 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  82              const ex & f4) : inherited(f1,f2,f3,f4)
  83 {
  84         debugmsg("ncmul constructor from 4 ex",LOGLEVEL_CONSTRUCT);
  85         tinfo_key = TINFO_ncmul;
  86 }
  87
  88 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  89              const ex & f4, const ex & f5) : inherited(f1,f2,f3,f4,f5)
  90 {
  91         debugmsg("ncmul constructor from 5 ex",LOGLEVEL_CONSTRUCT);
  92         tinfo_key = TINFO_ncmul;
  93 }
  94
  95 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  96              const ex & f4, const ex & f5, const ex & f6) : inherited(f1,f2,f3,f4,f5,f6)
  97 {
  98         debugmsg("ncmul constructor from 6 ex",LOGLEVEL_CONSTRUCT);
  99         tinfo_key = TINFO_ncmul;
 100 }
 101
 102 ncmul::ncmul(const exvector & v, bool discardable) : inherited(v,discardable)
 103 {
 104         debugmsg("ncmul constructor from exvector,bool",LOGLEVEL_CONSTRUCT);
 105         tinfo_key = TINFO_ncmul;
 106 }
 107
 108 ncmul::ncmul(exvector * vp) : inherited(vp)
 109 {
 110         debugmsg("ncmul constructor from exvector *",LOGLEVEL_CONSTRUCT);
 111         tinfo_key = TINFO_ncmul;
 112 }
 113
 114 //////////
 115 // archiving
 116 //////////
 117
 118 /** Construct object from archive_node. */
 119 ncmul::ncmul(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 120 {
 121         debugmsg("ncmul constructor from archive_node", LOGLEVEL_CONSTRUCT);
 122 }
 123
 124 /** Unarchive the object. */
 125 ex ncmul::unarchive(const archive_node &n, const lst &sym_lst)
 126 {
 127         return (new ncmul(n, sym_lst))->setflag(status_flags::dynallocated);
 128 }
 129
 130 /** Archive the object. */
 131 void ncmul::archive(archive_node &n) const
 132 {
 133         inherited::archive(n);
 134 }
 135
 136
 137 //////////
 138 // functions overriding virtual functions from bases classes
 139 //////////
 140
 141 // public
 142
 143 void ncmul::print(std::ostream & os, unsigned upper_precedence) const
 144 {
 145         debugmsg("ncmul print",LOGLEVEL_PRINT);
 146         printseq(os,'(','%',')',precedence,upper_precedence);
 147 }
 148
 149 void ncmul::printraw(std::ostream & os) const
 150 {
 151         debugmsg("ncmul printraw",LOGLEVEL_PRINT);
 152         os << "%(";
 153         for (exvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 154                 (*it).bp->printraw(os);
 155                 os << ",";
 156         }
 157         os << ",hash=" << hashvalue << ",flags=" << flags;
 158         os << ")";
 159 }
 160
 161 void ncmul::printcsrc(std::ostream & os, unsigned type, unsigned upper_precedence) const
 162 {
 163         debugmsg("ncmul print csrc",LOGLEVEL_PRINT);
 164         exvector::const_iterator it;
 165         exvector::const_iterator itend = seq.end()-1;
 166         os << "ncmul(";
 167         for (it=seq.begin(); it!=itend; ++it) {
 168                 (*it).bp->printcsrc(os,precedence);
 169                 os << ",";
 170         }
 171         (*it).bp->printcsrc(os,precedence);
 172         os << ")";
 173 }
 174
 175 bool ncmul::info(unsigned inf) const
 176 {
 177         throw(std::logic_error("which flags have to be implemented in ncmul::info()?"));
 178 }
 179
 180 typedef std::vector<int> intvector;
 181
 182 ex ncmul::expand(unsigned options) const
 183 {
 184         exvector sub_expanded_seq;
 185         intvector positions_of_adds;
 186         intvector number_of_add_operands;
 187
 188         exvector expanded_seq=expandchildren(options);
 189
 190         positions_of_adds.resize(expanded_seq.size());
 191         number_of_add_operands.resize(expanded_seq.size());
 192
 193         int number_of_adds=0;
 194         int number_of_expanded_terms=1;
 195
 196         unsigned current_position=0;
 197         exvector::const_iterator last=expanded_seq.end();
 198         for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 199                 if (is_ex_exactly_of_type((*cit),add)) {
 200                         positions_of_adds[number_of_adds]=current_position;
 201                         const add & expanded_addref=ex_to_add(*cit);
 202                         number_of_add_operands[number_of_adds]=expanded_addref.seq.size();
 203                         number_of_expanded_terms *= expanded_addref.seq.size();
 204                         number_of_adds++;
 205                 }
 206                 current_position++;
 207         }
 208
 209         if (number_of_adds==0) {
 210                 return (new ncmul(expanded_seq,1))->setflag(status_flags::dynallocated ||
 211                                                                                                         status_flags::expanded);
 212         }
 213
 214         exvector distrseq;
 215         distrseq.reserve(number_of_expanded_terms);
 216
 217         intvector k;
 218         k.resize(number_of_adds);
 219
 220         int l;
 221         for (l=0; l<number_of_adds; l++) {
 222                 k[l]=0;
 223         }
 224
 225         while (1) {
 226                 exvector term;
 227                 term=expanded_seq;
 228                 for (l=0; l<number_of_adds; l++) {
 229                         GINAC_ASSERT(is_ex_exactly_of_type(expanded_seq[positions_of_adds[l]],add));
 230                         const add & addref=ex_to_add(expanded_seq[positions_of_adds[l]]);
 231                         term[positions_of_adds[l]]=addref.recombine_pair_to_ex(addref.seq[k[l]]);
 232                 }
 233                 distrseq.push_back((new ncmul(term,1))->setflag(status_flags::dynallocated |
 234                                                                                                                 status_flags::expanded));
 235
 236                 // increment k[]
 237                 l=number_of_adds-1;
 238                 while ((l>=0)&&((++k[l])>=number_of_add_operands[l])) {
 239                         k[l]=0;
 240                         l--;
 241                 }
 242                 if (l<0) break;
 243         }
 244
 245         return (new add(distrseq))->setflag(status_flags::dynallocated |
 246                                                                                 status_flags::expanded);
 247 }
 248
 249 int ncmul::degree(const symbol & s) const
 250 {
 251         int deg_sum=0;
 252         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 253                 deg_sum+=(*cit).degree(s);
 254         }
 255         return deg_sum;
 256 }
 257
 258 int ncmul::ldegree(const symbol & s) const
 259 {
 260         int deg_sum=0;
 261         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 262                 deg_sum+=(*cit).ldegree(s);
 263         }
 264         return deg_sum;
 265 }
 266
 267 ex ncmul::coeff(const symbol & s, int n) const
 268 {
 269         exvector coeffseq;
 270         coeffseq.reserve(seq.size());
 271
 272         if (n==0) {
 273                 // product of individual coeffs
 274                 // if a non-zero power of s is found, the resulting product will be 0
 275                 exvector::const_iterator it=seq.begin();
 276                 while (it!=seq.end()) {
 277                         coeffseq.push_back((*it).coeff(s,n));
 278                         ++it;
 279                 }
 280                 return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 281         }
 282
 283         exvector::const_iterator it=seq.begin();
 284         bool coeff_found=0;
 285         while (it!=seq.end()) {
 286                 ex c=(*it).coeff(s,n);
 287                 if (!c.is_zero()) {
 288                         coeffseq.push_back(c);
 289                         coeff_found=1;
 290                 } else {
 291                         coeffseq.push_back(*it);
 292                 }
 293                 ++it;
 294         }
 295
 296         if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 297
 298         return _ex0();
 299 }
 300
 301 unsigned ncmul::count_factors(const ex & e) const
 302 {
 303         if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
 304                 (is_ex_exactly_of_type(e,ncmul))) {
 305                 unsigned factors=0;
 306                 for (unsigned i=0; i<e.nops(); i++)
 307                         factors += count_factors(e.op(i));
 308
 309                 return factors;
 310         }
 311         return 1;
 312 }
 313
 314 void ncmul::append_factors(exvector & v, const ex & e) const
 315 {
 316         if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
 317                 (is_ex_exactly_of_type(e,ncmul))) {
 318                 for (unsigned i=0; i<e.nops(); i++)
 319                         append_factors(v,e.op(i));
 320
 321                 return;
 322         }
 323         v.push_back(e);
 324 }
 325
 326 typedef std::vector<unsigned> unsignedvector;
 327 typedef std::vector<exvector> exvectorvector;
 328
 329 ex ncmul::eval(int level) const
 330 {
 331         // simplifications: ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 332         //                      ncmul(...,x1,x2,...,x3,x4,...) (associativity)
 333         //                  ncmul(x) -> x
 334         //                  ncmul() -> 1
 335         //                  ncmul(...,c1,...,c2,...)
 336         //                      *(c1,c2,ncmul(...)) (pull out commutative elements)
 337         //                  ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 338         //                      (collect elements of same type)
 339         //                  ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)
 340         // the following rule would be nice, but produces a recursion,
 341         // which must be trapped by introducing a flag that the sub-ncmuls()
 342         // are already evaluated (maybe later...)
 343         //                  ncmul(x1,x2,...,X,y1,y2,...) ->
 344         //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
 345         //                      (X noncommutative_composite)
 346
 347         if ((level==1)&&(flags & status_flags::evaluated)) {
 348                 return *this;
 349         }
 350
 351         exvector evaledseq=evalchildren(level);
 352
 353         // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 354         //     ncmul(...,x1,x2,...,x3,x4,...) (associativity)
 355         unsigned factors=0;
 356         for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit) {
 357                 factors += count_factors(*cit);
 358         }
 359
 360         exvector assocseq;
 361         assocseq.reserve(factors);
 362         for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit) {
 363                 append_factors(assocseq,*cit);
 364         }
 365
 366         // ncmul(x) -> x
 367         if (assocseq.size()==1) return *(seq.begin());
 368
 369         // ncmul() -> 1
 370         if (assocseq.size()==0) return _ex1();
 371
 372         // determine return types
 373         unsignedvector rettypes;
 374         rettypes.reserve(assocseq.size());
 375         unsigned i=0;
 376         unsigned count_commutative=0;
 377         unsigned count_noncommutative=0;
 378         unsigned count_noncommutative_composite=0;
 379         for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
 380                 switch (rettypes[i]=(*cit).return_type()) {
 381                 case return_types::commutative:
 382                         count_commutative++;
 383                         break;
 384                 case return_types::noncommutative:
 385                         count_noncommutative++;
 386                         break;
 387                 case return_types::noncommutative_composite:
 388                         count_noncommutative_composite++;
 389                         break;
 390                 default:
 391                         throw(std::logic_error("ncmul::eval(): invalid return type"));
 392                 }
 393                 ++i;
 394         }
 395         GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
 396
 397         // ncmul(...,c1,...,c2,...) ->
 398         //     *(c1,c2,ncmul(...)) (pull out commutative elements)
 399         if (count_commutative!=0) {
 400                 exvector commutativeseq;
 401                 commutativeseq.reserve(count_commutative+1);
 402                 exvector noncommutativeseq;
 403                 noncommutativeseq.reserve(assocseq.size()-count_commutative);
 404                 for (i=0; i<assocseq.size(); ++i) {
 405                         if (rettypes[i]==return_types::commutative) {
 406                                 commutativeseq.push_back(assocseq[i]);
 407                         } else {
 408                                 noncommutativeseq.push_back(assocseq[i]);
 409                         }
 410                 }
 411                 commutativeseq.push_back((new ncmul(noncommutativeseq,1))->setflag(status_flags::dynallocated));
 412                 return (new mul(commutativeseq))->setflag(status_flags::dynallocated);
 413         }
 414
 415         // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 416         //     (collect elements of same type)
 417
 418         if (count_noncommutative_composite==0) {
 419                 // there are neither commutative nor noncommutative_composite
 420                 // elements in assocseq
 421                 GINAC_ASSERT(count_commutative==0);
 422
 423                 exvectorvector evv;
 424                 unsignedvector rttinfos;
 425                 evv.reserve(assocseq.size());
 426                 rttinfos.reserve(assocseq.size());
 427
 428                 for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
 429                         unsigned ti=(*cit).return_type_tinfo();
 430                         // search type in vector of known types
 431                         for (i=0; i<rttinfos.size(); ++i) {
 432                                 if (ti==rttinfos[i]) {
 433                                         evv[i].push_back(*cit);
 434                                         break;
 435                                 }
 436                         }
 437                         if (i>=rttinfos.size()) {
 438                                 // new type
 439                                 rttinfos.push_back(ti);
 440                                 evv.push_back(exvector());
 441                                 (*(evv.end()-1)).reserve(assocseq.size());
 442                                 (*(evv.end()-1)).push_back(*cit);
 443                         }
 444                 }
 445
 446 #ifdef DO_GINAC_ASSERT
 447                 GINAC_ASSERT(evv.size()==rttinfos.size());
 448                 GINAC_ASSERT(evv.size()>0);
 449                 unsigned s=0;
 450                 for (i=0; i<evv.size(); ++i) {
 451                         s += evv[i].size();
 452                 }
 453                 GINAC_ASSERT(s==assocseq.size());
 454 #endif // def DO_GINAC_ASSERT
 455
 456                 // if all elements are of same type, simplify the string
 457                 if (evv.size()==1) {
 458                         return evv[0][0].simplify_ncmul(evv[0]);
 459                 }
 460
 461                 exvector splitseq;
 462                 splitseq.reserve(evv.size());
 463                 for (i=0; i<evv.size(); ++i) {
 464                         splitseq.push_back((new ncmul(evv[i]))->setflag(status_flags::dynallocated));
 465                 }
 466
 467                 return (new mul(splitseq))->setflag(status_flags::dynallocated);
 468         }
 469
 470         return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
 471                                                                                   status_flags::evaluated);
 472 }
 473
 474 exvector ncmul::get_indices(void) const
 475 {
 476         // return union of indices of factors
 477         exvector iv;
 478         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 479                 exvector subiv=(*cit).get_indices();
 480                 iv.reserve(iv.size()+subiv.size());
 481                 for (exvector::const_iterator cit2=subiv.begin(); cit2!=subiv.end(); ++cit2) {
 482                         iv.push_back(*cit2);
 483                 }
 484         }
 485         return iv;
 486 }
 487
 488 ex ncmul::subs(const lst & ls, const lst & lr) const
 489 {
 490         return ncmul(subschildren(ls, lr));
 491 }
 492
 493 ex ncmul::thisexprseq(const exvector & v) const
 494 {
 495         return (new ncmul(v))->setflag(status_flags::dynallocated);
 496 }
 497
 498 ex ncmul::thisexprseq(exvector * vp) const
 499 {
 500         return (new ncmul(vp))->setflag(status_flags::dynallocated);
 501 }
 502
 503 // protected
 504
 505 /** Implementation of ex::diff() for a non-commutative product. It always returns 0.
 506  *  @see ex::diff */
 507 ex ncmul::derivative(const symbol & s) const
 508 {
 509         return _ex0();
 510 }
 511
 512 int ncmul::compare_same_type(const basic & other) const
 513 {
 514         return inherited::compare_same_type(other);
 515 }
 516
 517 unsigned ncmul::return_type(void) const
 518 {
 519         if (seq.size()==0) {
 520                 // ncmul without factors: should not happen, but commutes
 521                 return return_types::commutative;
 522         }
 523
 524         bool all_commutative=1;
 525         unsigned rt;
 526         exvector::const_iterator cit_noncommutative_element; // point to first found nc element
 527
 528         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 529                 rt=(*cit).return_type();
 530                 if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
 531                 if ((rt==return_types::noncommutative)&&(all_commutative)) {
 532                         // first nc element found, remember position
 533                         cit_noncommutative_element=cit;
 534                         all_commutative=0;
 535                 }
 536                 if ((rt==return_types::noncommutative)&&(!all_commutative)) {
 537                         // another nc element found, compare type_infos
 538                         if ((*cit_noncommutative_element).return_type_tinfo()!=(*cit).return_type_tinfo()) {
 539                                 // diffent types -> mul is ncc
 540                                 return return_types::noncommutative_composite;
 541                         }
 542                 }
 543         }
 544         // all factors checked
 545         GINAC_ASSERT(!all_commutative); // not all factors should commute, because this is a ncmul();
 546         return all_commutative ? return_types::commutative : return_types::noncommutative;
 547 }
 548
 549 unsigned ncmul::return_type_tinfo(void) const
 550 {
 551         if (seq.size()==0) {
 552                 // mul without factors: should not happen
 553                 return tinfo_key;
 554         }
 555         // return type_info of first noncommutative element
 556         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 557                 if ((*cit).return_type()==return_types::noncommutative) {
 558                         return (*cit).return_type_tinfo();
 559                 }
 560         }
 561         // no noncommutative element found, should not happen
 562         return tinfo_key;
 563 }
 564
 565 //////////
 566 // new virtual functions which can be overridden by derived classes
 567 //////////
 568
 569 // none
 570
 571 //////////
 572 // non-virtual functions in this class
 573 //////////
 574
 575 exvector ncmul::expandchildren(unsigned options) const
 576 {
 577         exvector s;
 578         s.reserve(seq.size());
 579
 580         for (exvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 581                 s.push_back((*it).expand(options));
 582         }
 583         return s;
 584 }
 585
 586 const exvector & ncmul::get_factors(void) const
 587 {
 588         return seq;
 589 }
 590
 591 //////////
 592 // static member variables
 593 //////////
 594
 595 // protected
 596
 597 unsigned ncmul::precedence = 50;
 598
 599 //////////
 600 // friend functions
 601 //////////
 602
 603 ex nonsimplified_ncmul(const exvector & v)
 604 {
 605         return (new ncmul(v))->setflag(status_flags::dynallocated);
 606 }
 607
 608 ex simplified_ncmul(const exvector & v)
 609 {
 610         if (v.size()==0) {
 611                 return _ex1();
 612         } else if (v.size()==1) {
 613                 return v[0];
 614         }
 615         return (new ncmul(v))->setflag(status_flags::dynallocated |
 616                                        status_flags::evaluated);
 617 }
 618
 619 } // namespace GiNaC