ginac/ncmul.cpp

   1 /** @file ncmul.cpp
   2  *
   3  *  Implementation of GiNaC's non-commutative products of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2005 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., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  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 "matrix.h"
  32 #include "archive.h"
  33 #include "indexed.h"
  34 #include "utils.h"
  35
  36 namespace GiNaC {
  37
  38 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(ncmul, exprseq,
  39   print_func<print_context>(&ncmul::do_print).
  40   print_func<print_tree>(&ncmul::do_print_tree).
  41   print_func<print_csrc>(&ncmul::do_print_csrc).
  42   print_func<print_python_repr>(&ncmul::do_print_csrc))
  43
  44
  45 //////////
  46 // default constructor
  47 //////////
  48
  49 ncmul::ncmul()
  50 {
  51         tinfo_key = TINFO_ncmul;
  52 }
  53
  54 //////////
  55 // other constructors
  56 //////////
  57
  58 // public
  59
  60 ncmul::ncmul(const ex & lh, const ex & rh) : inherited(lh,rh)
  61 {
  62         tinfo_key = TINFO_ncmul;
  63 }
  64
  65 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3) : inherited(f1,f2,f3)
  66 {
  67         tinfo_key = TINFO_ncmul;
  68 }
  69
  70 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  71              const ex & f4) : inherited(f1,f2,f3,f4)
  72 {
  73         tinfo_key = TINFO_ncmul;
  74 }
  75
  76 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  77              const ex & f4, const ex & f5) : inherited(f1,f2,f3,f4,f5)
  78 {
  79         tinfo_key = TINFO_ncmul;
  80 }
  81
  82 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  83              const ex & f4, const ex & f5, const ex & f6) : inherited(f1,f2,f3,f4,f5,f6)
  84 {
  85         tinfo_key = TINFO_ncmul;
  86 }
  87
  88 ncmul::ncmul(const exvector & v, bool discardable) : inherited(v,discardable)
  89 {
  90         tinfo_key = TINFO_ncmul;
  91 }
  92
  93 ncmul::ncmul(std::auto_ptr<exvector> vp) : inherited(vp)
  94 {
  95         tinfo_key = TINFO_ncmul;
  96 }
  97
  98 //////////
  99 // archiving
 100 //////////
 101
 102 DEFAULT_ARCHIVING(ncmul)
 103
 104 //////////
 105 // functions overriding virtual functions from base classes
 106 //////////
 107
 108 // public
 109
 110 void ncmul::do_print(const print_context & c, unsigned level) const
 111 {
 112         printseq(c, '(', '*', ')', precedence(), level);
 113 }
 114
 115 void ncmul::do_print_csrc(const print_context & c, unsigned level) const
 116 {
 117         c.s << class_name();
 118         printseq(c, '(', ',', ')', precedence(), precedence());
 119 }
 120
 121 bool ncmul::info(unsigned inf) const
 122 {
 123         return inherited::info(inf);
 124 }
 125
 126 typedef std::vector<int> intvector;
 127
 128 ex ncmul::expand(unsigned options) const
 129 {
 130         // First, expand the children
 131         std::auto_ptr<exvector> vp = expandchildren(options);
 132         const exvector &expanded_seq = vp.get() ? *vp : this->seq;
 133
 134         // Now, look for all the factors that are sums and remember their
 135         // position and number of terms.
 136         intvector positions_of_adds(expanded_seq.size());
 137         intvector number_of_add_operands(expanded_seq.size());
 138
 139         size_t number_of_adds = 0;
 140         size_t number_of_expanded_terms = 1;
 141
 142         size_t current_position = 0;
 143         exvector::const_iterator last = expanded_seq.end();
 144         for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 145                 if (is_exactly_a<add>(*cit)) {
 146                         positions_of_adds[number_of_adds] = current_position;
 147                         size_t num_ops = cit->nops();
 148                         number_of_add_operands[number_of_adds] = num_ops;
 149                         number_of_expanded_terms *= num_ops;
 150                         number_of_adds++;
 151                 }
 152                 ++current_position;
 153         }
 154
 155         // If there are no sums, we are done
 156         if (number_of_adds == 0) {
 157                 if (vp.get())
 158                         return (new ncmul(vp))->
 159                                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 160                 else
 161                         return *this;
 162         }
 163
 164         // Now, form all possible products of the terms of the sums with the
 165         // remaining factors, and add them together
 166         exvector distrseq;
 167         distrseq.reserve(number_of_expanded_terms);
 168
 169         intvector k(number_of_adds);
 170
 171         /* Rename indices in the static members of the product */
 172         exvector expanded_seq_mod;
 173         size_t j = 0;
 174         size_t i;
 175         for (i=0; i<expanded_seq.size(); i++) {
 176                 if (i == positions_of_adds[j]) {
 177                         expanded_seq_mod.push_back(_ex1);
 178                         j++;
 179                 } else {
 180                         expanded_seq_mod.push_back(rename_dummy_indices_uniquely(ncmul(expanded_seq_mod), expanded_seq[i]));
 181                 }
 182         }
 183
 184         while (true) {
 185                 exvector term = expanded_seq_mod;
 186                 for (i=0; i<number_of_adds; i++) {
 187                         term[positions_of_adds[i]] = rename_dummy_indices_uniquely(ncmul(term), expanded_seq[positions_of_adds[i]].op(k[i]));
 188                 }
 189
 190                 distrseq.push_back((new ncmul(term, true))->
 191                                     setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 192
 193                 // increment k[]
 194                 int l = number_of_adds-1;
 195                 while ((l>=0) && ((++k[l]) >= number_of_add_operands[l])) {
 196                         k[l] = 0;
 197                         l--;
 198                 }
 199                 if (l<0)
 200                         break;
 201         }
 202
 203         return (new add(distrseq))->
 204                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 205 }
 206
 207 int ncmul::degree(const ex & s) const
 208 {
 209         if (is_equal(ex_to<basic>(s)))
 210                 return 1;
 211
 212         // Sum up degrees of factors
 213         int deg_sum = 0;
 214         exvector::const_iterator i = seq.begin(), end = seq.end();
 215         while (i != end) {
 216                 deg_sum += i->degree(s);
 217                 ++i;
 218         }
 219         return deg_sum;
 220 }
 221
 222 int ncmul::ldegree(const ex & s) const
 223 {
 224         if (is_equal(ex_to<basic>(s)))
 225                 return 1;
 226
 227         // Sum up degrees of factors
 228         int deg_sum = 0;
 229         exvector::const_iterator i = seq.begin(), end = seq.end();
 230         while (i != end) {
 231                 deg_sum += i->degree(s);
 232                 ++i;
 233         }
 234         return deg_sum;
 235 }
 236
 237 ex ncmul::coeff(const ex & s, int n) const
 238 {
 239         if (is_equal(ex_to<basic>(s)))
 240                 return n==1 ? _ex1 : _ex0;
 241
 242         exvector coeffseq;
 243         coeffseq.reserve(seq.size());
 244
 245         if (n == 0) {
 246                 // product of individual coeffs
 247                 // if a non-zero power of s is found, the resulting product will be 0
 248                 exvector::const_iterator it=seq.begin();
 249                 while (it!=seq.end()) {
 250                         coeffseq.push_back((*it).coeff(s,n));
 251                         ++it;
 252                 }
 253                 return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 254         }
 255
 256         exvector::const_iterator i = seq.begin(), end = seq.end();
 257         bool coeff_found = false;
 258         while (i != end) {
 259                 ex c = i->coeff(s,n);
 260                 if (c.is_zero()) {
 261                         coeffseq.push_back(*i);
 262                 } else {
 263                         coeffseq.push_back(c);
 264                         coeff_found = true;
 265                 }
 266                 ++i;
 267         }
 268
 269         if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 270
 271         return _ex0;
 272 }
 273
 274 size_t ncmul::count_factors(const ex & e) const
 275 {
 276         if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
 277                 (is_exactly_a<ncmul>(e))) {
 278                 size_t factors=0;
 279                 for (size_t i=0; i<e.nops(); i++)
 280                         factors += count_factors(e.op(i));
 281
 282                 return factors;
 283         }
 284         return 1;
 285 }
 286
 287 void ncmul::append_factors(exvector & v, const ex & e) const
 288 {
 289         if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
 290                 (is_exactly_a<ncmul>(e))) {
 291                 for (size_t i=0; i<e.nops(); i++)
 292                         append_factors(v, e.op(i));
 293         } else
 294                 v.push_back(e);
 295 }
 296
 297 typedef std::vector<unsigned> unsignedvector;
 298 typedef std::vector<exvector> exvectorvector;
 299
 300 /** Perform automatic term rewriting rules in this class.  In the following
 301  *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
 302  *  stand for such expressions that contain a plain number.
 303  *  - ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) -> ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 304  *  - ncmul(x) -> x
 305  *  - ncmul() -> 1
 306  *  - ncmul(...,c1,...,c2,...) -> *(c1,c2,ncmul(...))  (pull out commutative elements)
 307  *  - ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))  (collect elements of same type)
 308  *  - ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)
 309  *
 310  *  @param level cut-off in recursive evaluation */
 311 ex ncmul::eval(int level) const
 312 {
 313         // The following additional rule would be nice, but produces a recursion,
 314         // which must be trapped by introducing a flag that the sub-ncmuls()
 315         // are already evaluated (maybe later...)
 316         //                  ncmul(x1,x2,...,X,y1,y2,...) ->
 317         //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
 318         //                      (X noncommutative_composite)
 319
 320         if ((level==1) && (flags & status_flags::evaluated)) {
 321                 return *this;
 322         }
 323
 324         exvector evaledseq=evalchildren(level);
 325
 326         // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 327         //     ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 328         size_t factors = 0;
 329         exvector::const_iterator cit = evaledseq.begin(), citend = evaledseq.end();
 330         while (cit != citend)
 331                 factors += count_factors(*cit++);
 332
 333         exvector assocseq;
 334         assocseq.reserve(factors);
 335         cit = evaledseq.begin();
 336         while (cit != citend)
 337                 append_factors(assocseq, *cit++);
 338
 339         // ncmul(x) -> x
 340         if (assocseq.size()==1) return *(seq.begin());
 341
 342         // ncmul() -> 1
 343         if (assocseq.empty()) return _ex1;
 344
 345         // determine return types
 346         unsignedvector rettypes;
 347         rettypes.reserve(assocseq.size());
 348         size_t i = 0;
 349         size_t count_commutative=0;
 350         size_t count_noncommutative=0;
 351         size_t count_noncommutative_composite=0;
 352         cit = assocseq.begin(); citend = assocseq.end();
 353         while (cit != citend) {
 354                 switch (rettypes[i] = cit->return_type()) {
 355                 case return_types::commutative:
 356                         count_commutative++;
 357                         break;
 358                 case return_types::noncommutative:
 359                         count_noncommutative++;
 360                         break;
 361                 case return_types::noncommutative_composite:
 362                         count_noncommutative_composite++;
 363                         break;
 364                 default:
 365                         throw(std::logic_error("ncmul::eval(): invalid return type"));
 366                 }
 367                 ++i; ++cit;
 368         }
 369         GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
 370
 371         // ncmul(...,c1,...,c2,...) ->
 372         //     *(c1,c2,ncmul(...)) (pull out commutative elements)
 373         if (count_commutative!=0) {
 374                 exvector commutativeseq;
 375                 commutativeseq.reserve(count_commutative+1);
 376                 exvector noncommutativeseq;
 377                 noncommutativeseq.reserve(assocseq.size()-count_commutative);
 378                 size_t num = assocseq.size();
 379                 for (size_t i=0; i<num; ++i) {
 380                         if (rettypes[i]==return_types::commutative)
 381                                 commutativeseq.push_back(assocseq[i]);
 382                         else
 383                                 noncommutativeseq.push_back(assocseq[i]);
 384                 }
 385                 commutativeseq.push_back((new ncmul(noncommutativeseq,1))->setflag(status_flags::dynallocated));
 386                 return (new mul(commutativeseq))->setflag(status_flags::dynallocated);
 387         }
 388
 389         // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 390         //     (collect elements of same type)
 391
 392         if (count_noncommutative_composite==0) {
 393                 // there are neither commutative nor noncommutative_composite
 394                 // elements in assocseq
 395                 GINAC_ASSERT(count_commutative==0);
 396
 397                 size_t assoc_num = assocseq.size();
 398                 exvectorvector evv;
 399                 unsignedvector rttinfos;
 400                 evv.reserve(assoc_num);
 401                 rttinfos.reserve(assoc_num);
 402
 403                 cit = assocseq.begin(), citend = assocseq.end();
 404                 while (cit != citend) {
 405                         unsigned ti = cit->return_type_tinfo();
 406                         size_t rtt_num = rttinfos.size();
 407                         // search type in vector of known types
 408                         for (i=0; i<rtt_num; ++i) {
 409                                 if (ti == rttinfos[i]) {
 410                                         evv[i].push_back(*cit);
 411                                         break;
 412                                 }
 413                         }
 414                         if (i >= rtt_num) {
 415                                 // new type
 416                                 rttinfos.push_back(ti);
 417                                 evv.push_back(exvector());
 418                                 (evv.end()-1)->reserve(assoc_num);
 419                                 (evv.end()-1)->push_back(*cit);
 420                         }
 421                         ++cit;
 422                 }
 423
 424                 size_t evv_num = evv.size();
 425 #ifdef DO_GINAC_ASSERT
 426                 GINAC_ASSERT(evv_num == rttinfos.size());
 427                 GINAC_ASSERT(evv_num > 0);
 428                 size_t s=0;
 429                 for (i=0; i<evv_num; ++i)
 430                         s += evv[i].size();
 431                 GINAC_ASSERT(s == assoc_num);
 432 #endif // def DO_GINAC_ASSERT
 433
 434                 // if all elements are of same type, simplify the string
 435                 if (evv_num == 1)
 436                         return evv[0][0].eval_ncmul(evv[0]);
 437
 438                 exvector splitseq;
 439                 splitseq.reserve(evv_num);
 440                 for (i=0; i<evv_num; ++i)
 441                         splitseq.push_back((new ncmul(evv[i]))->setflag(status_flags::dynallocated));
 442
 443                 return (new mul(splitseq))->setflag(status_flags::dynallocated);
 444         }
 445
 446         return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
 447                                                                                   status_flags::evaluated);
 448 }
 449
 450 ex ncmul::evalm() const
 451 {
 452         // Evaluate children first
 453         std::auto_ptr<exvector> s(new exvector);
 454         s->reserve(seq.size());
 455         exvector::const_iterator it = seq.begin(), itend = seq.end();
 456         while (it != itend) {
 457                 s->push_back(it->evalm());
 458                 it++;
 459         }
 460
 461         // If there are only matrices, simply multiply them
 462         it = s->begin(); itend = s->end();
 463         if (is_a<matrix>(*it)) {
 464                 matrix prod(ex_to<matrix>(*it));
 465                 it++;
 466                 while (it != itend) {
 467                         if (!is_a<matrix>(*it))
 468                                 goto no_matrix;
 469                         prod = prod.mul(ex_to<matrix>(*it));
 470                         it++;
 471                 }
 472                 return prod;
 473         }
 474
 475 no_matrix:
 476         return (new ncmul(s))->setflag(status_flags::dynallocated);
 477 }
 478
 479 ex ncmul::thiscontainer(const exvector & v) const
 480 {
 481         return (new ncmul(v))->setflag(status_flags::dynallocated);
 482 }
 483
 484 ex ncmul::thiscontainer(std::auto_ptr<exvector> vp) const
 485 {
 486         return (new ncmul(vp))->setflag(status_flags::dynallocated);
 487 }
 488
 489 ex ncmul::conjugate() const
 490 {
 491         if (return_type() != return_types::noncommutative) {
 492                 return exprseq::conjugate();
 493         }
 494
 495         if ((return_type_tinfo() & 0xffffff00U) != TINFO_clifford) {
 496                 return exprseq::conjugate();
 497         }
 498
 499         exvector ev;
 500         ev.reserve(nops());
 501         for (const_iterator i=end(); i!=begin();) {
 502                 --i;
 503                 ev.push_back(i->conjugate());
 504         }
 505         return (new ncmul(ev, true))->setflag(status_flags::dynallocated).eval();
 506 }
 507
 508 // protected
 509
 510 /** Implementation of ex::diff() for a non-commutative product. It applies
 511  *  the product rule.
 512  *  @see ex::diff */
 513 ex ncmul::derivative(const symbol & s) const
 514 {
 515         size_t num = seq.size();
 516         exvector addseq;
 517         addseq.reserve(num);
 518
 519         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 520         exvector ncmulseq = seq;
 521         for (size_t i=0; i<num; ++i) {
 522                 ex e = seq[i].diff(s);
 523                 e.swap(ncmulseq[i]);
 524                 addseq.push_back((new ncmul(ncmulseq))->setflag(status_flags::dynallocated));
 525                 e.swap(ncmulseq[i]);
 526         }
 527         return (new add(addseq))->setflag(status_flags::dynallocated);
 528 }
 529
 530 int ncmul::compare_same_type(const basic & other) const
 531 {
 532         return inherited::compare_same_type(other);
 533 }
 534
 535 unsigned ncmul::return_type() const
 536 {
 537         if (seq.empty())
 538                 return return_types::commutative;
 539
 540         bool all_commutative = true;
 541         exvector::const_iterator noncommutative_element; // point to first found nc element
 542
 543         exvector::const_iterator i = seq.begin(), end = seq.end();
 544         while (i != end) {
 545                 unsigned rt = i->return_type();
 546                 if (rt == return_types::noncommutative_composite)
 547                         return rt; // one ncc -> mul also ncc
 548                 if ((rt == return_types::noncommutative) && (all_commutative)) {
 549                         // first nc element found, remember position
 550                         noncommutative_element = i;
 551                         all_commutative = false;
 552                 }
 553                 if ((rt == return_types::noncommutative) && (!all_commutative)) {
 554                         // another nc element found, compare type_infos
 555                         if (noncommutative_element->return_type_tinfo() != i->return_type_tinfo()) {
 556                                 // diffent types -> mul is ncc
 557                                 return return_types::noncommutative_composite;
 558                         }
 559                 }
 560                 ++i;
 561         }
 562         // all factors checked
 563         GINAC_ASSERT(!all_commutative); // not all factors should commutate, because this is a ncmul();
 564         return all_commutative ? return_types::commutative : return_types::noncommutative;
 565 }
 566
 567 unsigned ncmul::return_type_tinfo() const
 568 {
 569         if (seq.empty())
 570                 return tinfo_key;
 571
 572         // return type_info of first noncommutative element
 573         exvector::const_iterator i = seq.begin(), end = seq.end();
 574         while (i != end) {
 575                 if (i->return_type() == return_types::noncommutative)
 576                         return i->return_type_tinfo();
 577                 ++i;
 578         }
 579
 580         // no noncommutative element found, should not happen
 581         return tinfo_key;
 582 }
 583
 584 //////////
 585 // new virtual functions which can be overridden by derived classes
 586 //////////
 587
 588 // none
 589
 590 //////////
 591 // non-virtual functions in this class
 592 //////////
 593
 594 std::auto_ptr<exvector> ncmul::expandchildren(unsigned options) const
 595 {
 596         const_iterator cit = this->seq.begin(), end = this->seq.end();
 597         while (cit != end) {
 598                 const ex & expanded_ex = cit->expand(options);
 599                 if (!are_ex_trivially_equal(*cit, expanded_ex)) {
 600
 601                         // copy first part of seq which hasn't changed
 602                         std::auto_ptr<exvector> s(new exvector(this->seq.begin(), cit));
 603                         reserve(*s, this->seq.size());
 604
 605                         // insert changed element
 606                         s->push_back(expanded_ex);
 607                         ++cit;
 608
 609                         // copy rest
 610                         while (cit != end) {
 611                                 s->push_back(cit->expand(options));
 612                                 ++cit;
 613                         }
 614
 615                         return s;
 616                 }
 617
 618                 ++cit;
 619         }
 620
 621         return std::auto_ptr<exvector>(0); // nothing has changed
 622 }
 623
 624 const exvector & ncmul::get_factors() const
 625 {
 626         return seq;
 627 }
 628
 629 //////////
 630 // friend functions
 631 //////////
 632
 633 ex reeval_ncmul(const exvector & v)
 634 {
 635         return (new ncmul(v))->setflag(status_flags::dynallocated);
 636 }
 637
 638 ex hold_ncmul(const exvector & v)
 639 {
 640         if (v.empty())
 641                 return _ex1;
 642         else if (v.size() == 1)
 643                 return v[0];
 644         else
 645                 return (new ncmul(v))->setflag(status_flags::dynallocated |
 646                                                status_flags::evaluated);
 647 }
 648
 649 } // namespace GiNaC