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         exvector va;
 175
 176         for (size_t i=0; i<expanded_seq.size(); i++) {
 177                 if (i == positions_of_adds[j]) {
 178                         expanded_seq_mod.push_back(_ex1);
 179                         j++;
 180                 } else {
 181                         expanded_seq_mod.push_back(rename_dummy_indices_uniquely(va, expanded_seq[i], true));
 182                 }
 183         }
 184
 185         while (true) {
 186                 exvector term = expanded_seq_mod;
 187                 for (size_t i=0; i<number_of_adds; i++) {
 188                         term[positions_of_adds[i]] = rename_dummy_indices_uniquely(va, expanded_seq[positions_of_adds[i]].op(k[i]), true);
 189                 }
 190
 191                 distrseq.push_back((new ncmul(term, true))->
 192                                     setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 193
 194                 // increment k[]
 195                 int l = number_of_adds-1;
 196                 while ((l>=0) && ((++k[l]) >= number_of_add_operands[l])) {
 197                         k[l] = 0;
 198                         l--;
 199                 }
 200                 if (l<0)
 201                         break;
 202         }
 203
 204         return (new add(distrseq))->
 205                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 206 }
 207
 208 int ncmul::degree(const ex & s) const
 209 {
 210         if (is_equal(ex_to<basic>(s)))
 211                 return 1;
 212
 213         // Sum up degrees of factors
 214         int deg_sum = 0;
 215         exvector::const_iterator i = seq.begin(), end = seq.end();
 216         while (i != end) {
 217                 deg_sum += i->degree(s);
 218                 ++i;
 219         }
 220         return deg_sum;
 221 }
 222
 223 int ncmul::ldegree(const ex & s) const
 224 {
 225         if (is_equal(ex_to<basic>(s)))
 226                 return 1;
 227
 228         // Sum up degrees of factors
 229         int deg_sum = 0;
 230         exvector::const_iterator i = seq.begin(), end = seq.end();
 231         while (i != end) {
 232                 deg_sum += i->degree(s);
 233                 ++i;
 234         }
 235         return deg_sum;
 236 }
 237
 238 ex ncmul::coeff(const ex & s, int n) const
 239 {
 240         if (is_equal(ex_to<basic>(s)))
 241                 return n==1 ? _ex1 : _ex0;
 242
 243         exvector coeffseq;
 244         coeffseq.reserve(seq.size());
 245
 246         if (n == 0) {
 247                 // product of individual coeffs
 248                 // if a non-zero power of s is found, the resulting product will be 0
 249                 exvector::const_iterator it=seq.begin();
 250                 while (it!=seq.end()) {
 251                         coeffseq.push_back((*it).coeff(s,n));
 252                         ++it;
 253                 }
 254                 return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 255         }
 256
 257         exvector::const_iterator i = seq.begin(), end = seq.end();
 258         bool coeff_found = false;
 259         while (i != end) {
 260                 ex c = i->coeff(s,n);
 261                 if (c.is_zero()) {
 262                         coeffseq.push_back(*i);
 263                 } else {
 264                         coeffseq.push_back(c);
 265                         coeff_found = true;
 266                 }
 267                 ++i;
 268         }
 269
 270         if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 271
 272         return _ex0;
 273 }
 274
 275 size_t ncmul::count_factors(const ex & e) const
 276 {
 277         if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
 278                 (is_exactly_a<ncmul>(e))) {
 279                 size_t factors=0;
 280                 for (size_t i=0; i<e.nops(); i++)
 281                         factors += count_factors(e.op(i));
 282
 283                 return factors;
 284         }
 285         return 1;
 286 }
 287
 288 void ncmul::append_factors(exvector & v, const ex & e) const
 289 {
 290         if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
 291                 (is_exactly_a<ncmul>(e))) {
 292                 for (size_t i=0; i<e.nops(); i++)
 293                         append_factors(v, e.op(i));
 294         } else
 295                 v.push_back(e);
 296 }
 297
 298 typedef std::vector<unsigned> unsignedvector;
 299 typedef std::vector<exvector> exvectorvector;
 300
 301 /** Perform automatic term rewriting rules in this class.  In the following
 302  *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
 303  *  stand for such expressions that contain a plain number.
 304  *  - ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) -> ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 305  *  - ncmul(x) -> x
 306  *  - ncmul() -> 1
 307  *  - ncmul(...,c1,...,c2,...) -> *(c1,c2,ncmul(...))  (pull out commutative elements)
 308  *  - ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))  (collect elements of same type)
 309  *  - ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)
 310  *
 311  *  @param level cut-off in recursive evaluation */
 312 ex ncmul::eval(int level) const
 313 {
 314         // The following additional rule would be nice, but produces a recursion,
 315         // which must be trapped by introducing a flag that the sub-ncmuls()
 316         // are already evaluated (maybe later...)
 317         //                  ncmul(x1,x2,...,X,y1,y2,...) ->
 318         //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
 319         //                      (X noncommutative_composite)
 320
 321         if ((level==1) && (flags & status_flags::evaluated)) {
 322                 return *this;
 323         }
 324
 325         exvector evaledseq=evalchildren(level);
 326
 327         // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 328         //     ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 329         size_t factors = 0;
 330         exvector::const_iterator cit = evaledseq.begin(), citend = evaledseq.end();
 331         while (cit != citend)
 332                 factors += count_factors(*cit++);
 333
 334         exvector assocseq;
 335         assocseq.reserve(factors);
 336         cit = evaledseq.begin();
 337         while (cit != citend)
 338                 append_factors(assocseq, *cit++);
 339
 340         // ncmul(x) -> x
 341         if (assocseq.size()==1) return *(seq.begin());
 342
 343         // ncmul() -> 1
 344         if (assocseq.empty()) return _ex1;
 345
 346         // determine return types
 347         unsignedvector rettypes;
 348         rettypes.reserve(assocseq.size());
 349         size_t i = 0;
 350         size_t count_commutative=0;
 351         size_t count_noncommutative=0;
 352         size_t count_noncommutative_composite=0;
 353         cit = assocseq.begin(); citend = assocseq.end();
 354         while (cit != citend) {
 355                 switch (rettypes[i] = cit->return_type()) {
 356                 case return_types::commutative:
 357                         count_commutative++;
 358                         break;
 359                 case return_types::noncommutative:
 360                         count_noncommutative++;
 361                         break;
 362                 case return_types::noncommutative_composite:
 363                         count_noncommutative_composite++;
 364                         break;
 365                 default:
 366                         throw(std::logic_error("ncmul::eval(): invalid return type"));
 367                 }
 368                 ++i; ++cit;
 369         }
 370         GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
 371
 372         // ncmul(...,c1,...,c2,...) ->
 373         //     *(c1,c2,ncmul(...)) (pull out commutative elements)
 374         if (count_commutative!=0) {
 375                 exvector commutativeseq;
 376                 commutativeseq.reserve(count_commutative+1);
 377                 exvector noncommutativeseq;
 378                 noncommutativeseq.reserve(assocseq.size()-count_commutative);
 379                 size_t num = assocseq.size();
 380                 for (size_t i=0; i<num; ++i) {
 381                         if (rettypes[i]==return_types::commutative)
 382                                 commutativeseq.push_back(assocseq[i]);
 383                         else
 384                                 noncommutativeseq.push_back(assocseq[i]);
 385                 }
 386                 commutativeseq.push_back((new ncmul(noncommutativeseq,1))->setflag(status_flags::dynallocated));
 387                 return (new mul(commutativeseq))->setflag(status_flags::dynallocated);
 388         }
 389
 390         // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 391         //     (collect elements of same type)
 392
 393         if (count_noncommutative_composite==0) {
 394                 // there are neither commutative nor noncommutative_composite
 395                 // elements in assocseq
 396                 GINAC_ASSERT(count_commutative==0);
 397
 398                 size_t assoc_num = assocseq.size();
 399                 exvectorvector evv;
 400                 unsignedvector rttinfos;
 401                 evv.reserve(assoc_num);
 402                 rttinfos.reserve(assoc_num);
 403
 404                 cit = assocseq.begin(), citend = assocseq.end();
 405                 while (cit != citend) {
 406                         unsigned ti = cit->return_type_tinfo();
 407                         size_t rtt_num = rttinfos.size();
 408                         // search type in vector of known types
 409                         for (i=0; i<rtt_num; ++i) {
 410                                 if (ti == rttinfos[i]) {
 411                                         evv[i].push_back(*cit);
 412                                         break;
 413                                 }
 414                         }
 415                         if (i >= rtt_num) {
 416                                 // new type
 417                                 rttinfos.push_back(ti);
 418                                 evv.push_back(exvector());
 419                                 (evv.end()-1)->reserve(assoc_num);
 420                                 (evv.end()-1)->push_back(*cit);
 421                         }
 422                         ++cit;
 423                 }
 424
 425                 size_t evv_num = evv.size();
 426 #ifdef DO_GINAC_ASSERT
 427                 GINAC_ASSERT(evv_num == rttinfos.size());
 428                 GINAC_ASSERT(evv_num > 0);
 429                 size_t s=0;
 430                 for (i=0; i<evv_num; ++i)
 431                         s += evv[i].size();
 432                 GINAC_ASSERT(s == assoc_num);
 433 #endif // def DO_GINAC_ASSERT
 434
 435                 // if all elements are of same type, simplify the string
 436                 if (evv_num == 1)
 437                         return evv[0][0].eval_ncmul(evv[0]);
 438
 439                 exvector splitseq;
 440                 splitseq.reserve(evv_num);
 441                 for (i=0; i<evv_num; ++i)
 442                         splitseq.push_back((new ncmul(evv[i]))->setflag(status_flags::dynallocated));
 443
 444                 return (new mul(splitseq))->setflag(status_flags::dynallocated);
 445         }
 446
 447         return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
 448                                                                                   status_flags::evaluated);
 449 }
 450
 451 ex ncmul::evalm() const
 452 {
 453         // Evaluate children first
 454         std::auto_ptr<exvector> s(new exvector);
 455         s->reserve(seq.size());
 456         exvector::const_iterator it = seq.begin(), itend = seq.end();
 457         while (it != itend) {
 458                 s->push_back(it->evalm());
 459                 it++;
 460         }
 461
 462         // If there are only matrices, simply multiply them
 463         it = s->begin(); itend = s->end();
 464         if (is_a<matrix>(*it)) {
 465                 matrix prod(ex_to<matrix>(*it));
 466                 it++;
 467                 while (it != itend) {
 468                         if (!is_a<matrix>(*it))
 469                                 goto no_matrix;
 470                         prod = prod.mul(ex_to<matrix>(*it));
 471                         it++;
 472                 }
 473                 return prod;
 474         }
 475
 476 no_matrix:
 477         return (new ncmul(s))->setflag(status_flags::dynallocated);
 478 }
 479
 480 ex ncmul::thiscontainer(const exvector & v) const
 481 {
 482         return (new ncmul(v))->setflag(status_flags::dynallocated);
 483 }
 484
 485 ex ncmul::thiscontainer(std::auto_ptr<exvector> vp) const
 486 {
 487         return (new ncmul(vp))->setflag(status_flags::dynallocated);
 488 }
 489
 490 ex ncmul::conjugate() const
 491 {
 492         if (return_type() != return_types::noncommutative) {
 493                 return exprseq::conjugate();
 494         }
 495
 496         if ((return_type_tinfo() & 0xffffff00U) != TINFO_clifford) {
 497                 return exprseq::conjugate();
 498         }
 499
 500         exvector ev;
 501         ev.reserve(nops());
 502         for (const_iterator i=end(); i!=begin();) {
 503                 --i;
 504                 ev.push_back(i->conjugate());
 505         }
 506         return (new ncmul(ev, true))->setflag(status_flags::dynallocated).eval();
 507 }
 508
 509 // protected
 510
 511 /** Implementation of ex::diff() for a non-commutative product. It applies
 512  *  the product rule.
 513  *  @see ex::diff */
 514 ex ncmul::derivative(const symbol & s) const
 515 {
 516         size_t num = seq.size();
 517         exvector addseq;
 518         addseq.reserve(num);
 519
 520         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 521         exvector ncmulseq = seq;
 522         for (size_t i=0; i<num; ++i) {
 523                 ex e = seq[i].diff(s);
 524                 e.swap(ncmulseq[i]);
 525                 addseq.push_back((new ncmul(ncmulseq))->setflag(status_flags::dynallocated));
 526                 e.swap(ncmulseq[i]);
 527         }
 528         return (new add(addseq))->setflag(status_flags::dynallocated);
 529 }
 530
 531 int ncmul::compare_same_type(const basic & other) const
 532 {
 533         return inherited::compare_same_type(other);
 534 }
 535
 536 unsigned ncmul::return_type() const
 537 {
 538         if (seq.empty())
 539                 return return_types::commutative;
 540
 541         bool all_commutative = true;
 542         exvector::const_iterator noncommutative_element; // point to first found nc element
 543
 544         exvector::const_iterator i = seq.begin(), end = seq.end();
 545         while (i != end) {
 546                 unsigned rt = i->return_type();
 547                 if (rt == return_types::noncommutative_composite)
 548                         return rt; // one ncc -> mul also ncc
 549                 if ((rt == return_types::noncommutative) && (all_commutative)) {
 550                         // first nc element found, remember position
 551                         noncommutative_element = i;
 552                         all_commutative = false;
 553                 }
 554                 if ((rt == return_types::noncommutative) && (!all_commutative)) {
 555                         // another nc element found, compare type_infos
 556                         if (noncommutative_element->return_type_tinfo() != i->return_type_tinfo()) {
 557                                 // diffent types -> mul is ncc
 558                                 return return_types::noncommutative_composite;
 559                         }
 560                 }
 561                 ++i;
 562         }
 563         // all factors checked
 564         GINAC_ASSERT(!all_commutative); // not all factors should commutate, because this is a ncmul();
 565         return all_commutative ? return_types::commutative : return_types::noncommutative;
 566 }
 567
 568 unsigned ncmul::return_type_tinfo() const
 569 {
 570         if (seq.empty())
 571                 return tinfo_key;
 572
 573         // return type_info of first noncommutative element
 574         exvector::const_iterator i = seq.begin(), end = seq.end();
 575         while (i != end) {
 576                 if (i->return_type() == return_types::noncommutative)
 577                         return i->return_type_tinfo();
 578                 ++i;
 579         }
 580
 581         // no noncommutative element found, should not happen
 582         return tinfo_key;
 583 }
 584
 585 //////////
 586 // new virtual functions which can be overridden by derived classes
 587 //////////
 588
 589 // none
 590
 591 //////////
 592 // non-virtual functions in this class
 593 //////////
 594
 595 std::auto_ptr<exvector> ncmul::expandchildren(unsigned options) const
 596 {
 597         const_iterator cit = this->seq.begin(), end = this->seq.end();
 598         while (cit != end) {
 599                 const ex & expanded_ex = cit->expand(options);
 600                 if (!are_ex_trivially_equal(*cit, expanded_ex)) {
 601
 602                         // copy first part of seq which hasn't changed
 603                         std::auto_ptr<exvector> s(new exvector(this->seq.begin(), cit));
 604                         reserve(*s, this->seq.size());
 605
 606                         // insert changed element
 607                         s->push_back(expanded_ex);
 608                         ++cit;
 609
 610                         // copy rest
 611                         while (cit != end) {
 612                                 s->push_back(cit->expand(options));
 613                                 ++cit;
 614                         }
 615
 616                         return s;
 617                 }
 618
 619                 ++cit;
 620         }
 621
 622         return std::auto_ptr<exvector>(0); // nothing has changed
 623 }
 624
 625 const exvector & ncmul::get_factors() const
 626 {
 627         return seq;
 628 }
 629
 630 //////////
 631 // friend functions
 632 //////////
 633
 634 ex reeval_ncmul(const exvector & v)
 635 {
 636         return (new ncmul(v))->setflag(status_flags::dynallocated);
 637 }
 638
 639 ex hold_ncmul(const exvector & v)
 640 {
 641         if (v.empty())
 642                 return _ex1;
 643         else if (v.size() == 1)
 644                 return v[0];
 645         else
 646                 return (new ncmul(v))->setflag(status_flags::dynallocated |
 647                                                status_flags::evaluated);
 648 }
 649
 650 } // namespace GiNaC