ginac/ncmul.cpp

   1 /** @file ncmul.cpp
   2  *
   3  *  Implementation of GiNaC's non-commutative products of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2004 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 "matrix.h"
  32 #include "archive.h"
  33 #include "utils.h"
  34
  35 namespace GiNaC {
  36
  37 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(ncmul, exprseq,
  38   print_func<print_context>(&ncmul::do_print).
  39   print_func<print_tree>(&ncmul::do_print_tree).
  40   print_func<print_csrc>(&ncmul::do_print_csrc).
  41   print_func<print_python_repr>(&ncmul::do_print_csrc))
  42
  43
  44 //////////
  45 // default constructor
  46 //////////
  47
  48 ncmul::ncmul()
  49 {
  50         tinfo_key = TINFO_ncmul;
  51 }
  52
  53 //////////
  54 // other constructors
  55 //////////
  56
  57 // public
  58
  59 ncmul::ncmul(const ex & lh, const ex & rh) : inherited(lh,rh)
  60 {
  61         tinfo_key = TINFO_ncmul;
  62 }
  63
  64 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3) : inherited(f1,f2,f3)
  65 {
  66         tinfo_key = TINFO_ncmul;
  67 }
  68
  69 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  70              const ex & f4) : inherited(f1,f2,f3,f4)
  71 {
  72         tinfo_key = TINFO_ncmul;
  73 }
  74
  75 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  76              const ex & f4, const ex & f5) : inherited(f1,f2,f3,f4,f5)
  77 {
  78         tinfo_key = TINFO_ncmul;
  79 }
  80
  81 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  82              const ex & f4, const ex & f5, const ex & f6) : inherited(f1,f2,f3,f4,f5,f6)
  83 {
  84         tinfo_key = TINFO_ncmul;
  85 }
  86
  87 ncmul::ncmul(const exvector & v, bool discardable) : inherited(v,discardable)
  88 {
  89         tinfo_key = TINFO_ncmul;
  90 }
  91
  92 ncmul::ncmul(std::auto_ptr<exvector> vp) : inherited(vp)
  93 {
  94         tinfo_key = TINFO_ncmul;
  95 }
  96
  97 //////////
  98 // archiving
  99 //////////
 100
 101 DEFAULT_ARCHIVING(ncmul)
 102
 103 //////////
 104 // functions overriding virtual functions from base classes
 105 //////////
 106
 107 // public
 108
 109 void ncmul::do_print(const print_context & c, unsigned level) const
 110 {
 111         printseq(c, '(', '*', ')', precedence(), level);
 112 }
 113
 114 void ncmul::do_print_csrc(const print_context & c, unsigned level) const
 115 {
 116         c.s << class_name();
 117         printseq(c, '(', ',', ')', precedence(), precedence());
 118 }
 119
 120 bool ncmul::info(unsigned inf) const
 121 {
 122         return inherited::info(inf);
 123 }
 124
 125 typedef std::vector<int> intvector;
 126
 127 ex ncmul::expand(unsigned options) const
 128 {
 129         // First, expand the children
 130         std::auto_ptr<exvector> vp = expandchildren(options);
 131         const exvector &expanded_seq = vp.get() ? *vp : this->seq;
 132
 133         // Now, look for all the factors that are sums and remember their
 134         // position and number of terms.
 135         intvector positions_of_adds(expanded_seq.size());
 136         intvector number_of_add_operands(expanded_seq.size());
 137
 138         size_t number_of_adds = 0;
 139         size_t number_of_expanded_terms = 1;
 140
 141         size_t current_position = 0;
 142         exvector::const_iterator last = expanded_seq.end();
 143         for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 144                 if (is_exactly_a<add>(*cit)) {
 145                         positions_of_adds[number_of_adds] = current_position;
 146                         size_t num_ops = cit->nops();
 147                         number_of_add_operands[number_of_adds] = num_ops;
 148                         number_of_expanded_terms *= num_ops;
 149                         number_of_adds++;
 150                 }
 151                 ++current_position;
 152         }
 153
 154         // If there are no sums, we are done
 155         if (number_of_adds == 0) {
 156                 if (vp.get())
 157                         return (new ncmul(vp))->
 158                                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 159                 else
 160                         return *this;
 161         }
 162
 163         // Now, form all possible products of the terms of the sums with the
 164         // remaining factors, and add them together
 165         exvector distrseq;
 166         distrseq.reserve(number_of_expanded_terms);
 167
 168         intvector k(number_of_adds);
 169
 170         while (true) {
 171                 exvector term = expanded_seq;
 172                 for (size_t i=0; i<number_of_adds; i++)
 173                         term[positions_of_adds[i]] = expanded_seq[positions_of_adds[i]].op(k[i]);
 174                 distrseq.push_back((new ncmul(term, true))->
 175                                     setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 176
 177                 // increment k[]
 178                 int l = number_of_adds-1;
 179                 while ((l>=0) && ((++k[l]) >= number_of_add_operands[l])) {
 180                         k[l] = 0;
 181                         l--;
 182                 }
 183                 if (l<0)
 184                         break;
 185         }
 186
 187         return (new add(distrseq))->
 188                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 189 }
 190
 191 int ncmul::degree(const ex & s) const
 192 {
 193         if (is_equal(ex_to<basic>(s)))
 194                 return 1;
 195
 196         // Sum up degrees of factors
 197         int deg_sum = 0;
 198         exvector::const_iterator i = seq.begin(), end = seq.end();
 199         while (i != end) {
 200                 deg_sum += i->degree(s);
 201                 ++i;
 202         }
 203         return deg_sum;
 204 }
 205
 206 int ncmul::ldegree(const ex & s) const
 207 {
 208         if (is_equal(ex_to<basic>(s)))
 209                 return 1;
 210
 211         // Sum up degrees of factors
 212         int deg_sum = 0;
 213         exvector::const_iterator i = seq.begin(), end = seq.end();
 214         while (i != end) {
 215                 deg_sum += i->degree(s);
 216                 ++i;
 217         }
 218         return deg_sum;
 219 }
 220
 221 ex ncmul::coeff(const ex & s, int n) const
 222 {
 223         if (is_equal(ex_to<basic>(s)))
 224                 return n==1 ? _ex1 : _ex0;
 225
 226         exvector coeffseq;
 227         coeffseq.reserve(seq.size());
 228
 229         if (n == 0) {
 230                 // product of individual coeffs
 231                 // if a non-zero power of s is found, the resulting product will be 0
 232                 exvector::const_iterator it=seq.begin();
 233                 while (it!=seq.end()) {
 234                         coeffseq.push_back((*it).coeff(s,n));
 235                         ++it;
 236                 }
 237                 return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 238         }
 239
 240         exvector::const_iterator i = seq.begin(), end = seq.end();
 241         bool coeff_found = false;
 242         while (i != end) {
 243                 ex c = i->coeff(s,n);
 244                 if (c.is_zero()) {
 245                         coeffseq.push_back(*i);
 246                 } else {
 247                         coeffseq.push_back(c);
 248                         coeff_found = true;
 249                 }
 250                 ++i;
 251         }
 252
 253         if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 254
 255         return _ex0;
 256 }
 257
 258 size_t ncmul::count_factors(const ex & e) const
 259 {
 260         if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
 261                 (is_exactly_a<ncmul>(e))) {
 262                 size_t factors=0;
 263                 for (size_t i=0; i<e.nops(); i++)
 264                         factors += count_factors(e.op(i));
 265
 266                 return factors;
 267         }
 268         return 1;
 269 }
 270
 271 void ncmul::append_factors(exvector & v, const ex & e) const
 272 {
 273         if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
 274                 (is_exactly_a<ncmul>(e))) {
 275                 for (size_t i=0; i<e.nops(); i++)
 276                         append_factors(v, e.op(i));
 277         } else
 278                 v.push_back(e);
 279 }
 280
 281 typedef std::vector<unsigned> unsignedvector;
 282 typedef std::vector<exvector> exvectorvector;
 283
 284 /** Perform automatic term rewriting rules in this class.  In the following
 285  *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
 286  *  stand for such expressions that contain a plain number.
 287  *  - ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) -> ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 288  *  - ncmul(x) -> x
 289  *  - ncmul() -> 1
 290  *  - ncmul(...,c1,...,c2,...) -> *(c1,c2,ncmul(...))  (pull out commutative elements)
 291  *  - ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))  (collect elements of same type)
 292  *  - ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)
 293  *
 294  *  @param level cut-off in recursive evaluation */
 295 ex ncmul::eval(int level) const
 296 {
 297         // The following additional rule would be nice, but produces a recursion,
 298         // which must be trapped by introducing a flag that the sub-ncmuls()
 299         // are already evaluated (maybe later...)
 300         //                  ncmul(x1,x2,...,X,y1,y2,...) ->
 301         //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
 302         //                      (X noncommutative_composite)
 303
 304         if ((level==1) && (flags & status_flags::evaluated)) {
 305                 return *this;
 306         }
 307
 308         exvector evaledseq=evalchildren(level);
 309
 310         // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 311         //     ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 312         size_t factors = 0;
 313         exvector::const_iterator cit = evaledseq.begin(), citend = evaledseq.end();
 314         while (cit != citend)
 315                 factors += count_factors(*cit++);
 316
 317         exvector assocseq;
 318         assocseq.reserve(factors);
 319         cit = evaledseq.begin();
 320         while (cit != citend)
 321                 append_factors(assocseq, *cit++);
 322
 323         // ncmul(x) -> x
 324         if (assocseq.size()==1) return *(seq.begin());
 325
 326         // ncmul() -> 1
 327         if (assocseq.empty()) return _ex1;
 328
 329         // determine return types
 330         unsignedvector rettypes;
 331         rettypes.reserve(assocseq.size());
 332         size_t i = 0;
 333         size_t count_commutative=0;
 334         size_t count_noncommutative=0;
 335         size_t count_noncommutative_composite=0;
 336         cit = assocseq.begin(); citend = assocseq.end();
 337         while (cit != citend) {
 338                 switch (rettypes[i] = cit->return_type()) {
 339                 case return_types::commutative:
 340                         count_commutative++;
 341                         break;
 342                 case return_types::noncommutative:
 343                         count_noncommutative++;
 344                         break;
 345                 case return_types::noncommutative_composite:
 346                         count_noncommutative_composite++;
 347                         break;
 348                 default:
 349                         throw(std::logic_error("ncmul::eval(): invalid return type"));
 350                 }
 351                 ++i; ++cit;
 352         }
 353         GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
 354
 355         // ncmul(...,c1,...,c2,...) ->
 356         //     *(c1,c2,ncmul(...)) (pull out commutative elements)
 357         if (count_commutative!=0) {
 358                 exvector commutativeseq;
 359                 commutativeseq.reserve(count_commutative+1);
 360                 exvector noncommutativeseq;
 361                 noncommutativeseq.reserve(assocseq.size()-count_commutative);
 362                 size_t num = assocseq.size();
 363                 for (size_t i=0; i<num; ++i) {
 364                         if (rettypes[i]==return_types::commutative)
 365                                 commutativeseq.push_back(assocseq[i]);
 366                         else
 367                                 noncommutativeseq.push_back(assocseq[i]);
 368                 }
 369                 commutativeseq.push_back((new ncmul(noncommutativeseq,1))->setflag(status_flags::dynallocated));
 370                 return (new mul(commutativeseq))->setflag(status_flags::dynallocated);
 371         }
 372
 373         // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 374         //     (collect elements of same type)
 375
 376         if (count_noncommutative_composite==0) {
 377                 // there are neither commutative nor noncommutative_composite
 378                 // elements in assocseq
 379                 GINAC_ASSERT(count_commutative==0);
 380
 381                 size_t assoc_num = assocseq.size();
 382                 exvectorvector evv;
 383                 unsignedvector rttinfos;
 384                 evv.reserve(assoc_num);
 385                 rttinfos.reserve(assoc_num);
 386
 387                 cit = assocseq.begin(), citend = assocseq.end();
 388                 while (cit != citend) {
 389                         unsigned ti = cit->return_type_tinfo();
 390                         size_t rtt_num = rttinfos.size();
 391                         // search type in vector of known types
 392                         for (i=0; i<rtt_num; ++i) {
 393                                 if (ti == rttinfos[i]) {
 394                                         evv[i].push_back(*cit);
 395                                         break;
 396                                 }
 397                         }
 398                         if (i >= rtt_num) {
 399                                 // new type
 400                                 rttinfos.push_back(ti);
 401                                 evv.push_back(exvector());
 402                                 (evv.end()-1)->reserve(assoc_num);
 403                                 (evv.end()-1)->push_back(*cit);
 404                         }
 405                         ++cit;
 406                 }
 407
 408                 size_t evv_num = evv.size();
 409 #ifdef DO_GINAC_ASSERT
 410                 GINAC_ASSERT(evv_num == rttinfos.size());
 411                 GINAC_ASSERT(evv_num > 0);
 412                 size_t s=0;
 413                 for (i=0; i<evv_num; ++i)
 414                         s += evv[i].size();
 415                 GINAC_ASSERT(s == assoc_num);
 416 #endif // def DO_GINAC_ASSERT
 417
 418                 // if all elements are of same type, simplify the string
 419                 if (evv_num == 1)
 420                         return evv[0][0].eval_ncmul(evv[0]);
 421
 422                 exvector splitseq;
 423                 splitseq.reserve(evv_num);
 424                 for (i=0; i<evv_num; ++i)
 425                         splitseq.push_back((new ncmul(evv[i]))->setflag(status_flags::dynallocated));
 426
 427                 return (new mul(splitseq))->setflag(status_flags::dynallocated);
 428         }
 429
 430         return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
 431                                                                                   status_flags::evaluated);
 432 }
 433
 434 ex ncmul::evalm() const
 435 {
 436         // Evaluate children first
 437         std::auto_ptr<exvector> s(new exvector);
 438         s->reserve(seq.size());
 439         exvector::const_iterator it = seq.begin(), itend = seq.end();
 440         while (it != itend) {
 441                 s->push_back(it->evalm());
 442                 it++;
 443         }
 444
 445         // If there are only matrices, simply multiply them
 446         it = s->begin(); itend = s->end();
 447         if (is_a<matrix>(*it)) {
 448                 matrix prod(ex_to<matrix>(*it));
 449                 it++;
 450                 while (it != itend) {
 451                         if (!is_a<matrix>(*it))
 452                                 goto no_matrix;
 453                         prod = prod.mul(ex_to<matrix>(*it));
 454                         it++;
 455                 }
 456                 return prod;
 457         }
 458
 459 no_matrix:
 460         return (new ncmul(s))->setflag(status_flags::dynallocated);
 461 }
 462
 463 ex ncmul::thiscontainer(const exvector & v) const
 464 {
 465         return (new ncmul(v))->setflag(status_flags::dynallocated);
 466 }
 467
 468 ex ncmul::thiscontainer(std::auto_ptr<exvector> vp) const
 469 {
 470         return (new ncmul(vp))->setflag(status_flags::dynallocated);
 471 }
 472
 473 ex ncmul::conjugate() const
 474 {
 475         if (return_type() != return_types::noncommutative) {
 476                 return exprseq::conjugate();
 477         }
 478
 479         if ((return_type_tinfo() & 0xffffff00U) != TINFO_clifford) {
 480                 return exprseq::conjugate();
 481         }
 482
 483         exvector ev;
 484         ev.reserve(nops());
 485         for (const_iterator i=end(); i!=begin();) {
 486                 --i;
 487                 ev.push_back(i->conjugate());
 488         }
 489         return (new ncmul(ev, true))->setflag(status_flags::dynallocated).eval();
 490 }
 491
 492 // protected
 493
 494 /** Implementation of ex::diff() for a non-commutative product. It applies
 495  *  the product rule.
 496  *  @see ex::diff */
 497 ex ncmul::derivative(const symbol & s) const
 498 {
 499         size_t num = seq.size();
 500         exvector addseq;
 501         addseq.reserve(num);
 502
 503         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 504         exvector ncmulseq = seq;
 505         for (size_t i=0; i<num; ++i) {
 506                 ex e = seq[i].diff(s);
 507                 e.swap(ncmulseq[i]);
 508                 addseq.push_back((new ncmul(ncmulseq))->setflag(status_flags::dynallocated));
 509                 e.swap(ncmulseq[i]);
 510         }
 511         return (new add(addseq))->setflag(status_flags::dynallocated);
 512 }
 513
 514 int ncmul::compare_same_type(const basic & other) const
 515 {
 516         return inherited::compare_same_type(other);
 517 }
 518
 519 unsigned ncmul::return_type() const
 520 {
 521         if (seq.empty())
 522                 return return_types::commutative;
 523
 524         bool all_commutative = true;
 525         exvector::const_iterator noncommutative_element; // point to first found nc element
 526
 527         exvector::const_iterator i = seq.begin(), end = seq.end();
 528         while (i != end) {
 529                 unsigned rt = i->return_type();
 530                 if (rt == return_types::noncommutative_composite)
 531                         return rt; // one ncc -> mul also ncc
 532                 if ((rt == return_types::noncommutative) && (all_commutative)) {
 533                         // first nc element found, remember position
 534                         noncommutative_element = i;
 535                         all_commutative = false;
 536                 }
 537                 if ((rt == return_types::noncommutative) && (!all_commutative)) {
 538                         // another nc element found, compare type_infos
 539                         if (noncommutative_element->return_type_tinfo() != i->return_type_tinfo()) {
 540                                 // diffent types -> mul is ncc
 541                                 return return_types::noncommutative_composite;
 542                         }
 543                 }
 544                 ++i;
 545         }
 546         // all factors checked
 547         GINAC_ASSERT(!all_commutative); // not all factors should commutate, because this is a ncmul();
 548         return all_commutative ? return_types::commutative : return_types::noncommutative;
 549 }
 550
 551 unsigned ncmul::return_type_tinfo() const
 552 {
 553         if (seq.empty())
 554                 return tinfo_key;
 555
 556         // return type_info of first noncommutative element
 557         exvector::const_iterator i = seq.begin(), end = seq.end();
 558         while (i != end) {
 559                 if (i->return_type() == return_types::noncommutative)
 560                         return i->return_type_tinfo();
 561                 ++i;
 562         }
 563
 564         // no noncommutative element found, should not happen
 565         return tinfo_key;
 566 }
 567
 568 //////////
 569 // new virtual functions which can be overridden by derived classes
 570 //////////
 571
 572 // none
 573
 574 //////////
 575 // non-virtual functions in this class
 576 //////////
 577
 578 std::auto_ptr<exvector> ncmul::expandchildren(unsigned options) const
 579 {
 580         const_iterator cit = this->seq.begin(), end = this->seq.end();
 581         while (cit != end) {
 582                 const ex & expanded_ex = cit->expand(options);
 583                 if (!are_ex_trivially_equal(*cit, expanded_ex)) {
 584
 585                         // copy first part of seq which hasn't changed
 586                         std::auto_ptr<exvector> s(new exvector(this->seq.begin(), cit));
 587                         reserve(*s, this->seq.size());
 588
 589                         // insert changed element
 590                         s->push_back(expanded_ex);
 591                         ++cit;
 592
 593                         // copy rest
 594                         while (cit != end) {
 595                                 s->push_back(cit->expand(options));
 596                                 ++cit;
 597                         }
 598
 599                         return s;
 600                 }
 601
 602                 ++cit;
 603         }
 604
 605         return std::auto_ptr<exvector>(0); // nothing has changed
 606 }
 607
 608 const exvector & ncmul::get_factors() const
 609 {
 610         return seq;
 611 }
 612
 613 //////////
 614 // friend functions
 615 //////////
 616
 617 ex reeval_ncmul(const exvector & v)
 618 {
 619         return (new ncmul(v))->setflag(status_flags::dynallocated);
 620 }
 621
 622 ex hold_ncmul(const exvector & v)
 623 {
 624         if (v.empty())
 625                 return _ex1;
 626         else if (v.size() == 1)
 627                 return v[0];
 628         else
 629                 return (new ncmul(v))->setflag(status_flags::dynallocated |
 630                                                status_flags::evaluated);
 631 }
 632
 633 } // namespace GiNaC