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