ginac/ncmul.cpp

   1 /** @file ncmul.cpp
   2  *
   3  *  Implementation of GiNaC's non-commutative products of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2020 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 "ncmul.h"
  24 #include "ex.h"
  25 #include "add.h"
  26 #include "mul.h"
  27 #include "clifford.h"
  28 #include "matrix.h"
  29 #include "archive.h"
  30 #include "indexed.h"
  31 #include "utils.h"
  32
  33 #include <algorithm>
  34 #include <iostream>
  35 #include <stdexcept>
  36
  37 namespace GiNaC {
  38
  39 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(ncmul, exprseq,
  40   print_func<print_context>(&ncmul::do_print).
  41   print_func<print_tree>(&ncmul::do_print_tree).
  42   print_func<print_csrc>(&ncmul::do_print_csrc).
  43   print_func<print_python_repr>(&ncmul::do_print_csrc))
  44
  45
  46 //////////
  47 // default constructor
  48 //////////
  49
  50 ncmul::ncmul()
  51 {
  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 }
  63
  64 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3) : inherited{f1,f2,f3}
  65 {
  66 }
  67
  68 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  69              const ex & f4) : inherited{f1,f2,f3,f4}
  70 {
  71 }
  72
  73 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  74              const ex & f4, const ex & f5) : inherited{f1,f2,f3,f4,f5}
  75 {
  76 }
  77
  78 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  79              const ex & f4, const ex & f5, const ex & f6) : inherited{f1,f2,f3,f4,f5,f6}
  80 {
  81 }
  82
  83 ncmul::ncmul(const exvector & v) : inherited(v)
  84 {
  85 }
  86
  87 ncmul::ncmul(exvector && v) : inherited(std::move(v))
  88 {
  89 }
  90
  91 //////////
  92 // archiving
  93 //////////
  94
  95
  96 //////////
  97 // functions overriding virtual functions from base classes
  98 //////////
  99
 100 // public
 101
 102 void ncmul::do_print(const print_context & c, unsigned level) const
 103 {
 104         printseq(c, '(', '*', ')', precedence(), level);
 105 }
 106
 107 void ncmul::do_print_csrc(const print_context & c, unsigned level) const
 108 {
 109         c.s << class_name();
 110         printseq(c, '(', ',', ')', precedence(), precedence());
 111 }
 112
 113 bool ncmul::info(unsigned inf) const
 114 {
 115         return inherited::info(inf);
 116 }
 117
 118 typedef std::vector<std::size_t> uintvector;
 119
 120 ex ncmul::expand(unsigned options) const
 121 {
 122         // First, expand the children
 123         exvector v = expandchildren(options);
 124         const exvector &expanded_seq = v.empty() ? this->seq : v;
 125
 126         // Now, look for all the factors that are sums and remember their
 127         // position and number of terms.
 128         uintvector positions_of_adds(expanded_seq.size());
 129         uintvector number_of_add_operands(expanded_seq.size());
 130
 131         size_t number_of_adds = 0;
 132         size_t number_of_expanded_terms = 1;
 133
 134         size_t current_position = 0;
 135         for (auto & it : expanded_seq) {
 136                 if (is_exactly_a<add>(it)) {
 137                         positions_of_adds[number_of_adds] = current_position;
 138                         size_t num_ops = it.nops();
 139                         number_of_add_operands[number_of_adds] = num_ops;
 140                         number_of_expanded_terms *= num_ops;
 141                         number_of_adds++;
 142                 }
 143                 ++current_position;
 144         }
 145
 146         // If there are no sums, we are done
 147         if (number_of_adds == 0) {
 148                 if (!v.empty())
 149                         return dynallocate<ncmul>(std::move(v)).setflag(options == 0 ? status_flags::expanded : 0);
 150                 else
 151                         return *this;
 152         }
 153
 154         // Now, form all possible products of the terms of the sums with the
 155         // remaining factors, and add them together
 156         exvector distrseq;
 157         distrseq.reserve(number_of_expanded_terms);
 158
 159         uintvector k(number_of_adds);
 160
 161         /* Rename indices in the static members of the product */
 162         exvector expanded_seq_mod;
 163         size_t j = 0;
 164         exvector va;
 165
 166         for (size_t i=0; i<expanded_seq.size(); i++) {
 167                 if (i == positions_of_adds[j]) {
 168                         expanded_seq_mod.push_back(_ex1);
 169                         j++;
 170                 } else {
 171                         expanded_seq_mod.push_back(rename_dummy_indices_uniquely(va, expanded_seq[i], true));
 172                 }
 173         }
 174
 175         while (true) {
 176                 exvector term = expanded_seq_mod;
 177                 for (size_t i=0; i<number_of_adds; i++) {
 178                         term[positions_of_adds[i]] = rename_dummy_indices_uniquely(va, expanded_seq[positions_of_adds[i]].op(k[i]), true);
 179                 }
 180
 181                 distrseq.push_back(dynallocate<ncmul>(std::move(term)).setflag(options == 0 ? status_flags::expanded : 0));
 182
 183                 // increment k[]
 184                 int l = number_of_adds-1;
 185                 while ((l>=0) && ((++k[l]) >= number_of_add_operands[l])) {
 186                         k[l] = 0;
 187                         l--;
 188                 }
 189                 if (l<0)
 190                         break;
 191         }
 192
 193         return dynallocate<add>(distrseq).setflag(options == 0 ? status_flags::expanded : 0);
 194 }
 195
 196 int ncmul::degree(const ex & s) const
 197 {
 198         if (is_equal(ex_to<basic>(s)))
 199                 return 1;
 200
 201         // Sum up degrees of factors
 202         int deg_sum = 0;
 203         for (auto & i : seq)
 204                 deg_sum += i.degree(s);
 205         return deg_sum;
 206 }
 207
 208 int ncmul::ldegree(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         for (auto & i : seq)
 216                 deg_sum += i.degree(s);
 217         return deg_sum;
 218 }
 219
 220 ex ncmul::coeff(const ex & s, int n) const
 221 {
 222         if (is_equal(ex_to<basic>(s)))
 223                 return n==1 ? _ex1 : _ex0;
 224
 225         exvector coeffseq;
 226         coeffseq.reserve(seq.size());
 227
 228         if (n == 0) {
 229                 // product of individual coeffs
 230                 // if a non-zero power of s is found, the resulting product will be 0
 231                 for (auto & it : seq)
 232                         coeffseq.push_back(it.coeff(s,n));
 233                 return dynallocate<ncmul>(std::move(coeffseq));
 234         }
 235
 236         bool coeff_found = false;
 237         for (auto & i : seq) {
 238                 ex c = i.coeff(s,n);
 239                 if (c.is_zero()) {
 240                         coeffseq.push_back(i);
 241                 } else {
 242                         coeffseq.push_back(c);
 243                         coeff_found = true;
 244                 }
 245         }
 246
 247         if (coeff_found)
 248                 return dynallocate<ncmul>(std::move(coeffseq));
 249
 250         return _ex0;
 251 }
 252
 253 size_t ncmul::count_factors(const ex & e) const
 254 {
 255         if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
 256                 (is_exactly_a<ncmul>(e))) {
 257                 size_t factors=0;
 258                 for (size_t i=0; i<e.nops(); i++)
 259                         factors += count_factors(e.op(i));
 260
 261                 return factors;
 262         }
 263         return 1;
 264 }
 265
 266 void ncmul::append_factors(exvector & v, const ex & e) const
 267 {
 268         if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
 269                 (is_exactly_a<ncmul>(e))) {
 270                 for (size_t i=0; i<e.nops(); i++)
 271                         append_factors(v, e.op(i));
 272         } else
 273                 v.push_back(e);
 274 }
 275
 276 typedef std::vector<unsigned> unsignedvector;
 277 typedef std::vector<exvector> exvectorvector;
 278
 279 /** Perform automatic term rewriting rules in this class.  In the following
 280  *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
 281  *  stand for such expressions that contain a plain number.
 282  *  - ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) -> ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 283  *  - ncmul(x) -> x
 284  *  - ncmul() -> 1
 285  *  - ncmul(...,c1,...,c2,...) -> *(c1,c2,ncmul(...))  (pull out commutative elements)
 286  *  - ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))  (collect elements of same type)
 287  *  - ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)
 288  */
 289 ex ncmul::eval() const
 290 {
 291         // The following additional rule would be nice, but produces a recursion,
 292         // which must be trapped by introducing a flag that the sub-ncmuls()
 293         // are already evaluated (maybe later...)
 294         //                  ncmul(x1,x2,...,X,y1,y2,...) ->
 295         //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
 296         //                      (X noncommutative_composite)
 297
 298         if (flags & status_flags::evaluated) {
 299                 return *this;
 300         }
 301
 302         // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 303         //     ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 304         size_t factors = 0;
 305         for (auto & it : seq)
 306                 factors += count_factors(it);
 307
 308         exvector assocseq;
 309         assocseq.reserve(factors);
 310         make_flat_inserter mf(seq, true);
 311         for (auto & it : seq) {
 312                 ex factor = mf.handle_factor(it, 1);
 313                 append_factors(assocseq, factor);
 314         }
 315
 316         // ncmul(x) -> x
 317         if (assocseq.size()==1) return *(seq.begin());
 318
 319         // ncmul() -> 1
 320         if (assocseq.empty()) return _ex1;
 321
 322         // determine return types
 323         unsignedvector rettypes(assocseq.size());
 324         size_t i = 0;
 325         size_t count_commutative=0;
 326         size_t count_noncommutative=0;
 327         size_t count_noncommutative_composite=0;
 328         for (auto & it : assocseq) {
 329                 rettypes[i] = it.return_type();
 330                 switch (rettypes[i]) {
 331                 case return_types::commutative:
 332                         count_commutative++;
 333                         break;
 334                 case return_types::noncommutative:
 335                         count_noncommutative++;
 336                         break;
 337                 case return_types::noncommutative_composite:
 338                         count_noncommutative_composite++;
 339                         break;
 340                 default:
 341                         throw(std::logic_error("ncmul::eval(): invalid return type"));
 342                 }
 343                 ++i;
 344         }
 345         GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
 346
 347         // ncmul(...,c1,...,c2,...) ->
 348         //     *(c1,c2,ncmul(...)) (pull out commutative elements)
 349         if (count_commutative!=0) {
 350                 exvector commutativeseq;
 351                 commutativeseq.reserve(count_commutative+1);
 352                 exvector noncommutativeseq;
 353                 noncommutativeseq.reserve(assocseq.size()-count_commutative);
 354                 size_t num = assocseq.size();
 355                 for (size_t i=0; i<num; ++i) {
 356                         if (rettypes[i]==return_types::commutative)
 357                                 commutativeseq.push_back(assocseq[i]);
 358                         else
 359                                 noncommutativeseq.push_back(assocseq[i]);
 360                 }
 361                 commutativeseq.push_back(dynallocate<ncmul>(std::move(noncommutativeseq)));
 362                 return dynallocate<mul>(std::move(commutativeseq));
 363         }
 364
 365         // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 366         //     (collect elements of same type)
 367
 368         if (count_noncommutative_composite==0) {
 369                 // there are neither commutative nor noncommutative_composite
 370                 // elements in assocseq
 371                 GINAC_ASSERT(count_commutative==0);
 372
 373                 size_t assoc_num = assocseq.size();
 374                 exvectorvector evv;
 375                 std::vector<return_type_t> rttinfos;
 376                 evv.reserve(assoc_num);
 377                 rttinfos.reserve(assoc_num);
 378
 379                 for (auto & it : assocseq) {
 380                         return_type_t ti = it.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(it);
 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(it);
 395                         }
 396                 }
 397
 398                 size_t evv_num = evv.size();
 399 #ifdef DO_GINAC_ASSERT
 400                 GINAC_ASSERT(evv_num == rttinfos.size());
 401                 GINAC_ASSERT(evv_num > 0);
 402                 size_t s=0;
 403                 for (i=0; i<evv_num; ++i)
 404                         s += evv[i].size();
 405                 GINAC_ASSERT(s == assoc_num);
 406 #endif // def DO_GINAC_ASSERT
 407
 408                 // if all elements are of same type, simplify the string
 409                 if (evv_num == 1) {
 410                         return evv[0][0].eval_ncmul(evv[0]);
 411                 }
 412
 413                 exvector splitseq;
 414                 splitseq.reserve(evv_num);
 415                 for (i=0; i<evv_num; ++i)
 416                         splitseq.push_back(dynallocate<ncmul>(evv[i]));
 417
 418                 return dynallocate<mul>(splitseq);
 419         }
 420
 421         return dynallocate<ncmul>(assocseq).setflag(status_flags::evaluated);
 422 }
 423
 424 ex ncmul::evalm() const
 425 {
 426         // Evaluate children first
 427         exvector s;
 428         s.reserve(seq.size());
 429         for (auto & it : seq)
 430                 s.push_back(it.evalm());
 431
 432         // If there are only matrices, simply multiply them
 433         auto it = s.begin(), itend = s.end();
 434         if (is_a<matrix>(*it)) {
 435                 matrix prod(ex_to<matrix>(*it));
 436                 it++;
 437                 while (it != itend) {
 438                         if (!is_a<matrix>(*it))
 439                                 goto no_matrix;
 440                         prod = prod.mul(ex_to<matrix>(*it));
 441                         it++;
 442                 }
 443                 return prod;
 444         }
 445
 446 no_matrix:
 447         return dynallocate<ncmul>(std::move(s));
 448 }
 449
 450 ex ncmul::thiscontainer(const exvector & v) const
 451 {
 452         return dynallocate<ncmul>(v);
 453 }
 454
 455 ex ncmul::thiscontainer(exvector && v) const
 456 {
 457         return dynallocate<ncmul>(std::move(v));
 458 }
 459
 460 ex ncmul::conjugate() const
 461 {
 462         if (return_type() != return_types::noncommutative) {
 463                 return exprseq::conjugate();
 464         }
 465
 466         if (!is_clifford_tinfo(return_type_tinfo())) {
 467                 return exprseq::conjugate();
 468         }
 469
 470         exvector ev;
 471         ev.reserve(nops());
 472         for (auto i=end(); i!=begin();) {
 473                 --i;
 474                 ev.push_back(i->conjugate());
 475         }
 476         return dynallocate<ncmul>(std::move(ev));
 477 }
 478
 479 ex ncmul::real_part() const
 480 {
 481         return basic::real_part();
 482 }
 483
 484 ex ncmul::imag_part() const
 485 {
 486         return basic::imag_part();
 487 }
 488
 489 // protected
 490
 491 /** Implementation of ex::diff() for a non-commutative product. It applies
 492  *  the product rule.
 493  *  @see ex::diff */
 494 ex ncmul::derivative(const symbol & s) const
 495 {
 496         size_t num = seq.size();
 497         exvector addseq;
 498         addseq.reserve(num);
 499
 500         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 501         exvector ncmulseq = seq;
 502         for (size_t i=0; i<num; ++i) {
 503                 ex e = seq[i].diff(s);
 504                 e.swap(ncmulseq[i]);
 505                 addseq.push_back(dynallocate<ncmul>(ncmulseq));
 506                 e.swap(ncmulseq[i]);
 507         }
 508         return dynallocate<add>(addseq);
 509 }
 510
 511 int ncmul::compare_same_type(const basic & other) const
 512 {
 513         return inherited::compare_same_type(other);
 514 }
 515
 516 unsigned ncmul::return_type() const
 517 {
 518         if (seq.empty())
 519                 return return_types::commutative;
 520
 521         bool all_commutative = true;
 522         exvector::const_iterator noncommutative_element; // point to first found nc element
 523
 524         auto i = seq.begin(), end = seq.end();
 525         while (i != end) {
 526                 unsigned rt = i->return_type();
 527                 if (rt == return_types::noncommutative_composite)
 528                         return rt; // one ncc -> mul also ncc
 529                 if ((rt == return_types::noncommutative) && (all_commutative)) {
 530                         // first nc element found, remember position
 531                         noncommutative_element = i;
 532                         all_commutative = false;
 533                 }
 534                 if ((rt == return_types::noncommutative) && (!all_commutative)) {
 535                         // another nc element found, compare type_infos
 536                         if(noncommutative_element->return_type_tinfo() != i->return_type_tinfo())
 537                                         return return_types::noncommutative_composite;
 538                 }
 539                 ++i;
 540         }
 541         // all factors checked
 542         GINAC_ASSERT(!all_commutative); // not all factors should commutate, because this is a ncmul();
 543         return all_commutative ? return_types::commutative : return_types::noncommutative;
 544 }
 545
 546 return_type_t ncmul::return_type_tinfo() const
 547 {
 548         if (seq.empty())
 549                 return make_return_type_t<ncmul>();
 550
 551         // return type_info of first noncommutative element
 552         for (auto & i : seq)
 553                 if (i.return_type() == return_types::noncommutative)
 554                         return i.return_type_tinfo();
 555
 556         // no noncommutative element found, should not happen
 557         return make_return_type_t<ncmul>();
 558 }
 559
 560 //////////
 561 // new virtual functions which can be overridden by derived classes
 562 //////////
 563
 564 // none
 565
 566 //////////
 567 // non-virtual functions in this class
 568 //////////
 569
 570 exvector ncmul::expandchildren(unsigned options) const
 571 {
 572         auto cit = this->seq.begin(), end = this->seq.end();
 573         while (cit != end) {
 574                 const ex & expanded_ex = cit->expand(options);
 575                 if (!are_ex_trivially_equal(*cit, expanded_ex)) {
 576
 577                         // copy first part of seq which hasn't changed
 578                         exvector s(this->seq.begin(), cit);
 579                         s.reserve(this->seq.size());
 580
 581                         // insert changed element
 582                         s.push_back(expanded_ex);
 583                         ++cit;
 584
 585                         // copy rest
 586                         while (cit != end) {
 587                                 s.push_back(cit->expand(options));
 588                                 ++cit;
 589                         }
 590
 591                         return s;
 592                 }
 593
 594                 ++cit;
 595         }
 596
 597         return exvector(); // nothing has changed
 598 }
 599
 600 const exvector & ncmul::get_factors() const
 601 {
 602         return seq;
 603 }
 604
 605 //////////
 606 // friend functions
 607 //////////
 608
 609 ex reeval_ncmul(const exvector & v)
 610 {
 611         return dynallocate<ncmul>(v);
 612 }
 613
 614 ex hold_ncmul(const exvector & v)
 615 {
 616         if (v.empty())
 617                 return _ex1;
 618         else if (v.size() == 1)
 619                 return v[0];
 620         else
 621                 return dynallocate<ncmul>(v).setflag(status_flags::evaluated);
 622 }
 623
 624 GINAC_BIND_UNARCHIVER(ncmul);
 625
 626 } // namespace GiNaC