ginac/ncmul.cpp

   1 /** @file ncmul.cpp
   2  *
   3  *  Implementation of GiNaC's non-commutative products of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2025 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 <stdexcept>
  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 }
  52
  53 //////////
  54 // other constructors
  55 //////////
  56
  57 // public
  58
  59 ncmul::ncmul(const ex & lh, const ex & rh) : inherited{lh,rh}
  60 {
  61 }
  62
  63 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3) : inherited{f1,f2,f3}
  64 {
  65 }
  66
  67 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  68              const ex & f4) : inherited{f1,f2,f3,f4}
  69 {
  70 }
  71
  72 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  73              const ex & f4, const ex & f5) : inherited{f1,f2,f3,f4,f5}
  74 {
  75 }
  76
  77 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  78              const ex & f4, const ex & f5, const ex & f6) : inherited{f1,f2,f3,f4,f5,f6}
  79 {
  80 }
  81
  82 ncmul::ncmul(const exvector & v) : inherited(v)
  83 {
  84 }
  85
  86 ncmul::ncmul(exvector && v) : inherited(std::move(v))
  87 {
  88 }
  89
  90 //////////
  91 // archiving
  92 //////////
  93
  94
  95 //////////
  96 // functions overriding virtual functions from base classes
  97 //////////
  98
  99 // public
 100
 101 void ncmul::do_print(const print_context & c, unsigned level) const
 102 {
 103         printseq(c, '(', '*', ')', precedence(), level);
 104 }
 105
 106 void ncmul::do_print_csrc(const print_context & c, unsigned level) const
 107 {
 108         c.s << class_name();
 109         printseq(c, '(', ',', ')', precedence(), precedence());
 110 }
 111
 112 bool ncmul::info(unsigned inf) const
 113 {
 114         return inherited::info(inf);
 115 }
 116
 117 typedef std::vector<std::size_t> uintvector;
 118
 119 ex ncmul::expand(unsigned options) const
 120 {
 121         // First, expand the children
 122         exvector v = expandchildren(options);
 123         const exvector &expanded_seq = v.empty() ? this->seq : v;
 124
 125         // Now, look for all the factors that are sums and remember their
 126         // position and number of terms.
 127         uintvector positions_of_adds(expanded_seq.size());
 128         uintvector number_of_add_operands(expanded_seq.size());
 129
 130         size_t number_of_adds = 0;
 131         size_t number_of_expanded_terms = 1;
 132
 133         size_t current_position = 0;
 134         for (auto & it : expanded_seq) {
 135                 if (is_exactly_a<add>(it)) {
 136                         positions_of_adds[number_of_adds] = current_position;
 137                         size_t num_ops = it.nops();
 138                         number_of_add_operands[number_of_adds] = num_ops;
 139                         number_of_expanded_terms *= num_ops;
 140                         number_of_adds++;
 141                 }
 142                 ++current_position;
 143         }
 144
 145         // If there are no sums, we are done
 146         if (number_of_adds == 0) {
 147                 if (!v.empty())
 148                         return dynallocate<ncmul>(std::move(v)).setflag(options == 0 ? status_flags::expanded : 0);
 149                 else
 150                         return *this;
 151         }
 152
 153         // Now, form all possible products of the terms of the sums with the
 154         // remaining factors, and add them together
 155         exvector distrseq;
 156         distrseq.reserve(number_of_expanded_terms);
 157
 158         uintvector k(number_of_adds);
 159
 160         /* Rename indices in the static members of the product */
 161         exvector expanded_seq_mod;
 162         size_t j = 0;
 163         exvector va;
 164
 165         for (size_t i=0; i<expanded_seq.size(); i++) {
 166                 if (i == positions_of_adds[j]) {
 167                         expanded_seq_mod.push_back(_ex1);
 168                         j++;
 169                 } else {
 170                         expanded_seq_mod.push_back(rename_dummy_indices_uniquely(va, expanded_seq[i], true));
 171                 }
 172         }
 173
 174         while (true) {
 175                 exvector term = expanded_seq_mod;
 176                 for (size_t i=0; i<number_of_adds; i++) {
 177                         term[positions_of_adds[i]] = rename_dummy_indices_uniquely(va, expanded_seq[positions_of_adds[i]].op(k[i]), true);
 178                 }
 179
 180                 distrseq.push_back(dynallocate<ncmul>(std::move(term)).setflag(options == 0 ? status_flags::expanded : 0));
 181
 182                 // increment k[]
 183                 int l = number_of_adds-1;
 184                 while ((l>=0) && ((++k[l]) >= number_of_add_operands[l])) {
 185                         k[l] = 0;
 186                         l--;
 187                 }
 188                 if (l<0)
 189                         break;
 190         }
 191
 192         return dynallocate<add>(distrseq).setflag(options == 0 ? status_flags::expanded : 0);
 193 }
 194
 195 int ncmul::degree(const ex & s) const
 196 {
 197         if (is_equal(ex_to<basic>(s)))
 198                 return 1;
 199
 200         // Sum up degrees of factors
 201         int deg_sum = 0;
 202         for (auto & i : seq)
 203                 deg_sum += i.degree(s);
 204         return deg_sum;
 205 }
 206
 207 int ncmul::ldegree(const ex & s) const
 208 {
 209         if (is_equal(ex_to<basic>(s)))
 210                 return 1;
 211
 212         // Sum up degrees of factors
 213         int deg_sum = 0;
 214         for (auto & i : seq)
 215                 deg_sum += i.degree(s);
 216         return deg_sum;
 217 }
 218
 219 ex ncmul::coeff(const ex & s, int n) const
 220 {
 221         if (is_equal(ex_to<basic>(s)))
 222                 return n==1 ? _ex1 : _ex0;
 223
 224         exvector coeffseq;
 225         coeffseq.reserve(seq.size());
 226
 227         if (n == 0) {
 228                 // product of individual coeffs
 229                 // if a non-zero power of s is found, the resulting product will be 0
 230                 for (auto & it : seq)
 231                         coeffseq.push_back(it.coeff(s,n));
 232                 return dynallocate<ncmul>(std::move(coeffseq));
 233         }
 234
 235         bool coeff_found = false;
 236         for (auto & i : seq) {
 237                 ex c = i.coeff(s,n);
 238                 if (c.is_zero()) {
 239                         coeffseq.push_back(i);
 240                 } else {
 241                         coeffseq.push_back(c);
 242                         coeff_found = true;
 243                 }
 244         }
 245
 246         if (coeff_found)
 247                 return dynallocate<ncmul>(std::move(coeffseq));
 248
 249         return _ex0;
 250 }
 251
 252 size_t ncmul::count_factors(const ex & e) const
 253 {
 254         if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
 255                 (is_exactly_a<ncmul>(e))) {
 256                 size_t factors=0;
 257                 for (size_t i=0; i<e.nops(); i++)
 258                         factors += count_factors(e.op(i));
 259
 260                 return factors;
 261         }
 262         return 1;
 263 }
 264
 265 void ncmul::append_factors(exvector & v, const ex & e) const
 266 {
 267         if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
 268                 (is_exactly_a<ncmul>(e))) {
 269                 for (size_t i=0; i<e.nops(); i++)
 270                         append_factors(v, e.op(i));
 271         } else
 272                 v.push_back(e);
 273 }
 274
 275 typedef std::vector<unsigned> unsignedvector;
 276 typedef std::vector<exvector> exvectorvector;
 277
 278 /** Perform automatic term rewriting rules in this class.  In the following
 279  *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
 280  *  stand for such expressions that contain a plain number.
 281  *  - ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) -> ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 282  *  - ncmul(x) -> x
 283  *  - ncmul() -> 1
 284  *  - ncmul(...,c1,...,c2,...) -> *(c1,c2,ncmul(...))  (pull out commutative elements)
 285  *  - ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))  (collect elements of same type)
 286  *  - ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)
 287  */
 288 ex ncmul::eval() const
 289 {
 290         // The following additional rule would be nice, but produces a recursion,
 291         // which must be trapped by introducing a flag that the sub-ncmuls()
 292         // are already evaluated (maybe later...)
 293         //                  ncmul(x1,x2,...,X,y1,y2,...) ->
 294         //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
 295         //                      (X noncommutative_composite)
 296
 297         if (flags & status_flags::evaluated) {
 298                 return *this;
 299         }
 300
 301         // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 302         //     ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 303         size_t factors = 0;
 304         for (auto & it : seq)
 305                 factors += count_factors(it);
 306
 307         exvector assocseq;
 308         assocseq.reserve(factors);
 309         make_flat_inserter mf(seq, true);
 310         for (auto & it : seq) {
 311                 ex factor = mf.handle_factor(it, 1);
 312                 append_factors(assocseq, factor);
 313         }
 314
 315         // ncmul(x) -> x
 316         if (assocseq.size()==1) return *(seq.begin());
 317
 318         // ncmul() -> 1
 319         if (assocseq.empty()) return _ex1;
 320
 321         // determine return types
 322         unsignedvector rettypes(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         for (auto & it : assocseq) {
 328                 rettypes[i] = it.return_type();
 329                 switch (rettypes[i]) {
 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;
 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(dynallocate<ncmul>(std::move(noncommutativeseq)));
 361                 return dynallocate<mul>(std::move(commutativeseq));
 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                 std::vector<return_type_t> rttinfos;
 375                 evv.reserve(assoc_num);
 376                 rttinfos.reserve(assoc_num);
 377
 378                 for (auto & it : assocseq) {
 379                         return_type_t ti = it.return_type_tinfo();
 380                         size_t rtt_num = rttinfos.size();
 381                         // search type in vector of known types
 382                         for (i=0; i<rtt_num; ++i) {
 383                                 if(ti == rttinfos[i]) {
 384                                         evv[i].push_back(it);
 385                                         break;
 386                                 }
 387                         }
 388                         if (i >= rtt_num) {
 389                                 // new type
 390                                 rttinfos.push_back(ti);
 391                                 evv.push_back(exvector());
 392                                 (evv.end()-1)->reserve(assoc_num);
 393                                 (evv.end()-1)->push_back(it);
 394                         }
 395                 }
 396
 397                 size_t evv_num = evv.size();
 398 #ifdef DO_GINAC_ASSERT
 399                 GINAC_ASSERT(evv_num == rttinfos.size());
 400                 GINAC_ASSERT(evv_num > 0);
 401                 size_t s=0;
 402                 for (i=0; i<evv_num; ++i)
 403                         s += evv[i].size();
 404                 GINAC_ASSERT(s == assoc_num);
 405 #endif // def DO_GINAC_ASSERT
 406
 407                 // if all elements are of same type, simplify the string
 408                 if (evv_num == 1) {
 409                         return evv[0][0].eval_ncmul(evv[0]);
 410                 }
 411
 412                 exvector splitseq;
 413                 splitseq.reserve(evv_num);
 414                 for (i=0; i<evv_num; ++i)
 415                         splitseq.push_back(dynallocate<ncmul>(evv[i]));
 416
 417                 return dynallocate<mul>(splitseq);
 418         }
 419
 420         return dynallocate<ncmul>(assocseq).setflag(status_flags::evaluated);
 421 }
 422
 423 ex ncmul::evalm() const
 424 {
 425         // Evaluate children first
 426         exvector s;
 427         s.reserve(seq.size());
 428         for (auto & it : seq)
 429                 s.push_back(it.evalm());
 430
 431         // If there are only matrices, simply multiply them
 432         auto it = s.begin(), itend = s.end();
 433         if (is_a<matrix>(*it)) {
 434                 matrix prod(ex_to<matrix>(*it));
 435                 it++;
 436                 while (it != itend) {
 437                         if (!is_a<matrix>(*it))
 438                                 goto no_matrix;
 439                         prod = prod.mul(ex_to<matrix>(*it));
 440                         it++;
 441                 }
 442                 return prod;
 443         }
 444
 445 no_matrix:
 446         return dynallocate<ncmul>(std::move(s));
 447 }
 448
 449 ex ncmul::thiscontainer(const exvector & v) const
 450 {
 451         return dynallocate<ncmul>(v);
 452 }
 453
 454 ex ncmul::thiscontainer(exvector && v) const
 455 {
 456         return dynallocate<ncmul>(std::move(v));
 457 }
 458
 459 ex ncmul::conjugate() const
 460 {
 461         if (return_type() != return_types::noncommutative) {
 462                 return exprseq::conjugate();
 463         }
 464
 465         if (!is_clifford_tinfo(return_type_tinfo())) {
 466                 return exprseq::conjugate();
 467         }
 468
 469         exvector ev;
 470         ev.reserve(nops());
 471         for (auto i=end(); i!=begin();) {
 472                 --i;
 473                 ev.push_back(i->conjugate());
 474         }
 475         return dynallocate<ncmul>(std::move(ev));
 476 }
 477
 478 ex ncmul::real_part() const
 479 {
 480         return basic::real_part();
 481 }
 482
 483 ex ncmul::imag_part() const
 484 {
 485         return basic::imag_part();
 486 }
 487
 488 // protected
 489
 490 /** Implementation of ex::diff() for a non-commutative product. It applies
 491  *  the product rule.
 492  *  @see ex::diff */
 493 ex ncmul::derivative(const symbol & s) const
 494 {
 495         size_t num = seq.size();
 496         exvector addseq;
 497         addseq.reserve(num);
 498
 499         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 500         exvector ncmulseq = seq;
 501         for (size_t i=0; i<num; ++i) {
 502                 ex e = seq[i].diff(s);
 503                 e.swap(ncmulseq[i]);
 504                 addseq.push_back(dynallocate<ncmul>(ncmulseq));
 505                 e.swap(ncmulseq[i]);
 506         }
 507         return dynallocate<add>(addseq);
 508 }
 509
 510 int ncmul::compare_same_type(const basic & other) const
 511 {
 512         return inherited::compare_same_type(other);
 513 }
 514
 515 unsigned ncmul::return_type() const
 516 {
 517         if (seq.empty())
 518                 return return_types::commutative;
 519
 520         bool all_commutative = true;
 521         exvector::const_iterator noncommutative_element; // point to first found nc element
 522
 523         auto i = seq.begin(), end = seq.end();
 524         while (i != end) {
 525                 unsigned rt = i->return_type();
 526                 if (rt == return_types::noncommutative_composite)
 527                         return rt; // one ncc -> mul also ncc
 528                 if ((rt == return_types::noncommutative) && (all_commutative)) {
 529                         // first nc element found, remember position
 530                         noncommutative_element = i;
 531                         all_commutative = false;
 532                 }
 533                 if ((rt == return_types::noncommutative) && (!all_commutative)) {
 534                         // another nc element found, compare type_infos
 535                         if(noncommutative_element->return_type_tinfo() != i->return_type_tinfo())
 536                                         return return_types::noncommutative_composite;
 537                 }
 538                 ++i;
 539         }
 540         // all factors checked
 541         GINAC_ASSERT(!all_commutative); // not all factors should commutate, because this is a ncmul();
 542         return all_commutative ? return_types::commutative : return_types::noncommutative;
 543 }
 544
 545 return_type_t ncmul::return_type_tinfo() const
 546 {
 547         if (seq.empty())
 548                 return make_return_type_t<ncmul>();
 549
 550         // return type_info of first noncommutative element
 551         for (auto & i : seq)
 552                 if (i.return_type() == return_types::noncommutative)
 553                         return i.return_type_tinfo();
 554
 555         // no noncommutative element found, should not happen
 556         return make_return_type_t<ncmul>();
 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 exvector ncmul::expandchildren(unsigned options) const
 570 {
 571         auto 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                         exvector s(this->seq.begin(), cit);
 578                         s.reserve(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 exvector(); // 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 dynallocate<ncmul>(v);
 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 dynallocate<ncmul>(v).setflag(status_flags::evaluated);
 621 }
 622
 623 GINAC_BIND_UNARCHIVER(ncmul);
 624
 625 } // namespace GiNaC