ginac/ncmul.cpp

   1 /** @file ncmul.cpp
   2  *
   3  *  Implementation of GiNaC's non-commutative products of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2006 Johannes Gutenberg University Mainz, Germany
   7  *
   8  *  This program is free software; you can redistribute it and/or modify
   9  *  it under the terms of the GNU General Public License as published by
  10  *  the Free Software Foundation; either version 2 of the License, or
  11  *  (at your option) any later version.
  12  *
  13  *  This program is distributed in the hope that it will be useful,
  14  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
  15  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  16  *  GNU General Public License for more details.
  17  *
  18  *  You should have received a copy of the GNU General Public License
  19  *  along with this program; if not, write to the Free Software
  20  *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
  21  */
  22
  23 #include <algorithm>
  24 #include <iostream>
  25 #include <stdexcept>
  26
  27 #include "ncmul.h"
  28 #include "ex.h"
  29 #include "add.h"
  30 #include "mul.h"
  31 #include "clifford.h"
  32 #include "color.h"
  33 #include "matrix.h"
  34 #include "archive.h"
  35 #include "indexed.h"
  36 #include "utils.h"
  37
  38 namespace GiNaC {
  39
  40 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(ncmul, exprseq,
  41   print_func<print_context>(&ncmul::do_print).
  42   print_func<print_tree>(&ncmul::do_print_tree).
  43   print_func<print_csrc>(&ncmul::do_print_csrc).
  44   print_func<print_python_repr>(&ncmul::do_print_csrc))
  45
  46
  47 //////////
  48 // default constructor
  49 //////////
  50
  51 ncmul::ncmul()
  52 {
  53         tinfo_key = &ncmul::tinfo_static;
  54 }
  55
  56 //////////
  57 // other constructors
  58 //////////
  59
  60 // public
  61
  62 ncmul::ncmul(const ex & lh, const ex & rh) : inherited(lh,rh)
  63 {
  64         tinfo_key = &ncmul::tinfo_static;
  65 }
  66
  67 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3) : inherited(f1,f2,f3)
  68 {
  69         tinfo_key = &ncmul::tinfo_static;
  70 }
  71
  72 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  73              const ex & f4) : inherited(f1,f2,f3,f4)
  74 {
  75         tinfo_key = &ncmul::tinfo_static;
  76 }
  77
  78 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  79              const ex & f4, const ex & f5) : inherited(f1,f2,f3,f4,f5)
  80 {
  81         tinfo_key = &ncmul::tinfo_static;
  82 }
  83
  84 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  85              const ex & f4, const ex & f5, const ex & f6) : inherited(f1,f2,f3,f4,f5,f6)
  86 {
  87         tinfo_key = &ncmul::tinfo_static;
  88 }
  89
  90 ncmul::ncmul(const exvector & v, bool discardable) : inherited(v,discardable)
  91 {
  92         tinfo_key = &ncmul::tinfo_static;
  93 }
  94
  95 ncmul::ncmul(std::auto_ptr<exvector> vp) : inherited(vp)
  96 {
  97         tinfo_key = &ncmul::tinfo_static;
  98 }
  99
 100 //////////
 101 // archiving
 102 //////////
 103
 104 DEFAULT_ARCHIVING(ncmul)
 105
 106 //////////
 107 // functions overriding virtual functions from base classes
 108 //////////
 109
 110 // public
 111
 112 void ncmul::do_print(const print_context & c, unsigned level) const
 113 {
 114         printseq(c, '(', '*', ')', precedence(), level);
 115 }
 116
 117 void ncmul::do_print_csrc(const print_context & c, unsigned level) const
 118 {
 119         c.s << class_name();
 120         printseq(c, '(', ',', ')', precedence(), precedence());
 121 }
 122
 123 bool ncmul::info(unsigned inf) const
 124 {
 125         return inherited::info(inf);
 126 }
 127
 128 typedef std::vector<int> intvector;
 129
 130 ex ncmul::expand(unsigned options) const
 131 {
 132         // First, expand the children
 133         std::auto_ptr<exvector> vp = expandchildren(options);
 134         const exvector &expanded_seq = vp.get() ? *vp : this->seq;
 135
 136         // Now, look for all the factors that are sums and remember their
 137         // position and number of terms.
 138         intvector positions_of_adds(expanded_seq.size());
 139         intvector number_of_add_operands(expanded_seq.size());
 140
 141         size_t number_of_adds = 0;
 142         size_t number_of_expanded_terms = 1;
 143
 144         size_t current_position = 0;
 145         exvector::const_iterator last = expanded_seq.end();
 146         for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 147                 if (is_exactly_a<add>(*cit)) {
 148                         positions_of_adds[number_of_adds] = current_position;
 149                         size_t num_ops = cit->nops();
 150                         number_of_add_operands[number_of_adds] = num_ops;
 151                         number_of_expanded_terms *= num_ops;
 152                         number_of_adds++;
 153                 }
 154                 ++current_position;
 155         }
 156
 157         // If there are no sums, we are done
 158         if (number_of_adds == 0) {
 159                 if (vp.get())
 160                         return (new ncmul(vp))->
 161                                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 162                 else
 163                         return *this;
 164         }
 165
 166         // Now, form all possible products of the terms of the sums with the
 167         // remaining factors, and add them together
 168         exvector distrseq;
 169         distrseq.reserve(number_of_expanded_terms);
 170
 171         intvector k(number_of_adds);
 172
 173         /* Rename indices in the static members of the product */
 174         exvector expanded_seq_mod;
 175         size_t j = 0;
 176         exvector va;
 177
 178         for (size_t i=0; i<expanded_seq.size(); i++) {
 179                 if (i == positions_of_adds[j]) {
 180                         expanded_seq_mod.push_back(_ex1);
 181                         j++;
 182                 } else {
 183                         expanded_seq_mod.push_back(rename_dummy_indices_uniquely(va, expanded_seq[i], true));
 184                 }
 185         }
 186
 187         while (true) {
 188                 exvector term = expanded_seq_mod;
 189                 for (size_t i=0; i<number_of_adds; i++) {
 190                         term[positions_of_adds[i]] = rename_dummy_indices_uniquely(va, expanded_seq[positions_of_adds[i]].op(k[i]), true);
 191                 }
 192
 193                 distrseq.push_back((new ncmul(term, true))->
 194                                     setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 195
 196                 // increment k[]
 197                 int l = number_of_adds-1;
 198                 while ((l>=0) && ((++k[l]) >= number_of_add_operands[l])) {
 199                         k[l] = 0;
 200                         l--;
 201                 }
 202                 if (l<0)
 203                         break;
 204         }
 205
 206         return (new add(distrseq))->
 207                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 208 }
 209
 210 int ncmul::degree(const ex & s) const
 211 {
 212         if (is_equal(ex_to<basic>(s)))
 213                 return 1;
 214
 215         // Sum up degrees of factors
 216         int deg_sum = 0;
 217         exvector::const_iterator i = seq.begin(), end = seq.end();
 218         while (i != end) {
 219                 deg_sum += i->degree(s);
 220                 ++i;
 221         }
 222         return deg_sum;
 223 }
 224
 225 int ncmul::ldegree(const ex & s) const
 226 {
 227         if (is_equal(ex_to<basic>(s)))
 228                 return 1;
 229
 230         // Sum up degrees of factors
 231         int deg_sum = 0;
 232         exvector::const_iterator i = seq.begin(), end = seq.end();
 233         while (i != end) {
 234                 deg_sum += i->degree(s);
 235                 ++i;
 236         }
 237         return deg_sum;
 238 }
 239
 240 ex ncmul::coeff(const ex & s, int n) const
 241 {
 242         if (is_equal(ex_to<basic>(s)))
 243                 return n==1 ? _ex1 : _ex0;
 244
 245         exvector coeffseq;
 246         coeffseq.reserve(seq.size());
 247
 248         if (n == 0) {
 249                 // product of individual coeffs
 250                 // if a non-zero power of s is found, the resulting product will be 0
 251                 exvector::const_iterator it=seq.begin();
 252                 while (it!=seq.end()) {
 253                         coeffseq.push_back((*it).coeff(s,n));
 254                         ++it;
 255                 }
 256                 return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 257         }
 258
 259         exvector::const_iterator i = seq.begin(), end = seq.end();
 260         bool coeff_found = false;
 261         while (i != end) {
 262                 ex c = i->coeff(s,n);
 263                 if (c.is_zero()) {
 264                         coeffseq.push_back(*i);
 265                 } else {
 266                         coeffseq.push_back(c);
 267                         coeff_found = true;
 268                 }
 269                 ++i;
 270         }
 271
 272         if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 273
 274         return _ex0;
 275 }
 276
 277 size_t ncmul::count_factors(const ex & e) const
 278 {
 279         if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
 280                 (is_exactly_a<ncmul>(e))) {
 281                 size_t factors=0;
 282                 for (size_t i=0; i<e.nops(); i++)
 283                         factors += count_factors(e.op(i));
 284
 285                 return factors;
 286         }
 287         return 1;
 288 }
 289
 290 void ncmul::append_factors(exvector & v, const ex & e) const
 291 {
 292         if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
 293                 (is_exactly_a<ncmul>(e))) {
 294                 for (size_t i=0; i<e.nops(); i++)
 295                         append_factors(v, e.op(i));
 296         } else
 297                 v.push_back(e);
 298 }
 299
 300 typedef std::vector<unsigned> unsignedvector;
 301 typedef std::vector<exvector> exvectorvector;
 302
 303 /** Perform automatic term rewriting rules in this class.  In the following
 304  *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
 305  *  stand for such expressions that contain a plain number.
 306  *  - ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) -> ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 307  *  - ncmul(x) -> x
 308  *  - ncmul() -> 1
 309  *  - ncmul(...,c1,...,c2,...) -> *(c1,c2,ncmul(...))  (pull out commutative elements)
 310  *  - ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))  (collect elements of same type)
 311  *  - ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)
 312  *
 313  *  @param level cut-off in recursive evaluation */
 314 ex ncmul::eval(int level) const
 315 {
 316         // The following additional rule would be nice, but produces a recursion,
 317         // which must be trapped by introducing a flag that the sub-ncmuls()
 318         // are already evaluated (maybe later...)
 319         //                  ncmul(x1,x2,...,X,y1,y2,...) ->
 320         //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
 321         //                      (X noncommutative_composite)
 322
 323         if ((level==1) && (flags & status_flags::evaluated)) {
 324                 return *this;
 325         }
 326
 327         exvector evaledseq=evalchildren(level);
 328
 329         // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 330         //     ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 331         size_t factors = 0;
 332         exvector::const_iterator cit = evaledseq.begin(), citend = evaledseq.end();
 333         while (cit != citend)
 334                 factors += count_factors(*cit++);
 335
 336         exvector assocseq;
 337         assocseq.reserve(factors);
 338         cit = evaledseq.begin();
 339         while (cit != citend)
 340                 append_factors(assocseq, *cit++);
 341
 342         // ncmul(x) -> x
 343         if (assocseq.size()==1) return *(seq.begin());
 344
 345         // ncmul() -> 1
 346         if (assocseq.empty()) return _ex1;
 347
 348         // determine return types
 349         unsignedvector rettypes;
 350         rettypes.reserve(assocseq.size());
 351         size_t i = 0;
 352         size_t count_commutative=0;
 353         size_t count_noncommutative=0;
 354         size_t count_noncommutative_composite=0;
 355         cit = assocseq.begin(); citend = assocseq.end();
 356         while (cit != citend) {
 357                 switch (rettypes[i] = cit->return_type()) {
 358                 case return_types::commutative:
 359                         count_commutative++;
 360                         break;
 361                 case return_types::noncommutative:
 362                         count_noncommutative++;
 363                         break;
 364                 case return_types::noncommutative_composite:
 365                         count_noncommutative_composite++;
 366                         break;
 367                 default:
 368                         throw(std::logic_error("ncmul::eval(): invalid return type"));
 369                 }
 370                 ++i; ++cit;
 371         }
 372         GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
 373
 374         // ncmul(...,c1,...,c2,...) ->
 375         //     *(c1,c2,ncmul(...)) (pull out commutative elements)
 376         if (count_commutative!=0) {
 377                 exvector commutativeseq;
 378                 commutativeseq.reserve(count_commutative+1);
 379                 exvector noncommutativeseq;
 380                 noncommutativeseq.reserve(assocseq.size()-count_commutative);
 381                 size_t num = assocseq.size();
 382                 for (size_t i=0; i<num; ++i) {
 383                         if (rettypes[i]==return_types::commutative)
 384                                 commutativeseq.push_back(assocseq[i]);
 385                         else
 386                                 noncommutativeseq.push_back(assocseq[i]);
 387                 }
 388                 commutativeseq.push_back((new ncmul(noncommutativeseq,1))->setflag(status_flags::dynallocated));
 389                 return (new mul(commutativeseq))->setflag(status_flags::dynallocated);
 390         }
 391
 392         // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 393         //     (collect elements of same type)
 394
 395         if (count_noncommutative_composite==0) {
 396                 // there are neither commutative nor noncommutative_composite
 397                 // elements in assocseq
 398                 GINAC_ASSERT(count_commutative==0);
 399
 400                 size_t assoc_num = assocseq.size();
 401                 exvectorvector evv;
 402                 std::vector<const basic*> rttinfos;
 403                 evv.reserve(assoc_num);
 404                 rttinfos.reserve(assoc_num);
 405
 406                 cit = assocseq.begin(), citend = assocseq.end();
 407                 while (cit != citend) {
 408                         const basic* ti = cit->return_type_tinfo();
 409                         size_t rtt_num = rttinfos.size();
 410                         // search type in vector of known types
 411                         for (i=0; i<rtt_num; ++i) {
 412                                 tinfo_t tinf = ti->tinfo();
 413                                 if (tinf == rttinfos[i]->tinfo()) {
 414                                         if (tinf == &clifford::tinfo_static) {
 415                                                 if (((clifford*)ti)->get_representation_label() == ((clifford*)rttinfos[i])->get_representation_label()) {
 416                                                         evv[i].push_back(*cit);
 417                                                         break;
 418                                                 }
 419                                         } else if (tinf == &color::tinfo_static) {
 420                                                 if (((color*)ti)->get_representation_label() == ((color*)rttinfos[i])->get_representation_label()) {
 421                                                         evv[i].push_back(*cit);
 422                                                         break;
 423                                                 }
 424                                         } else {
 425                                                 evv[i].push_back(*cit);
 426                                                 break;
 427                                         }
 428                                 }
 429                         }
 430                         if (i >= rtt_num) {
 431                                 // new type
 432                                 rttinfos.push_back(ti);
 433                                 evv.push_back(exvector());
 434                                 (evv.end()-1)->reserve(assoc_num);
 435                                 (evv.end()-1)->push_back(*cit);
 436                         }
 437                         ++cit;
 438                 }
 439
 440                 size_t evv_num = evv.size();
 441 #ifdef DO_GINAC_ASSERT
 442                 GINAC_ASSERT(evv_num == rttinfos.size());
 443                 GINAC_ASSERT(evv_num > 0);
 444                 size_t s=0;
 445                 for (i=0; i<evv_num; ++i)
 446                         s += evv[i].size();
 447                 GINAC_ASSERT(s == assoc_num);
 448 #endif // def DO_GINAC_ASSERT
 449
 450                 // if all elements are of same type, simplify the string
 451                 if (evv_num == 1) {
 452                         return evv[0][0].eval_ncmul(evv[0]);
 453                 }
 454
 455                 exvector splitseq;
 456                 splitseq.reserve(evv_num);
 457                 for (i=0; i<evv_num; ++i)
 458                         splitseq.push_back((new ncmul(evv[i]))->setflag(status_flags::dynallocated));
 459
 460                 return (new mul(splitseq))->setflag(status_flags::dynallocated);
 461         }
 462
 463         return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
 464                                                                                   status_flags::evaluated);
 465 }
 466
 467 ex ncmul::evalm() const
 468 {
 469         // Evaluate children first
 470         std::auto_ptr<exvector> s(new exvector);
 471         s->reserve(seq.size());
 472         exvector::const_iterator it = seq.begin(), itend = seq.end();
 473         while (it != itend) {
 474                 s->push_back(it->evalm());
 475                 it++;
 476         }
 477
 478         // If there are only matrices, simply multiply them
 479         it = s->begin(); itend = s->end();
 480         if (is_a<matrix>(*it)) {
 481                 matrix prod(ex_to<matrix>(*it));
 482                 it++;
 483                 while (it != itend) {
 484                         if (!is_a<matrix>(*it))
 485                                 goto no_matrix;
 486                         prod = prod.mul(ex_to<matrix>(*it));
 487                         it++;
 488                 }
 489                 return prod;
 490         }
 491
 492 no_matrix:
 493         return (new ncmul(s))->setflag(status_flags::dynallocated);
 494 }
 495
 496 ex ncmul::thiscontainer(const exvector & v) const
 497 {
 498         return (new ncmul(v))->setflag(status_flags::dynallocated);
 499 }
 500
 501 ex ncmul::thiscontainer(std::auto_ptr<exvector> vp) const
 502 {
 503         return (new ncmul(vp))->setflag(status_flags::dynallocated);
 504 }
 505
 506 ex ncmul::conjugate() const
 507 {
 508         if (return_type() != return_types::noncommutative) {
 509                 return exprseq::conjugate();
 510         }
 511
 512         if (return_type_tinfo()->tinfo() != &clifford::tinfo_static) {
 513                 return exprseq::conjugate();
 514         }
 515
 516         exvector ev;
 517         ev.reserve(nops());
 518         for (const_iterator i=end(); i!=begin();) {
 519                 --i;
 520                 ev.push_back(i->conjugate());
 521         }
 522         return (new ncmul(ev, true))->setflag(status_flags::dynallocated).eval();
 523 }
 524
 525 // protected
 526
 527 /** Implementation of ex::diff() for a non-commutative product. It applies
 528  *  the product rule.
 529  *  @see ex::diff */
 530 ex ncmul::derivative(const symbol & s) const
 531 {
 532         size_t num = seq.size();
 533         exvector addseq;
 534         addseq.reserve(num);
 535
 536         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 537         exvector ncmulseq = seq;
 538         for (size_t i=0; i<num; ++i) {
 539                 ex e = seq[i].diff(s);
 540                 e.swap(ncmulseq[i]);
 541                 addseq.push_back((new ncmul(ncmulseq))->setflag(status_flags::dynallocated));
 542                 e.swap(ncmulseq[i]);
 543         }
 544         return (new add(addseq))->setflag(status_flags::dynallocated);
 545 }
 546
 547 int ncmul::compare_same_type(const basic & other) const
 548 {
 549         return inherited::compare_same_type(other);
 550 }
 551
 552 unsigned ncmul::return_type() const
 553 {
 554         if (seq.empty())
 555                 return return_types::commutative;
 556
 557         bool all_commutative = true;
 558         exvector::const_iterator noncommutative_element; // point to first found nc element
 559
 560         exvector::const_iterator i = seq.begin(), end = seq.end();
 561         while (i != end) {
 562                 unsigned rt = i->return_type();
 563                 if (rt == return_types::noncommutative_composite)
 564                         return rt; // one ncc -> mul also ncc
 565                 if ((rt == return_types::noncommutative) && (all_commutative)) {
 566                         // first nc element found, remember position
 567                         noncommutative_element = i;
 568                         all_commutative = false;
 569                 }
 570                 if ((rt == return_types::noncommutative) && (!all_commutative)) {
 571                         // another nc element found, compare type_infos
 572                         if (noncommutative_element->return_type_tinfo()->tinfo() == &clifford::tinfo_static) {
 573                                 if (i->return_type_tinfo()->tinfo() != &clifford::tinfo_static ||
 574                                     ((clifford*)(noncommutative_element->return_type_tinfo()))->get_representation_label() !=
 575                                     ((clifford*)(i->return_type_tinfo()))->get_representation_label()) {
 576                                         // diffent types -> mul is ncc
 577                                         return return_types::noncommutative_composite;
 578                                 }
 579                         } else if (noncommutative_element->return_type_tinfo()->tinfo() == &color::tinfo_static) {
 580                                 if (i->return_type_tinfo()->tinfo() != &color::tinfo_static ||
 581                                     ((color*)(noncommutative_element->return_type_tinfo()))->get_representation_label() !=
 582                                     ((color*)(i->return_type_tinfo()))->get_representation_label()) {
 583                                         // diffent types -> mul is ncc
 584                                         return return_types::noncommutative_composite;
 585                                 }
 586                         } else if (noncommutative_element->return_type_tinfo()->tinfo() != i->return_type_tinfo()->tinfo()) {
 587                                         return return_types::noncommutative_composite;
 588                         }
 589                 }
 590                 ++i;
 591         }
 592         // all factors checked
 593         GINAC_ASSERT(!all_commutative); // not all factors should commutate, because this is a ncmul();
 594         return all_commutative ? return_types::commutative : return_types::noncommutative;
 595 }
 596
 597 const basic* ncmul::return_type_tinfo() const
 598 {
 599         if (seq.empty())
 600                 return this;
 601
 602         // return type_info of first noncommutative element
 603         exvector::const_iterator i = seq.begin(), end = seq.end();
 604         while (i != end) {
 605                 if (i->return_type() == return_types::noncommutative)
 606                         return i->return_type_tinfo();
 607                 ++i;
 608         }
 609
 610         // no noncommutative element found, should not happen
 611         return this;
 612 }
 613
 614 //////////
 615 // new virtual functions which can be overridden by derived classes
 616 //////////
 617
 618 // none
 619
 620 //////////
 621 // non-virtual functions in this class
 622 //////////
 623
 624 std::auto_ptr<exvector> ncmul::expandchildren(unsigned options) const
 625 {
 626         const_iterator cit = this->seq.begin(), end = this->seq.end();
 627         while (cit != end) {
 628                 const ex & expanded_ex = cit->expand(options);
 629                 if (!are_ex_trivially_equal(*cit, expanded_ex)) {
 630
 631                         // copy first part of seq which hasn't changed
 632                         std::auto_ptr<exvector> s(new exvector(this->seq.begin(), cit));
 633                         reserve(*s, this->seq.size());
 634
 635                         // insert changed element
 636                         s->push_back(expanded_ex);
 637                         ++cit;
 638
 639                         // copy rest
 640                         while (cit != end) {
 641                                 s->push_back(cit->expand(options));
 642                                 ++cit;
 643                         }
 644
 645                         return s;
 646                 }
 647
 648                 ++cit;
 649         }
 650
 651         return std::auto_ptr<exvector>(0); // nothing has changed
 652 }
 653
 654 const exvector & ncmul::get_factors() const
 655 {
 656         return seq;
 657 }
 658
 659 //////////
 660 // friend functions
 661 //////////
 662
 663 ex reeval_ncmul(const exvector & v)
 664 {
 665         return (new ncmul(v))->setflag(status_flags::dynallocated);
 666 }
 667
 668 ex hold_ncmul(const exvector & v)
 669 {
 670         if (v.empty())
 671                 return _ex1;
 672         else if (v.size() == 1)
 673                 return v[0];
 674         else
 675                 return (new ncmul(v))->setflag(status_flags::dynallocated |
 676                                                status_flags::evaluated);
 677 }
 678
 679 } // namespace GiNaC