ginac/indexed.cpp

   1 /** @file indexed.cpp
   2  *
   3  *  Implementation of GiNaC's indexed 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 <iostream>
  24 #include <sstream>
  25 #include <stdexcept>
  26
  27 #include "indexed.h"
  28 #include "idx.h"
  29 #include "add.h"
  30 #include "mul.h"
  31 #include "ncmul.h"
  32 #include "power.h"
  33 #include "relational.h"
  34 #include "symmetry.h"
  35 #include "operators.h"
  36 #include "lst.h"
  37 #include "archive.h"
  38 #include "utils.h"
  39
  40 namespace GiNaC {
  41
  42 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(indexed, exprseq,
  43   print_func<print_context>(&indexed::do_print).
  44   print_func<print_latex>(&indexed::do_print_latex).
  45   print_func<print_tree>(&indexed::do_print_tree))
  46
  47 //////////
  48 // default constructor
  49 //////////
  50
  51 indexed::indexed() : symtree(not_symmetric())
  52 {
  53         tinfo_key = TINFO_indexed;
  54 }
  55
  56 //////////
  57 // other constructors
  58 //////////
  59
  60 indexed::indexed(const ex & b) : inherited(b), symtree(not_symmetric())
  61 {
  62         tinfo_key = TINFO_indexed;
  63         validate();
  64 }
  65
  66 indexed::indexed(const ex & b, const ex & i1) : inherited(b, i1), symtree(not_symmetric())
  67 {
  68         tinfo_key = TINFO_indexed;
  69         validate();
  70 }
  71
  72 indexed::indexed(const ex & b, const ex & i1, const ex & i2) : inherited(b, i1, i2), symtree(not_symmetric())
  73 {
  74         tinfo_key = TINFO_indexed;
  75         validate();
  76 }
  77
  78 indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symtree(not_symmetric())
  79 {
  80         tinfo_key = TINFO_indexed;
  81         validate();
  82 }
  83
  84 indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symtree(not_symmetric())
  85 {
  86         tinfo_key = TINFO_indexed;
  87         validate();
  88 }
  89
  90 indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2) : inherited(b, i1, i2), symtree(symm)
  91 {
  92         tinfo_key = TINFO_indexed;
  93         validate();
  94 }
  95
  96 indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symtree(symm)
  97 {
  98         tinfo_key = TINFO_indexed;
  99         validate();
 100 }
 101
 102 indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symtree(symm)
 103 {
 104         tinfo_key = TINFO_indexed;
 105         validate();
 106 }
 107
 108 indexed::indexed(const ex & b, const exvector & v) : inherited(b), symtree(not_symmetric())
 109 {
 110         seq.insert(seq.end(), v.begin(), v.end());
 111         tinfo_key = TINFO_indexed;
 112         validate();
 113 }
 114
 115 indexed::indexed(const ex & b, const symmetry & symm, const exvector & v) : inherited(b), symtree(symm)
 116 {
 117         seq.insert(seq.end(), v.begin(), v.end());
 118         tinfo_key = TINFO_indexed;
 119         validate();
 120 }
 121
 122 indexed::indexed(const symmetry & symm, const exprseq & es) : inherited(es), symtree(symm)
 123 {
 124         tinfo_key = TINFO_indexed;
 125 }
 126
 127 indexed::indexed(const symmetry & symm, const exvector & v, bool discardable) : inherited(v, discardable), symtree(symm)
 128 {
 129         tinfo_key = TINFO_indexed;
 130 }
 131
 132 indexed::indexed(const symmetry & symm, std::auto_ptr<exvector> vp) : inherited(vp), symtree(symm)
 133 {
 134         tinfo_key = TINFO_indexed;
 135 }
 136
 137 //////////
 138 // archiving
 139 //////////
 140
 141 indexed::indexed(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
 142 {
 143         if (!n.find_ex("symmetry", symtree, sym_lst)) {
 144                 // GiNaC versions <= 0.9.0 had an unsigned "symmetry" property
 145                 unsigned symm = 0;
 146                 n.find_unsigned("symmetry", symm);
 147                 switch (symm) {
 148                         case 1:
 149                                 symtree = sy_symm();
 150                                 break;
 151                         case 2:
 152                                 symtree = sy_anti();
 153                                 break;
 154                         default:
 155                                 symtree = not_symmetric();
 156                                 break;
 157                 }
 158                 const_cast<symmetry &>(ex_to<symmetry>(symtree)).validate(seq.size() - 1);
 159         }
 160 }
 161
 162 void indexed::archive(archive_node &n) const
 163 {
 164         inherited::archive(n);
 165         n.add_ex("symmetry", symtree);
 166 }
 167
 168 DEFAULT_UNARCHIVE(indexed)
 169
 170 //////////
 171 // functions overriding virtual functions from base classes
 172 //////////
 173
 174 void indexed::printindices(const print_context & c, unsigned level) const
 175 {
 176         if (seq.size() > 1) {
 177
 178                 exvector::const_iterator it=seq.begin() + 1, itend = seq.end();
 179
 180                 if (is_a<print_latex>(c)) {
 181
 182                         // TeX output: group by variance
 183                         bool first = true;
 184                         bool covariant = true;
 185
 186                         while (it != itend) {
 187                                 bool cur_covariant = (is_a<varidx>(*it) ? ex_to<varidx>(*it).is_covariant() : true);
 188                                 if (first || cur_covariant != covariant) { // Variance changed
 189                                         // The empty {} prevents indices from ending up on top of each other
 190                                         if (!first)
 191                                                 c.s << "}{}";
 192                                         covariant = cur_covariant;
 193                                         if (covariant)
 194                                                 c.s << "_{";
 195                                         else
 196                                                 c.s << "^{";
 197                                 }
 198                                 it->print(c, level);
 199                                 c.s << " ";
 200                                 first = false;
 201                                 it++;
 202                         }
 203                         c.s << "}";
 204
 205                 } else {
 206
 207                         // Ordinary output
 208                         while (it != itend) {
 209                                 it->print(c, level);
 210                                 it++;
 211                         }
 212                 }
 213         }
 214 }
 215
 216 void indexed::print_indexed(const print_context & c, const char *openbrace, const char *closebrace, unsigned level) const
 217 {
 218         if (precedence() <= level)
 219                 c.s << openbrace << '(';
 220         c.s << openbrace;
 221         seq[0].print(c, precedence());
 222         c.s << closebrace;
 223         printindices(c, level);
 224         if (precedence() <= level)
 225                 c.s << ')' << closebrace;
 226 }
 227
 228 void indexed::do_print(const print_context & c, unsigned level) const
 229 {
 230         print_indexed(c, "", "", level);
 231 }
 232
 233 void indexed::do_print_latex(const print_latex & c, unsigned level) const
 234 {
 235         print_indexed(c, "{", "}", level);
 236 }
 237
 238 void indexed::do_print_tree(const print_tree & c, unsigned level) const
 239 {
 240         c.s << std::string(level, ' ') << class_name() << " @" << this
 241             << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 242             << ", " << seq.size()-1 << " indices"
 243             << ", symmetry=" << symtree << std::endl;
 244         seq[0].print(c, level + c.delta_indent);
 245         printindices(c, level + c.delta_indent);
 246 }
 247
 248 bool indexed::info(unsigned inf) const
 249 {
 250         if (inf == info_flags::indexed) return true;
 251         if (inf == info_flags::has_indices) return seq.size() > 1;
 252         return inherited::info(inf);
 253 }
 254
 255 struct idx_is_not : public std::binary_function<ex, unsigned, bool> {
 256         bool operator() (const ex & e, unsigned inf) const {
 257                 return !(ex_to<idx>(e).get_value().info(inf));
 258         }
 259 };
 260
 261 bool indexed::all_index_values_are(unsigned inf) const
 262 {
 263         // No indices? Then no property can be fulfilled
 264         if (seq.size() < 2)
 265                 return false;
 266
 267         // Check all indices
 268         return find_if(seq.begin() + 1, seq.end(), bind2nd(idx_is_not(), inf)) == seq.end();
 269 }
 270
 271 int indexed::compare_same_type(const basic & other) const
 272 {
 273         GINAC_ASSERT(is_a<indexed>(other));
 274         return inherited::compare_same_type(other);
 275 }
 276
 277 ex indexed::eval(int level) const
 278 {
 279         // First evaluate children, then we will end up here again
 280         if (level > 1)
 281                 return indexed(ex_to<symmetry>(symtree), evalchildren(level));
 282
 283         const ex &base = seq[0];
 284
 285         // If the base object is 0, the whole object is 0
 286         if (base.is_zero())
 287                 return _ex0;
 288
 289         // If the base object is a product, pull out the numeric factor
 290         if (is_exactly_a<mul>(base) && is_exactly_a<numeric>(base.op(base.nops() - 1))) {
 291                 exvector v(seq);
 292                 ex f = ex_to<numeric>(base.op(base.nops() - 1));
 293                 v[0] = seq[0] / f;
 294                 return f * thiscontainer(v);
 295         }
 296
 297         // Canonicalize indices according to the symmetry properties
 298         if (seq.size() > 2) {
 299                 exvector v = seq;
 300                 GINAC_ASSERT(is_exactly_a<symmetry>(symtree));
 301                 int sig = canonicalize(v.begin() + 1, ex_to<symmetry>(symtree));
 302                 if (sig != INT_MAX) {
 303                         // Something has changed while sorting indices, more evaluations later
 304                         if (sig == 0)
 305                                 return _ex0;
 306                         return ex(sig) * thiscontainer(v);
 307                 }
 308         }
 309
 310         // Let the class of the base object perform additional evaluations
 311         return ex_to<basic>(base).eval_indexed(*this);
 312 }
 313
 314 ex indexed::thiscontainer(const exvector & v) const
 315 {
 316         return indexed(ex_to<symmetry>(symtree), v);
 317 }
 318
 319 ex indexed::thiscontainer(std::auto_ptr<exvector> vp) const
 320 {
 321         return indexed(ex_to<symmetry>(symtree), vp);
 322 }
 323
 324 ex indexed::expand(unsigned options) const
 325 {
 326         GINAC_ASSERT(seq.size() > 0);
 327
 328         if (options & expand_options::expand_indexed) {
 329                 ex newbase = seq[0].expand(options);
 330                 if (is_exactly_a<add>(newbase)) {
 331                         ex sum = _ex0;
 332                         for (size_t i=0; i<newbase.nops(); i++) {
 333                                 exvector s = seq;
 334                                 s[0] = newbase.op(i);
 335                                 sum += thiscontainer(s).expand(options);
 336                         }
 337                         return sum;
 338                 }
 339                 if (!are_ex_trivially_equal(newbase, seq[0])) {
 340                         exvector s = seq;
 341                         s[0] = newbase;
 342                         return ex_to<indexed>(thiscontainer(s)).inherited::expand(options);
 343                 }
 344         }
 345         return inherited::expand(options);
 346 }
 347
 348 //////////
 349 // virtual functions which can be overridden by derived classes
 350 //////////
 351
 352 // none
 353
 354 //////////
 355 // non-virtual functions in this class
 356 //////////
 357
 358 /** Check whether all indices are of class idx and validate the symmetry
 359  *  tree. This function is used internally to make sure that all constructed
 360  *  indexed objects really carry indices and not some other classes. */
 361 void indexed::validate() const
 362 {
 363         GINAC_ASSERT(seq.size() > 0);
 364         exvector::const_iterator it = seq.begin() + 1, itend = seq.end();
 365         while (it != itend) {
 366                 if (!is_a<idx>(*it))
 367                         throw(std::invalid_argument("indices of indexed object must be of type idx"));
 368                 it++;
 369         }
 370
 371         if (!symtree.is_zero()) {
 372                 if (!is_exactly_a<symmetry>(symtree))
 373                         throw(std::invalid_argument("symmetry of indexed object must be of type symmetry"));
 374                 const_cast<symmetry &>(ex_to<symmetry>(symtree)).validate(seq.size() - 1);
 375         }
 376 }
 377
 378 /** Implementation of ex::diff() for an indexed object always returns 0.
 379  *
 380  *  @see ex::diff */
 381 ex indexed::derivative(const symbol & s) const
 382 {
 383         return _ex0;
 384 }
 385
 386 //////////
 387 // global functions
 388 //////////
 389
 390 struct idx_is_equal_ignore_dim : public std::binary_function<ex, ex, bool> {
 391         bool operator() (const ex &lh, const ex &rh) const
 392         {
 393                 if (lh.is_equal(rh))
 394                         return true;
 395                 else
 396                         try {
 397                                 // Replacing the dimension might cause an error (e.g. with
 398                                 // index classes that only work in a fixed number of dimensions)
 399                                 return lh.is_equal(ex_to<idx>(rh).replace_dim(ex_to<idx>(lh).get_dim()));
 400                         } catch (...) {
 401                                 return false;
 402                         }
 403         }
 404 };
 405
 406 /** Check whether two sorted index vectors are consistent (i.e. equal). */
 407 static bool indices_consistent(const exvector & v1, const exvector & v2)
 408 {
 409         // Number of indices must be the same
 410         if (v1.size() != v2.size())
 411                 return false;
 412
 413         return equal(v1.begin(), v1.end(), v2.begin(), idx_is_equal_ignore_dim());
 414 }
 415
 416 exvector indexed::get_indices() const
 417 {
 418         GINAC_ASSERT(seq.size() >= 1);
 419         return exvector(seq.begin() + 1, seq.end());
 420 }
 421
 422 exvector indexed::get_dummy_indices() const
 423 {
 424         exvector free_indices, dummy_indices;
 425         find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices);
 426         return dummy_indices;
 427 }
 428
 429 exvector indexed::get_dummy_indices(const indexed & other) const
 430 {
 431         exvector indices = get_free_indices();
 432         exvector other_indices = other.get_free_indices();
 433         indices.insert(indices.end(), other_indices.begin(), other_indices.end());
 434         exvector dummy_indices;
 435         find_dummy_indices(indices, dummy_indices);
 436         return dummy_indices;
 437 }
 438
 439 bool indexed::has_dummy_index_for(const ex & i) const
 440 {
 441         exvector::const_iterator it = seq.begin() + 1, itend = seq.end();
 442         while (it != itend) {
 443                 if (is_dummy_pair(*it, i))
 444                         return true;
 445                 it++;
 446         }
 447         return false;
 448 }
 449
 450 exvector indexed::get_free_indices() const
 451 {
 452         exvector free_indices, dummy_indices;
 453         find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices);
 454         return free_indices;
 455 }
 456
 457 exvector add::get_free_indices() const
 458 {
 459         exvector free_indices;
 460         for (size_t i=0; i<nops(); i++) {
 461                 if (i == 0)
 462                         free_indices = op(i).get_free_indices();
 463                 else {
 464                         exvector free_indices_of_term = op(i).get_free_indices();
 465                         if (!indices_consistent(free_indices, free_indices_of_term))
 466                                 throw (std::runtime_error("add::get_free_indices: inconsistent indices in sum"));
 467                 }
 468         }
 469         return free_indices;
 470 }
 471
 472 exvector mul::get_free_indices() const
 473 {
 474         // Concatenate free indices of all factors
 475         exvector un;
 476         for (size_t i=0; i<nops(); i++) {
 477                 exvector free_indices_of_factor = op(i).get_free_indices();
 478                 un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
 479         }
 480
 481         // And remove the dummy indices
 482         exvector free_indices, dummy_indices;
 483         find_free_and_dummy(un, free_indices, dummy_indices);
 484         return free_indices;
 485 }
 486
 487 exvector ncmul::get_free_indices() const
 488 {
 489         // Concatenate free indices of all factors
 490         exvector un;
 491         for (size_t i=0; i<nops(); i++) {
 492                 exvector free_indices_of_factor = op(i).get_free_indices();
 493                 un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
 494         }
 495
 496         // And remove the dummy indices
 497         exvector free_indices, dummy_indices;
 498         find_free_and_dummy(un, free_indices, dummy_indices);
 499         return free_indices;
 500 }
 501
 502 struct is_summation_idx : public std::unary_function<ex, bool> {
 503         bool operator()(const ex & e)
 504         {
 505                 return is_dummy_pair(e, e);
 506         }
 507 };
 508
 509 exvector power::get_free_indices() const
 510 {
 511         // Get free indices of basis
 512         exvector basis_indices = basis.get_free_indices();
 513
 514         if (exponent.info(info_flags::even)) {
 515                 // If the exponent is an even number, then any "free" index that
 516                 // forms a dummy pair with itself is actually a summation index
 517                 exvector really_free;
 518                 std::remove_copy_if(basis_indices.begin(), basis_indices.end(),
 519                                     std::back_inserter(really_free), is_summation_idx());
 520                 return really_free;
 521         } else
 522                 return basis_indices;
 523 }
 524
 525 /** Rename dummy indices in an expression.
 526  *
 527  *  @param e Expression to work on
 528  *  @param local_dummy_indices The set of dummy indices that appear in the
 529  *    expression "e"
 530  *  @param global_dummy_indices The set of dummy indices that have appeared
 531  *    before and which we would like to use in "e", too. This gets updated
 532  *    by the function */
 533 static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, exvector & local_dummy_indices)
 534 {
 535         size_t global_size = global_dummy_indices.size(),
 536                local_size = local_dummy_indices.size();
 537
 538         // Any local dummy indices at all?
 539         if (local_size == 0)
 540                 return e;
 541
 542         if (global_size < local_size) {
 543
 544                 // More local indices than we encountered before, add the new ones
 545                 // to the global set
 546                 size_t old_global_size = global_size;
 547                 int remaining = local_size - global_size;
 548                 exvector::const_iterator it = local_dummy_indices.begin(), itend = local_dummy_indices.end();
 549                 while (it != itend && remaining > 0) {
 550                         if (find_if(global_dummy_indices.begin(), global_dummy_indices.end(), bind2nd(op0_is_equal(), *it)) == global_dummy_indices.end()) {
 551                                 global_dummy_indices.push_back(*it);
 552                                 global_size++;
 553                                 remaining--;
 554                         }
 555                         it++;
 556                 }
 557
 558                 // If this is the first set of local indices, do nothing
 559                 if (old_global_size == 0)
 560                         return e;
 561         }
 562         GINAC_ASSERT(local_size <= global_size);
 563
 564         // Construct vectors of index symbols
 565         exvector local_syms, global_syms;
 566         local_syms.reserve(local_size);
 567         global_syms.reserve(local_size);
 568         for (size_t i=0; i<local_size; i++)
 569                 local_syms.push_back(local_dummy_indices[i].op(0));
 570         shaker_sort(local_syms.begin(), local_syms.end(), ex_is_less(), ex_swap());
 571         for (size_t i=0; i<local_size; i++) // don't use more global symbols than necessary
 572                 global_syms.push_back(global_dummy_indices[i].op(0));
 573         shaker_sort(global_syms.begin(), global_syms.end(), ex_is_less(), ex_swap());
 574
 575         // Remove common indices
 576         exvector local_uniq, global_uniq;
 577         set_difference(local_syms.begin(), local_syms.end(), global_syms.begin(), global_syms.end(), std::back_insert_iterator<exvector>(local_uniq), ex_is_less());
 578         set_difference(global_syms.begin(), global_syms.end(), local_syms.begin(), local_syms.end(), std::back_insert_iterator<exvector>(global_uniq), ex_is_less());
 579
 580         // Replace remaining non-common local index symbols by global ones
 581         if (local_uniq.empty())
 582                 return e;
 583         else {
 584                 while (global_uniq.size() > local_uniq.size())
 585                         global_uniq.pop_back();
 586                 return e.subs(lst(local_uniq.begin(), local_uniq.end()), lst(global_uniq.begin(), global_uniq.end()), subs_options::no_pattern);
 587         }
 588 }
 589
 590 /** Given a set of indices, extract those of class varidx. */
 591 static void find_variant_indices(const exvector & v, exvector & variant_indices)
 592 {
 593         exvector::const_iterator it1, itend;
 594         for (it1 = v.begin(), itend = v.end(); it1 != itend; ++it1) {
 595                 if (is_exactly_a<varidx>(*it1))
 596                         variant_indices.push_back(*it1);
 597         }
 598 }
 599
 600 /** Raise/lower dummy indices in a single indexed objects to canonicalize their
 601  *  variance.
 602  *
 603  *  @param e Object to work on
 604  *  @param variant_dummy_indices The set of indices that might need repositioning (will be changed by this function)
 605  *  @param moved_indices The set of indices that have been repositioned (will be changed by this function)
 606  *  @return true if 'e' was changed */
 607 bool reposition_dummy_indices(ex & e, exvector & variant_dummy_indices, exvector & moved_indices)
 608 {
 609         bool something_changed = false;
 610
 611         // If a dummy index is encountered for the first time in the
 612         // product, pull it up, otherwise, pull it down
 613         exvector::const_iterator it2, it2start, it2end;
 614         for (it2start = ex_to<indexed>(e).seq.begin(), it2end = ex_to<indexed>(e).seq.end(), it2 = it2start + 1; it2 != it2end; ++it2) {
 615                 if (!is_exactly_a<varidx>(*it2))
 616                         continue;
 617
 618                 exvector::iterator vit, vitend;
 619                 for (vit = variant_dummy_indices.begin(), vitend = variant_dummy_indices.end(); vit != vitend; ++vit) {
 620                         if (it2->op(0).is_equal(vit->op(0))) {
 621                                 if (ex_to<varidx>(*it2).is_covariant()) {
 622                                         e = e.subs(lst(
 623                                                 *it2 == ex_to<varidx>(*it2).toggle_variance(),
 624                                                 ex_to<varidx>(*it2).toggle_variance() == *it2
 625                                         ), subs_options::no_pattern);
 626                                         something_changed = true;
 627                                         it2 = ex_to<indexed>(e).seq.begin() + (it2 - it2start);
 628                                         it2start = ex_to<indexed>(e).seq.begin();
 629                                         it2end = ex_to<indexed>(e).seq.end();
 630                                 }
 631                                 moved_indices.push_back(*vit);
 632                                 variant_dummy_indices.erase(vit);
 633                                 goto next_index;
 634                         }
 635                 }
 636
 637                 for (vit = moved_indices.begin(), vitend = moved_indices.end(); vit != vitend; ++vit) {
 638                         if (it2->op(0).is_equal(vit->op(0))) {
 639                                 if (ex_to<varidx>(*it2).is_contravariant()) {
 640                                         e = e.subs(*it2 == ex_to<varidx>(*it2).toggle_variance(), subs_options::no_pattern);
 641                                         something_changed = true;
 642                                         it2 = ex_to<indexed>(e).seq.begin() + (it2 - it2start);
 643                                         it2start = ex_to<indexed>(e).seq.begin();
 644                                         it2end = ex_to<indexed>(e).seq.end();
 645                                 }
 646                                 goto next_index;
 647                         }
 648                 }
 649
 650 next_index: ;
 651         }
 652
 653         return something_changed;
 654 }
 655
 656 /* Ordering that only compares the base expressions of indexed objects. */
 657 struct ex_base_is_less : public std::binary_function<ex, ex, bool> {
 658         bool operator() (const ex &lh, const ex &rh) const
 659         {
 660                 return (is_a<indexed>(lh) ? lh.op(0) : lh).compare(is_a<indexed>(rh) ? rh.op(0) : rh) < 0;
 661         }
 662 };
 663
 664 /** Simplify product of indexed expressions (commutative, noncommutative and
 665  *  simple squares), return list of free indices. */
 666 ex simplify_indexed_product(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp)
 667 {
 668         // Remember whether the product was commutative or noncommutative
 669         // (because we chop it into factors and need to reassemble later)
 670         bool non_commutative = is_exactly_a<ncmul>(e);
 671
 672         // Collect factors in an exvector, store squares twice
 673         exvector v;
 674         v.reserve(e.nops() * 2);
 675
 676         if (is_exactly_a<power>(e)) {
 677                 // We only get called for simple squares, split a^2 -> a*a
 678                 GINAC_ASSERT(e.op(1).is_equal(_ex2));
 679                 v.push_back(e.op(0));
 680                 v.push_back(e.op(0));
 681         } else {
 682                 for (size_t i=0; i<e.nops(); i++) {
 683                         ex f = e.op(i);
 684                         if (is_exactly_a<power>(f) && f.op(1).is_equal(_ex2)) {
 685                                 v.push_back(f.op(0));
 686                     v.push_back(f.op(0));
 687                         } else if (is_exactly_a<ncmul>(f)) {
 688                                 // Noncommutative factor found, split it as well
 689                                 non_commutative = true; // everything becomes noncommutative, ncmul will sort out the commutative factors later
 690                                 for (size_t j=0; j<f.nops(); j++)
 691                                         v.push_back(f.op(j));
 692                         } else
 693                                 v.push_back(f);
 694                 }
 695         }
 696
 697         // Perform contractions
 698         bool something_changed = false;
 699         GINAC_ASSERT(v.size() > 1);
 700         exvector::iterator it1, itend = v.end(), next_to_last = itend - 1;
 701         for (it1 = v.begin(); it1 != next_to_last; it1++) {
 702
 703 try_again:
 704                 if (!is_a<indexed>(*it1))
 705                         continue;
 706
 707                 bool first_noncommutative = (it1->return_type() != return_types::commutative);
 708
 709                 // Indexed factor found, get free indices and look for contraction
 710                 // candidates
 711                 exvector free1, dummy1;
 712                 find_free_and_dummy(ex_to<indexed>(*it1).seq.begin() + 1, ex_to<indexed>(*it1).seq.end(), free1, dummy1);
 713
 714                 exvector::iterator it2;
 715                 for (it2 = it1 + 1; it2 != itend; it2++) {
 716
 717                         if (!is_a<indexed>(*it2))
 718                                 continue;
 719
 720                         bool second_noncommutative = (it2->return_type() != return_types::commutative);
 721
 722                         // Find free indices of second factor and merge them with free
 723                         // indices of first factor
 724                         exvector un;
 725                         find_free_and_dummy(ex_to<indexed>(*it2).seq.begin() + 1, ex_to<indexed>(*it2).seq.end(), un, dummy1);
 726                         un.insert(un.end(), free1.begin(), free1.end());
 727
 728                         // Check whether the two factors share dummy indices
 729                         exvector free, dummy;
 730                         find_free_and_dummy(un, free, dummy);
 731                         size_t num_dummies = dummy.size();
 732                         if (num_dummies == 0)
 733                                 continue;
 734
 735                         // At least one dummy index, is it a defined scalar product?
 736                         bool contracted = false;
 737                         if (free.empty()) {
 738
 739                                 // Find minimal dimension of all indices of both factors
 740                                 exvector::const_iterator dit = ex_to<indexed>(*it1).seq.begin() + 1, ditend = ex_to<indexed>(*it1).seq.end();
 741                                 ex dim = ex_to<idx>(*dit).get_dim();
 742                                 ++dit;
 743                                 for (; dit != ditend; ++dit) {
 744                                         dim = minimal_dim(dim, ex_to<idx>(*dit).get_dim());
 745                                 }
 746                                 dit = ex_to<indexed>(*it2).seq.begin() + 1;
 747                                 ditend = ex_to<indexed>(*it2).seq.end();
 748                                 for (; dit != ditend; ++dit) {
 749                                         dim = minimal_dim(dim, ex_to<idx>(*dit).get_dim());
 750                                 }
 751
 752                                 // User-defined scalar product?
 753                                 if (sp.is_defined(*it1, *it2, dim)) {
 754
 755                                         // Yes, substitute it
 756                                         *it1 = sp.evaluate(*it1, *it2, dim);
 757                                         *it2 = _ex1;
 758                                         goto contraction_done;
 759                                 }
 760                         }
 761
 762                         // Try to contract the first one with the second one
 763                         contracted = ex_to<basic>(it1->op(0)).contract_with(it1, it2, v);
 764                         if (!contracted) {
 765
 766                                 // That didn't work; maybe the second object knows how to
 767                                 // contract itself with the first one
 768                                 contracted = ex_to<basic>(it2->op(0)).contract_with(it2, it1, v);
 769                         }
 770                         if (contracted) {
 771 contraction_done:
 772                                 if (first_noncommutative || second_noncommutative
 773                                  || is_exactly_a<add>(*it1) || is_exactly_a<add>(*it2)
 774                                  || is_exactly_a<mul>(*it1) || is_exactly_a<mul>(*it2)
 775                                  || is_exactly_a<ncmul>(*it1) || is_exactly_a<ncmul>(*it2)) {
 776
 777                                         // One of the factors became a sum or product:
 778                                         // re-expand expression and run again
 779                                         // Non-commutative products are always re-expanded to give
 780                                         // eval_ncmul() the chance to re-order and canonicalize
 781                                         // the product
 782                                         ex r = (non_commutative ? ex(ncmul(v, true)) : ex(mul(v)));
 783                                         return simplify_indexed(r, free_indices, dummy_indices, sp);
 784                                 }
 785
 786                                 // Both objects may have new indices now or they might
 787                                 // even not be indexed objects any more, so we have to
 788                                 // start over
 789                                 something_changed = true;
 790                                 goto try_again;
 791                         }
 792                 }
 793         }
 794
 795         // Find free indices (concatenate them all and call find_free_and_dummy())
 796         // and all dummy indices that appear
 797         exvector un, individual_dummy_indices;
 798         for (it1 = v.begin(), itend = v.end(); it1 != itend; ++it1) {
 799                 exvector free_indices_of_factor;
 800                 if (is_a<indexed>(*it1)) {
 801                         exvector dummy_indices_of_factor;
 802                         find_free_and_dummy(ex_to<indexed>(*it1).seq.begin() + 1, ex_to<indexed>(*it1).seq.end(), free_indices_of_factor, dummy_indices_of_factor);
 803                         individual_dummy_indices.insert(individual_dummy_indices.end(), dummy_indices_of_factor.begin(), dummy_indices_of_factor.end());
 804                 } else
 805                         free_indices_of_factor = it1->get_free_indices();
 806                 un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
 807         }
 808         exvector local_dummy_indices;
 809         find_free_and_dummy(un, free_indices, local_dummy_indices);
 810         local_dummy_indices.insert(local_dummy_indices.end(), individual_dummy_indices.begin(), individual_dummy_indices.end());
 811
 812         // Filter out the dummy indices with variance
 813         exvector variant_dummy_indices;
 814         find_variant_indices(local_dummy_indices, variant_dummy_indices);
 815
 816         // Any indices with variance present at all?
 817         if (!variant_dummy_indices.empty()) {
 818
 819                 // Yes, bring the product into a canonical order that only depends on
 820                 // the base expressions of indexed objects
 821                 if (!non_commutative)
 822                         std::sort(v.begin(), v.end(), ex_base_is_less());
 823
 824                 exvector moved_indices;
 825
 826                 // Iterate over all indexed objects in the product
 827                 for (it1 = v.begin(), itend = v.end(); it1 != itend; ++it1) {
 828                         if (!is_a<indexed>(*it1))
 829                                 continue;
 830
 831                         if (reposition_dummy_indices(*it1, variant_dummy_indices, moved_indices))
 832                                 something_changed = true;
 833                 }
 834         }
 835
 836         ex r;
 837         if (something_changed)
 838                 r = non_commutative ? ex(ncmul(v, true)) : ex(mul(v));
 839         else
 840                 r = e;
 841
 842         // The result should be symmetric with respect to exchange of dummy
 843         // indices, so if the symmetrization vanishes, the whole expression is
 844         // zero. This detects things like eps.i.j.k * p.j * p.k = 0.
 845         if (local_dummy_indices.size() >= 2) {
 846                 exvector dummy_syms;
 847                 dummy_syms.reserve(local_dummy_indices.size());
 848                 for (exvector::const_iterator it = local_dummy_indices.begin(); it != local_dummy_indices.end(); ++it)
 849                         dummy_syms.push_back(it->op(0));
 850                 if (symmetrize(r, dummy_syms).is_zero()) {
 851                         free_indices.clear();
 852                         return _ex0;
 853                 }
 854         }
 855
 856         // Dummy index renaming
 857         r = rename_dummy_indices(r, dummy_indices, local_dummy_indices);
 858
 859         // Product of indexed object with a scalar?
 860         if (is_exactly_a<mul>(r) && r.nops() == 2
 861          && is_exactly_a<numeric>(r.op(1)) && is_a<indexed>(r.op(0)))
 862                 return ex_to<basic>(r.op(0).op(0)).scalar_mul_indexed(r.op(0), ex_to<numeric>(r.op(1)));
 863         else
 864                 return r;
 865 }
 866
 867 /** This structure stores the original and symmetrized versions of terms
 868  *  obtained during the simplification of sums. */
 869 class terminfo {
 870 public:
 871         terminfo(const ex & orig_, const ex & symm_) : orig(orig_), symm(symm_) {}
 872
 873         ex orig; /**< original term */
 874         ex symm; /**< symmtrized term */
 875 };
 876
 877 class terminfo_is_less {
 878 public:
 879         bool operator() (const terminfo & ti1, const terminfo & ti2) const
 880         {
 881                 return (ti1.symm.compare(ti2.symm) < 0);
 882         }
 883 };
 884
 885 /** This structure stores the individual symmetrized terms obtained during
 886  *  the simplification of sums. */
 887 class symminfo {
 888 public:
 889         symminfo() : num(0) {}
 890
 891         symminfo(const ex & symmterm_, const ex & orig_, size_t num_) : orig(orig_), num(num_)
 892         {
 893                 if (is_exactly_a<mul>(symmterm_) && is_exactly_a<numeric>(symmterm_.op(symmterm_.nops()-1))) {
 894                         coeff = symmterm_.op(symmterm_.nops()-1);
 895                         symmterm = symmterm_ / coeff;
 896                 } else {
 897                         coeff = 1;
 898                         symmterm = symmterm_;
 899                 }
 900         }
 901
 902         ex symmterm;  /**< symmetrized term */
 903         ex coeff;     /**< coefficient of symmetrized term */
 904         ex orig;      /**< original term */
 905         size_t num; /**< how many symmetrized terms resulted from the original term */
 906 };
 907
 908 class symminfo_is_less_by_symmterm {
 909 public:
 910         bool operator() (const symminfo & si1, const symminfo & si2) const
 911         {
 912                 return (si1.symmterm.compare(si2.symmterm) < 0);
 913         }
 914 };
 915
 916 class symminfo_is_less_by_orig {
 917 public:
 918         bool operator() (const symminfo & si1, const symminfo & si2) const
 919         {
 920                 return (si1.orig.compare(si2.orig) < 0);
 921         }
 922 };
 923
 924 /** Simplify indexed expression, return list of free indices. */
 925 ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp)
 926 {
 927         // Expand the expression
 928         ex e_expanded = e.expand();
 929
 930         // Simplification of single indexed object: just find the free indices
 931         // and perform dummy index renaming/repositioning
 932         if (is_a<indexed>(e_expanded)) {
 933
 934                 // Find the dummy indices
 935                 const indexed &i = ex_to<indexed>(e_expanded);
 936                 exvector local_dummy_indices;
 937                 find_free_and_dummy(i.seq.begin() + 1, i.seq.end(), free_indices, local_dummy_indices);
 938
 939                 // Filter out the dummy indices with variance
 940                 exvector variant_dummy_indices;
 941                 find_variant_indices(local_dummy_indices, variant_dummy_indices);
 942
 943                 // Any indices with variance present at all?
 944                 if (!variant_dummy_indices.empty()) {
 945
 946                         // Yes, reposition them
 947                         exvector moved_indices;
 948                         reposition_dummy_indices(e_expanded, variant_dummy_indices, moved_indices);
 949                 }
 950
 951                 // Rename the dummy indices
 952                 return rename_dummy_indices(e_expanded, dummy_indices, local_dummy_indices);
 953         }
 954
 955         // Simplification of sum = sum of simplifications, check consistency of
 956         // free indices in each term
 957         if (is_exactly_a<add>(e_expanded)) {
 958                 bool first = true;
 959                 ex sum;
 960                 free_indices.clear();
 961
 962                 for (size_t i=0; i<e_expanded.nops(); i++) {
 963                         exvector free_indices_of_term;
 964                         ex term = simplify_indexed(e_expanded.op(i), free_indices_of_term, dummy_indices, sp);
 965                         if (!term.is_zero()) {
 966                                 if (first) {
 967                                         free_indices = free_indices_of_term;
 968                                         sum = term;
 969                                         first = false;
 970                                 } else {
 971                                         if (!indices_consistent(free_indices, free_indices_of_term)) {
 972                                                 std::ostringstream s;
 973                                                 s << "simplify_indexed: inconsistent indices in sum: ";
 974                                                 s << exprseq(free_indices) << " vs. " << exprseq(free_indices_of_term);
 975                                                 throw (std::runtime_error(s.str()));
 976                                         }
 977                                         if (is_a<indexed>(sum) && is_a<indexed>(term))
 978                                                 sum = ex_to<basic>(sum.op(0)).add_indexed(sum, term);
 979                                         else
 980                                                 sum += term;
 981                                 }
 982                         }
 983                 }
 984
 985                 // If the sum turns out to be zero, we are finished
 986                 if (sum.is_zero()) {
 987                         free_indices.clear();
 988                         return sum;
 989                 }
 990
 991                 // More than one term and more than one dummy index?
 992                 size_t num_terms_orig = (is_exactly_a<add>(sum) ? sum.nops() : 1);
 993                 if (num_terms_orig < 2 || dummy_indices.size() < 2)
 994                         return sum;
 995
 996                 // Yes, construct vector of all dummy index symbols
 997                 exvector dummy_syms;
 998                 dummy_syms.reserve(dummy_indices.size());
 999                 for (exvector::const_iterator it = dummy_indices.begin(); it != dummy_indices.end(); ++it)
1000                         dummy_syms.push_back(it->op(0));
1001
1002                 // Chop the sum into terms and symmetrize each one over the dummy
1003                 // indices
1004                 std::vector<terminfo> terms;
1005                 for (size_t i=0; i<sum.nops(); i++) {
1006                         const ex & term = sum.op(i);
1007                         ex term_symm = symmetrize(term, dummy_syms);
1008                         if (term_symm.is_zero())
1009                                 continue;
1010                         terms.push_back(terminfo(term, term_symm));
1011                 }
1012
1013                 // Sort by symmetrized terms
1014                 std::sort(terms.begin(), terms.end(), terminfo_is_less());
1015
1016                 // Combine equal symmetrized terms
1017                 std::vector<terminfo> terms_pass2;
1018                 for (std::vector<terminfo>::const_iterator i=terms.begin(); i!=terms.end(); ) {
1019                         size_t num = 1;
1020                         std::vector<terminfo>::const_iterator j = i + 1;
1021                         while (j != terms.end() && j->symm == i->symm) {
1022                                 num++;
1023                                 j++;
1024                         }
1025                         terms_pass2.push_back(terminfo(i->orig * num, i->symm * num));
1026                         i = j;
1027                 }
1028
1029                 // If there is only one term left, we are finished
1030                 if (terms_pass2.size() == 1)
1031                         return terms_pass2[0].orig;
1032
1033                 // Chop the symmetrized terms into subterms
1034                 std::vector<symminfo> sy;
1035                 for (std::vector<terminfo>::const_iterator i=terms_pass2.begin(); i!=terms_pass2.end(); ++i) {
1036                         if (is_exactly_a<add>(i->symm)) {
1037                                 size_t num = i->symm.nops();
1038                                 for (size_t j=0; j<num; j++)
1039                                         sy.push_back(symminfo(i->symm.op(j), i->orig, num));
1040                         } else
1041                                 sy.push_back(symminfo(i->symm, i->orig, 1));
1042                 }
1043
1044                 // Sort by symmetrized subterms
1045                 std::sort(sy.begin(), sy.end(), symminfo_is_less_by_symmterm());
1046
1047                 // Combine equal symmetrized subterms
1048                 std::vector<symminfo> sy_pass2;
1049                 exvector result;
1050                 for (std::vector<symminfo>::const_iterator i=sy.begin(); i!=sy.end(); ) {
1051
1052                         // Combine equal terms
1053                         std::vector<symminfo>::const_iterator j = i + 1;
1054                         if (j != sy.end() && j->symmterm == i->symmterm) {
1055
1056                                 // More than one term, collect the coefficients
1057                                 ex coeff = i->coeff;
1058                                 while (j != sy.end() && j->symmterm == i->symmterm) {
1059                                         coeff += j->coeff;
1060                                         j++;
1061                                 }
1062
1063                                 // Add combined term to result
1064                                 if (!coeff.is_zero())
1065                                         result.push_back(coeff * i->symmterm);
1066
1067                         } else {
1068
1069                                 // Single term, store for second pass
1070                                 sy_pass2.push_back(*i);
1071                         }
1072
1073                         i = j;
1074                 }
1075
1076                 // Were there any remaining terms that didn't get combined?
1077                 if (sy_pass2.size() > 0) {
1078
1079                         // Yes, sort by their original terms
1080                         std::sort(sy_pass2.begin(), sy_pass2.end(), symminfo_is_less_by_orig());
1081
1082                         for (std::vector<symminfo>::const_iterator i=sy_pass2.begin(); i!=sy_pass2.end(); ) {
1083
1084                                 // How many symmetrized terms of this original term are left?
1085                                 size_t num = 1;
1086                                 std::vector<symminfo>::const_iterator j = i + 1;
1087                                 while (j != sy_pass2.end() && j->orig == i->orig) {
1088                                         num++;
1089                                         j++;
1090                                 }
1091
1092                                 if (num == i->num) {
1093
1094                                         // All terms left, then add the original term to the result
1095                                         result.push_back(i->orig);
1096
1097                                 } else {
1098
1099                                         // Some terms were combined with others, add up the remaining symmetrized terms
1100                                         std::vector<symminfo>::const_iterator k;
1101                                         for (k=i; k!=j; k++)
1102                                                 result.push_back(k->coeff * k->symmterm);
1103                                 }
1104
1105                                 i = j;
1106                         }
1107                 }
1108
1109                 // Add all resulting terms
1110                 ex sum_symm = (new add(result))->setflag(status_flags::dynallocated);
1111                 if (sum_symm.is_zero())
1112                         free_indices.clear();
1113                 return sum_symm;
1114         }
1115
1116         // Simplification of products
1117         if (is_exactly_a<mul>(e_expanded)
1118          || is_exactly_a<ncmul>(e_expanded)
1119          || (is_exactly_a<power>(e_expanded) && is_a<indexed>(e_expanded.op(0)) && e_expanded.op(1).is_equal(_ex2)))
1120                 return simplify_indexed_product(e_expanded, free_indices, dummy_indices, sp);
1121
1122         // Cannot do anything
1123         free_indices.clear();
1124         return e_expanded;
1125 }
1126
1127 /** Simplify/canonicalize expression containing indexed objects. This
1128  *  performs contraction of dummy indices where possible and checks whether
1129  *  the free indices in sums are consistent.
1130  *
1131  *  @return simplified expression */
1132 ex ex::simplify_indexed(unsigned options) const
1133 {
1134         exvector free_indices, dummy_indices;
1135         scalar_products sp;
1136         return GiNaC::simplify_indexed(*this, free_indices, dummy_indices, sp);
1137 }
1138
1139 /** Simplify/canonicalize expression containing indexed objects. This
1140  *  performs contraction of dummy indices where possible, checks whether
1141  *  the free indices in sums are consistent, and automatically replaces
1142  *  scalar products by known values if desired.
1143  *
1144  *  @param sp Scalar products to be replaced automatically
1145  *  @return simplified expression */
1146 ex ex::simplify_indexed(const scalar_products & sp, unsigned options) const
1147 {
1148         exvector free_indices, dummy_indices;
1149         return GiNaC::simplify_indexed(*this, free_indices, dummy_indices, sp);
1150 }
1151
1152 /** Symmetrize expression over its free indices. */
1153 ex ex::symmetrize() const
1154 {
1155         return GiNaC::symmetrize(*this, get_free_indices());
1156 }
1157
1158 /** Antisymmetrize expression over its free indices. */
1159 ex ex::antisymmetrize() const
1160 {
1161         return GiNaC::antisymmetrize(*this, get_free_indices());
1162 }
1163
1164 /** Symmetrize expression by cyclic permutation over its free indices. */
1165 ex ex::symmetrize_cyclic() const
1166 {
1167         return GiNaC::symmetrize_cyclic(*this, get_free_indices());
1168 }
1169
1170 //////////
1171 // helper classes
1172 //////////
1173
1174 spmapkey::spmapkey(const ex & v1_, const ex & v2_, const ex & dim_) : dim(dim_)
1175 {
1176         // If indexed, extract base objects
1177         ex s1 = is_a<indexed>(v1_) ? v1_.op(0) : v1_;
1178         ex s2 = is_a<indexed>(v2_) ? v2_.op(0) : v2_;
1179
1180         // Enforce canonical order in pair
1181         if (s1.compare(s2) > 0) {
1182                 v1 = s2;
1183                 v2 = s1;
1184         } else {
1185                 v1 = s1;
1186                 v2 = s2;
1187         }
1188 }
1189
1190 bool spmapkey::operator==(const spmapkey &other) const
1191 {
1192         if (!v1.is_equal(other.v1))
1193                 return false;
1194         if (!v2.is_equal(other.v2))
1195                 return false;
1196         if (is_a<wildcard>(dim) || is_a<wildcard>(other.dim))
1197                 return true;
1198         else
1199                 return dim.is_equal(other.dim);
1200 }
1201
1202 bool spmapkey::operator<(const spmapkey &other) const
1203 {
1204         int cmp = v1.compare(other.v1);
1205         if (cmp)
1206                 return cmp < 0;
1207         cmp = v2.compare(other.v2);
1208         if (cmp)
1209                 return cmp < 0;
1210
1211         // Objects are equal, now check dimensions
1212         if (is_a<wildcard>(dim) || is_a<wildcard>(other.dim))
1213                 return false;
1214         else
1215                 return dim.compare(other.dim) < 0;
1216 }
1217
1218 void spmapkey::debugprint() const
1219 {
1220         std::cerr << "(" << v1 << "," << v2 << "," << dim << ")";
1221 }
1222
1223 void scalar_products::add(const ex & v1, const ex & v2, const ex & sp)
1224 {
1225         spm[spmapkey(v1, v2)] = sp;
1226 }
1227
1228 void scalar_products::add(const ex & v1, const ex & v2, const ex & dim, const ex & sp)
1229 {
1230         spm[spmapkey(v1, v2, dim)] = sp;
1231 }
1232
1233 void scalar_products::add_vectors(const lst & l, const ex & dim)
1234 {
1235         // Add all possible pairs of products
1236         for (lst::const_iterator it1 = l.begin(); it1 != l.end(); ++it1)
1237                 for (lst::const_iterator it2 = l.begin(); it2 != l.end(); ++it2)
1238                         add(*it1, *it2, *it1 * *it2);
1239 }
1240
1241 void scalar_products::clear()
1242 {
1243         spm.clear();
1244 }
1245
1246 /** Check whether scalar product pair is defined. */
1247 bool scalar_products::is_defined(const ex & v1, const ex & v2, const ex & dim) const
1248 {
1249         return spm.find(spmapkey(v1, v2, dim)) != spm.end();
1250 }
1251
1252 /** Return value of defined scalar product pair. */
1253 ex scalar_products::evaluate(const ex & v1, const ex & v2, const ex & dim) const
1254 {
1255         return spm.find(spmapkey(v1, v2, dim))->second;
1256 }
1257
1258 void scalar_products::debugprint() const
1259 {
1260         std::cerr << "map size=" << spm.size() << std::endl;
1261         spmap::const_iterator i = spm.begin(), end = spm.end();
1262         while (i != end) {
1263                 const spmapkey & k = i->first;
1264                 std::cerr << "item key=";
1265                 k.debugprint();
1266                 std::cerr << ", value=" << i->second << std::endl;
1267                 ++i;
1268         }
1269 }
1270
1271 } // namespace GiNaC