ginac/indexed.cpp

   1 /** @file indexed.cpp
   2  *
   3  *  Implementation of GiNaC's indexed expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2005 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 <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 #include "integral.h"
  40
  41 namespace GiNaC {
  42
  43 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(indexed, exprseq,
  44   print_func<print_context>(&indexed::do_print).
  45   print_func<print_latex>(&indexed::do_print_latex).
  46   print_func<print_tree>(&indexed::do_print_tree))
  47
  48 //////////
  49 // default constructor
  50 //////////
  51
  52 indexed::indexed() : symtree(not_symmetric())
  53 {
  54         tinfo_key = TINFO_indexed;
  55 }
  56
  57 //////////
  58 // other constructors
  59 //////////
  60
  61 indexed::indexed(const ex & b) : inherited(b), symtree(not_symmetric())
  62 {
  63         tinfo_key = TINFO_indexed;
  64         validate();
  65 }
  66
  67 indexed::indexed(const ex & b, const ex & i1) : inherited(b, i1), symtree(not_symmetric())
  68 {
  69         tinfo_key = TINFO_indexed;
  70         validate();
  71 }
  72
  73 indexed::indexed(const ex & b, const ex & i1, const ex & i2) : inherited(b, i1, i2), symtree(not_symmetric())
  74 {
  75         tinfo_key = TINFO_indexed;
  76         validate();
  77 }
  78
  79 indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symtree(not_symmetric())
  80 {
  81         tinfo_key = TINFO_indexed;
  82         validate();
  83 }
  84
  85 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())
  86 {
  87         tinfo_key = TINFO_indexed;
  88         validate();
  89 }
  90
  91 indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2) : inherited(b, i1, i2), symtree(symm)
  92 {
  93         tinfo_key = TINFO_indexed;
  94         validate();
  95 }
  96
  97 indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symtree(symm)
  98 {
  99         tinfo_key = TINFO_indexed;
 100         validate();
 101 }
 102
 103 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)
 104 {
 105         tinfo_key = TINFO_indexed;
 106         validate();
 107 }
 108
 109 indexed::indexed(const ex & b, const exvector & v) : inherited(b), symtree(not_symmetric())
 110 {
 111         seq.insert(seq.end(), v.begin(), v.end());
 112         tinfo_key = TINFO_indexed;
 113         validate();
 114 }
 115
 116 indexed::indexed(const ex & b, const symmetry & symm, const exvector & v) : inherited(b), symtree(symm)
 117 {
 118         seq.insert(seq.end(), v.begin(), v.end());
 119         tinfo_key = TINFO_indexed;
 120         validate();
 121 }
 122
 123 indexed::indexed(const symmetry & symm, const exprseq & es) : inherited(es), symtree(symm)
 124 {
 125         tinfo_key = TINFO_indexed;
 126 }
 127
 128 indexed::indexed(const symmetry & symm, const exvector & v, bool discardable) : inherited(v, discardable), symtree(symm)
 129 {
 130         tinfo_key = TINFO_indexed;
 131 }
 132
 133 indexed::indexed(const symmetry & symm, std::auto_ptr<exvector> vp) : inherited(vp), symtree(symm)
 134 {
 135         tinfo_key = TINFO_indexed;
 136 }
 137
 138 //////////
 139 // archiving
 140 //////////
 141
 142 indexed::indexed(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
 143 {
 144         if (!n.find_ex("symmetry", symtree, sym_lst)) {
 145                 // GiNaC versions <= 0.9.0 had an unsigned "symmetry" property
 146                 unsigned symm = 0;
 147                 n.find_unsigned("symmetry", symm);
 148                 switch (symm) {
 149                         case 1:
 150                                 symtree = sy_symm();
 151                                 break;
 152                         case 2:
 153                                 symtree = sy_anti();
 154                                 break;
 155                         default:
 156                                 symtree = not_symmetric();
 157                                 break;
 158                 }
 159                 const_cast<symmetry &>(ex_to<symmetry>(symtree)).validate(seq.size() - 1);
 160         }
 161 }
 162
 163 void indexed::archive(archive_node &n) const
 164 {
 165         inherited::archive(n);
 166         n.add_ex("symmetry", symtree);
 167 }
 168
 169 DEFAULT_UNARCHIVE(indexed)
 170
 171 //////////
 172 // functions overriding virtual functions from base classes
 173 //////////
 174
 175 void indexed::printindices(const print_context & c, unsigned level) const
 176 {
 177         if (seq.size() > 1) {
 178
 179                 exvector::const_iterator it=seq.begin() + 1, itend = seq.end();
 180
 181                 if (is_a<print_latex>(c)) {
 182
 183                         // TeX output: group by variance
 184                         bool first = true;
 185                         bool covariant = true;
 186
 187                         while (it != itend) {
 188                                 bool cur_covariant = (is_a<varidx>(*it) ? ex_to<varidx>(*it).is_covariant() : true);
 189                                 if (first || cur_covariant != covariant) { // Variance changed
 190                                         // The empty {} prevents indices from ending up on top of each other
 191                                         if (!first)
 192                                                 c.s << "}{}";
 193                                         covariant = cur_covariant;
 194                                         if (covariant)
 195                                                 c.s << "_{";
 196                                         else
 197                                                 c.s << "^{";
 198                                 }
 199                                 it->print(c, level);
 200                                 c.s << " ";
 201                                 first = false;
 202                                 it++;
 203                         }
 204                         c.s << "}";
 205
 206                 } else {
 207
 208                         // Ordinary output
 209                         while (it != itend) {
 210                                 it->print(c, level);
 211                                 it++;
 212                         }
 213                 }
 214         }
 215 }
 216
 217 void indexed::print_indexed(const print_context & c, const char *openbrace, const char *closebrace, unsigned level) const
 218 {
 219         if (precedence() <= level)
 220                 c.s << openbrace << '(';
 221         c.s << openbrace;
 222         seq[0].print(c, precedence());
 223         c.s << closebrace;
 224         printindices(c, level);
 225         if (precedence() <= level)
 226                 c.s << ')' << closebrace;
 227 }
 228
 229 void indexed::do_print(const print_context & c, unsigned level) const
 230 {
 231         print_indexed(c, "", "", level);
 232 }
 233
 234 void indexed::do_print_latex(const print_latex & c, unsigned level) const
 235 {
 236         print_indexed(c, "{", "}", level);
 237 }
 238
 239 void indexed::do_print_tree(const print_tree & c, unsigned level) const
 240 {
 241         c.s << std::string(level, ' ') << class_name() << " @" << this
 242             << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 243             << ", " << seq.size()-1 << " indices"
 244             << ", symmetry=" << symtree << std::endl;
 245         seq[0].print(c, level + c.delta_indent);
 246         printindices(c, level + c.delta_indent);
 247 }
 248
 249 bool indexed::info(unsigned inf) const
 250 {
 251         if (inf == info_flags::indexed) return true;
 252         if (inf == info_flags::has_indices) return seq.size() > 1;
 253         return inherited::info(inf);
 254 }
 255
 256 struct idx_is_not : public std::binary_function<ex, unsigned, bool> {
 257         bool operator() (const ex & e, unsigned inf) const {
 258                 return !(ex_to<idx>(e).get_value().info(inf));
 259         }
 260 };
 261
 262 bool indexed::all_index_values_are(unsigned inf) const
 263 {
 264         // No indices? Then no property can be fulfilled
 265         if (seq.size() < 2)
 266                 return false;
 267
 268         // Check all indices
 269         return find_if(seq.begin() + 1, seq.end(), bind2nd(idx_is_not(), inf)) == seq.end();
 270 }
 271
 272 int indexed::compare_same_type(const basic & other) const
 273 {
 274         GINAC_ASSERT(is_a<indexed>(other));
 275         return inherited::compare_same_type(other);
 276 }
 277
 278 ex indexed::eval(int level) const
 279 {
 280         // First evaluate children, then we will end up here again
 281         if (level > 1)
 282                 return indexed(ex_to<symmetry>(symtree), evalchildren(level));
 283
 284         const ex &base = seq[0];
 285
 286         // If the base object is 0, the whole object is 0
 287         if (base.is_zero())
 288                 return _ex0;
 289
 290         // If the base object is a product, pull out the numeric factor
 291         if (is_exactly_a<mul>(base) && is_exactly_a<numeric>(base.op(base.nops() - 1))) {
 292                 exvector v(seq);
 293                 ex f = ex_to<numeric>(base.op(base.nops() - 1));
 294                 v[0] = seq[0] / f;
 295                 return f * thiscontainer(v);
 296         }
 297
 298         // Canonicalize indices according to the symmetry properties
 299         if (seq.size() > 2) {
 300                 exvector v = seq;
 301                 GINAC_ASSERT(is_exactly_a<symmetry>(symtree));
 302                 int sig = canonicalize(v.begin() + 1, ex_to<symmetry>(symtree));
 303                 if (sig != INT_MAX) {
 304                         // Something has changed while sorting indices, more evaluations later
 305                         if (sig == 0)
 306                                 return _ex0;
 307                         return ex(sig) * thiscontainer(v);
 308                 }
 309         }
 310
 311         // Let the class of the base object perform additional evaluations
 312         return ex_to<basic>(base).eval_indexed(*this);
 313 }
 314
 315 ex indexed::thiscontainer(const exvector & v) const
 316 {
 317         return indexed(ex_to<symmetry>(symtree), v);
 318 }
 319
 320 ex indexed::thiscontainer(std::auto_ptr<exvector> vp) const
 321 {
 322         return indexed(ex_to<symmetry>(symtree), vp);
 323 }
 324
 325 ex indexed::expand(unsigned options) const
 326 {
 327         GINAC_ASSERT(seq.size() > 0);
 328
 329         if (options & expand_options::expand_indexed) {
 330                 ex newbase = seq[0].expand(options);
 331                 if (is_exactly_a<add>(newbase)) {
 332                         ex sum = _ex0;
 333                         for (size_t i=0; i<newbase.nops(); i++) {
 334                                 exvector s = seq;
 335                                 s[0] = newbase.op(i);
 336                                 sum += thiscontainer(s).expand(options);
 337                         }
 338                         return sum;
 339                 }
 340                 if (!are_ex_trivially_equal(newbase, seq[0])) {
 341                         exvector s = seq;
 342                         s[0] = newbase;
 343                         return ex_to<indexed>(thiscontainer(s)).inherited::expand(options);
 344                 }
 345         }
 346         return inherited::expand(options);
 347 }
 348
 349 //////////
 350 // virtual functions which can be overridden by derived classes
 351 //////////
 352
 353 // none
 354
 355 //////////
 356 // non-virtual functions in this class
 357 //////////
 358
 359 /** Check whether all indices are of class idx and validate the symmetry
 360  *  tree. This function is used internally to make sure that all constructed
 361  *  indexed objects really carry indices and not some other classes. */
 362 void indexed::validate() const
 363 {
 364         GINAC_ASSERT(seq.size() > 0);
 365         exvector::const_iterator it = seq.begin() + 1, itend = seq.end();
 366         while (it != itend) {
 367                 if (!is_a<idx>(*it))
 368                         throw(std::invalid_argument("indices of indexed object must be of type idx"));
 369                 it++;
 370         }
 371
 372         if (!symtree.is_zero()) {
 373                 if (!is_exactly_a<symmetry>(symtree))
 374                         throw(std::invalid_argument("symmetry of indexed object must be of type symmetry"));
 375                 const_cast<symmetry &>(ex_to<symmetry>(symtree)).validate(seq.size() - 1);
 376         }
 377 }
 378
 379 /** Implementation of ex::diff() for an indexed object always returns 0.
 380  *
 381  *  @see ex::diff */
 382 ex indexed::derivative(const symbol & s) const
 383 {
 384         return _ex0;
 385 }
 386
 387 //////////
 388 // global functions
 389 //////////
 390
 391 struct idx_is_equal_ignore_dim : public std::binary_function<ex, ex, bool> {
 392         bool operator() (const ex &lh, const ex &rh) const
 393         {
 394                 if (lh.is_equal(rh))
 395                         return true;
 396                 else
 397                         try {
 398                                 // Replacing the dimension might cause an error (e.g. with
 399                                 // index classes that only work in a fixed number of dimensions)
 400                                 return lh.is_equal(ex_to<idx>(rh).replace_dim(ex_to<idx>(lh).get_dim()));
 401                         } catch (...) {
 402                                 return false;
 403                         }
 404         }
 405 };
 406
 407 /** Check whether two sorted index vectors are consistent (i.e. equal). */
 408 static bool indices_consistent(const exvector & v1, const exvector & v2)
 409 {
 410         // Number of indices must be the same
 411         if (v1.size() != v2.size())
 412                 return false;
 413
 414         return equal(v1.begin(), v1.end(), v2.begin(), idx_is_equal_ignore_dim());
 415 }
 416
 417 exvector indexed::get_indices() const
 418 {
 419         GINAC_ASSERT(seq.size() >= 1);
 420         return exvector(seq.begin() + 1, seq.end());
 421 }
 422
 423 exvector indexed::get_dummy_indices() const
 424 {
 425         exvector free_indices, dummy_indices;
 426         find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices);
 427         return dummy_indices;
 428 }
 429
 430 exvector indexed::get_dummy_indices(const indexed & other) const
 431 {
 432         exvector indices = get_free_indices();
 433         exvector other_indices = other.get_free_indices();
 434         indices.insert(indices.end(), other_indices.begin(), other_indices.end());
 435         exvector dummy_indices;
 436         find_dummy_indices(indices, dummy_indices);
 437         return dummy_indices;
 438 }
 439
 440 bool indexed::has_dummy_index_for(const ex & i) const
 441 {
 442         exvector::const_iterator it = seq.begin() + 1, itend = seq.end();
 443         while (it != itend) {
 444                 if (is_dummy_pair(*it, i))
 445                         return true;
 446                 it++;
 447         }
 448         return false;
 449 }
 450
 451 exvector indexed::get_free_indices() const
 452 {
 453         exvector free_indices, dummy_indices;
 454         find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices);
 455         return free_indices;
 456 }
 457
 458 exvector add::get_free_indices() const
 459 {
 460         exvector free_indices;
 461         for (size_t i=0; i<nops(); i++) {
 462                 if (i == 0)
 463                         free_indices = op(i).get_free_indices();
 464                 else {
 465                         exvector free_indices_of_term = op(i).get_free_indices();
 466                         if (!indices_consistent(free_indices, free_indices_of_term))
 467                                 throw (std::runtime_error("add::get_free_indices: inconsistent indices in sum"));
 468                 }
 469         }
 470         return free_indices;
 471 }
 472
 473 exvector mul::get_free_indices() const
 474 {
 475         // Concatenate free indices of all factors
 476         exvector un;
 477         for (size_t i=0; i<nops(); i++) {
 478                 exvector free_indices_of_factor = op(i).get_free_indices();
 479                 un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
 480         }
 481
 482         // And remove the dummy indices
 483         exvector free_indices, dummy_indices;
 484         find_free_and_dummy(un, free_indices, dummy_indices);
 485         return free_indices;
 486 }
 487
 488 exvector ncmul::get_free_indices() const
 489 {
 490         // Concatenate free indices of all factors
 491         exvector un;
 492         for (size_t i=0; i<nops(); i++) {
 493                 exvector free_indices_of_factor = op(i).get_free_indices();
 494                 un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
 495         }
 496
 497         // And remove the dummy indices
 498         exvector free_indices, dummy_indices;
 499         find_free_and_dummy(un, free_indices, dummy_indices);
 500         return free_indices;
 501 }
 502
 503 struct is_summation_idx : public std::unary_function<ex, bool> {
 504         bool operator()(const ex & e)
 505         {
 506                 return is_dummy_pair(e, e);
 507         }
 508 };
 509
 510 exvector power::get_free_indices() const
 511 {
 512         // Get free indices of basis
 513         exvector basis_indices = basis.get_free_indices();
 514
 515         if (exponent.info(info_flags::even)) {
 516                 // If the exponent is an even number, then any "free" index that
 517                 // forms a dummy pair with itself is actually a summation index
 518                 exvector really_free;
 519                 std::remove_copy_if(basis_indices.begin(), basis_indices.end(),
 520                                     std::back_inserter(really_free), is_summation_idx());
 521                 return really_free;
 522         } else
 523                 return basis_indices;
 524 }
 525
 526 exvector integral::get_free_indices() const
 527 {
 528         if (a.get_free_indices().size() || b.get_free_indices().size())
 529                 throw (std::runtime_error("integral::get_free_indices: boundary values should not have free indices"));
 530         return f.get_free_indices();
 531 }
 532
 533 /** Rename dummy indices in an expression.
 534  *
 535  *  @param e Expression to work on
 536  *  @param local_dummy_indices The set of dummy indices that appear in the
 537  *    expression "e"
 538  *  @param global_dummy_indices The set of dummy indices that have appeared
 539  *    before and which we would like to use in "e", too. This gets updated
 540  *    by the function */
 541 static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, exvector & local_dummy_indices)
 542 {
 543         size_t global_size = global_dummy_indices.size(),
 544                local_size = local_dummy_indices.size();
 545
 546         // Any local dummy indices at all?
 547         if (local_size == 0)
 548                 return e;
 549
 550         if (global_size < local_size) {
 551
 552                 // More local indices than we encountered before, add the new ones
 553                 // to the global set
 554                 size_t old_global_size = global_size;
 555                 int remaining = local_size - global_size;
 556                 exvector::const_iterator it = local_dummy_indices.begin(), itend = local_dummy_indices.end();
 557                 while (it != itend && remaining > 0) {
 558                         if (find_if(global_dummy_indices.begin(), global_dummy_indices.end(), bind2nd(op0_is_equal(), *it)) == global_dummy_indices.end()) {
 559                                 global_dummy_indices.push_back(*it);
 560                                 global_size++;
 561                                 remaining--;
 562                         }
 563                         it++;
 564                 }
 565
 566                 // If this is the first set of local indices, do nothing
 567                 if (old_global_size == 0)
 568                         return e;
 569         }
 570         GINAC_ASSERT(local_size <= global_size);
 571
 572         // Construct vectors of index symbols
 573         exvector local_syms, global_syms;
 574         local_syms.reserve(local_size);
 575         global_syms.reserve(local_size);
 576         for (size_t i=0; i<local_size; i++)
 577                 local_syms.push_back(local_dummy_indices[i].op(0));
 578         shaker_sort(local_syms.begin(), local_syms.end(), ex_is_less(), ex_swap());
 579         for (size_t i=0; i<local_size; i++) // don't use more global symbols than necessary
 580                 global_syms.push_back(global_dummy_indices[i].op(0));
 581         shaker_sort(global_syms.begin(), global_syms.end(), ex_is_less(), ex_swap());
 582
 583         // Remove common indices
 584         exvector local_uniq, global_uniq;
 585         set_difference(local_syms.begin(), local_syms.end(), global_syms.begin(), global_syms.end(), std::back_insert_iterator<exvector>(local_uniq), ex_is_less());
 586         set_difference(global_syms.begin(), global_syms.end(), local_syms.begin(), local_syms.end(), std::back_insert_iterator<exvector>(global_uniq), ex_is_less());
 587
 588         // Replace remaining non-common local index symbols by global ones
 589         if (local_uniq.empty())
 590                 return e;
 591         else {
 592                 while (global_uniq.size() > local_uniq.size())
 593                         global_uniq.pop_back();
 594                 return e.subs(lst(local_uniq.begin(), local_uniq.end()), lst(global_uniq.begin(), global_uniq.end()), subs_options::no_pattern);
 595         }
 596 }
 597
 598 /** Given a set of indices, extract those of class varidx. */
 599 static void find_variant_indices(const exvector & v, exvector & variant_indices)
 600 {
 601         exvector::const_iterator it1, itend;
 602         for (it1 = v.begin(), itend = v.end(); it1 != itend; ++it1) {
 603                 if (is_exactly_a<varidx>(*it1))
 604                         variant_indices.push_back(*it1);
 605         }
 606 }
 607
 608 /** Raise/lower dummy indices in a single indexed objects to canonicalize their
 609  *  variance.
 610  *
 611  *  @param e Object to work on
 612  *  @param variant_dummy_indices The set of indices that might need repositioning (will be changed by this function)
 613  *  @param moved_indices The set of indices that have been repositioned (will be changed by this function)
 614  *  @return true if 'e' was changed */
 615 bool reposition_dummy_indices(ex & e, exvector & variant_dummy_indices, exvector & moved_indices)
 616 {
 617         bool something_changed = false;
 618
 619         // If a dummy index is encountered for the first time in the
 620         // product, pull it up, otherwise, pull it down
 621         exvector::const_iterator it2, it2start, it2end;
 622         for (it2start = ex_to<indexed>(e).seq.begin(), it2end = ex_to<indexed>(e).seq.end(), it2 = it2start + 1; it2 != it2end; ++it2) {
 623                 if (!is_exactly_a<varidx>(*it2))
 624                         continue;
 625
 626                 exvector::iterator vit, vitend;
 627                 for (vit = variant_dummy_indices.begin(), vitend = variant_dummy_indices.end(); vit != vitend; ++vit) {
 628                         if (it2->op(0).is_equal(vit->op(0))) {
 629                                 if (ex_to<varidx>(*it2).is_covariant()) {
 630                                         e = e.subs(lst(
 631                                                 *it2 == ex_to<varidx>(*it2).toggle_variance(),
 632                                                 ex_to<varidx>(*it2).toggle_variance() == *it2
 633                                         ), subs_options::no_pattern);
 634                                         something_changed = true;
 635                                         it2 = ex_to<indexed>(e).seq.begin() + (it2 - it2start);
 636                                         it2start = ex_to<indexed>(e).seq.begin();
 637                                         it2end = ex_to<indexed>(e).seq.end();
 638                                 }
 639                                 moved_indices.push_back(*vit);
 640                                 variant_dummy_indices.erase(vit);
 641                                 goto next_index;
 642                         }
 643                 }
 644
 645                 for (vit = moved_indices.begin(), vitend = moved_indices.end(); vit != vitend; ++vit) {
 646                         if (it2->op(0).is_equal(vit->op(0))) {
 647                                 if (ex_to<varidx>(*it2).is_contravariant()) {
 648                                         e = e.subs(*it2 == ex_to<varidx>(*it2).toggle_variance(), subs_options::no_pattern);
 649                                         something_changed = true;
 650                                         it2 = ex_to<indexed>(e).seq.begin() + (it2 - it2start);
 651                                         it2start = ex_to<indexed>(e).seq.begin();
 652                                         it2end = ex_to<indexed>(e).seq.end();
 653                                 }
 654                                 goto next_index;
 655                         }
 656                 }
 657
 658 next_index: ;
 659         }
 660
 661         return something_changed;
 662 }
 663
 664 /* Ordering that only compares the base expressions of indexed objects. */
 665 struct ex_base_is_less : public std::binary_function<ex, ex, bool> {
 666         bool operator() (const ex &lh, const ex &rh) const
 667         {
 668                 return (is_a<indexed>(lh) ? lh.op(0) : lh).compare(is_a<indexed>(rh) ? rh.op(0) : rh) < 0;
 669         }
 670 };
 671
 672 /** Simplify product of indexed expressions (commutative, noncommutative and
 673  *  simple squares), return list of free indices. */
 674 ex simplify_indexed_product(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp)
 675 {
 676         // Remember whether the product was commutative or noncommutative
 677         // (because we chop it into factors and need to reassemble later)
 678         bool non_commutative = is_exactly_a<ncmul>(e);
 679
 680         // Collect factors in an exvector, store squares twice
 681         exvector v;
 682         v.reserve(e.nops() * 2);
 683
 684         if (is_exactly_a<power>(e)) {
 685                 // We only get called for simple squares, split a^2 -> a*a
 686                 GINAC_ASSERT(e.op(1).is_equal(_ex2));
 687                 v.push_back(e.op(0));
 688                 v.push_back(e.op(0));
 689         } else {
 690                 for (size_t i=0; i<e.nops(); i++) {
 691                         ex f = e.op(i);
 692                         if (is_exactly_a<power>(f) && f.op(1).is_equal(_ex2)) {
 693                                 v.push_back(f.op(0));
 694                     v.push_back(f.op(0));
 695                         } else if (is_exactly_a<ncmul>(f)) {
 696                                 // Noncommutative factor found, split it as well
 697                                 non_commutative = true; // everything becomes noncommutative, ncmul will sort out the commutative factors later
 698                                 for (size_t j=0; j<f.nops(); j++)
 699                                         v.push_back(f.op(j));
 700                         } else
 701                                 v.push_back(f);
 702                 }
 703         }
 704
 705         // Perform contractions
 706         bool something_changed = false;
 707         GINAC_ASSERT(v.size() > 1);
 708         exvector::iterator it1, itend = v.end(), next_to_last = itend - 1;
 709         for (it1 = v.begin(); it1 != next_to_last; it1++) {
 710
 711 try_again:
 712                 if (!is_a<indexed>(*it1))
 713                         continue;
 714
 715                 bool first_noncommutative = (it1->return_type() != return_types::commutative);
 716
 717                 // Indexed factor found, get free indices and look for contraction
 718                 // candidates
 719                 exvector free1, dummy1;
 720                 find_free_and_dummy(ex_to<indexed>(*it1).seq.begin() + 1, ex_to<indexed>(*it1).seq.end(), free1, dummy1);
 721
 722                 exvector::iterator it2;
 723                 for (it2 = it1 + 1; it2 != itend; it2++) {
 724
 725                         if (!is_a<indexed>(*it2))
 726                                 continue;
 727
 728                         bool second_noncommutative = (it2->return_type() != return_types::commutative);
 729
 730                         // Find free indices of second factor and merge them with free
 731                         // indices of first factor
 732                         exvector un;
 733                         find_free_and_dummy(ex_to<indexed>(*it2).seq.begin() + 1, ex_to<indexed>(*it2).seq.end(), un, dummy1);
 734                         un.insert(un.end(), free1.begin(), free1.end());
 735
 736                         // Check whether the two factors share dummy indices
 737                         exvector free, dummy;
 738                         find_free_and_dummy(un, free, dummy);
 739                         size_t num_dummies = dummy.size();
 740                         if (num_dummies == 0)
 741                                 continue;
 742
 743                         // At least one dummy index, is it a defined scalar product?
 744                         bool contracted = false;
 745                         if (free.empty()) {
 746
 747                                 // Find minimal dimension of all indices of both factors
 748                                 exvector::const_iterator dit = ex_to<indexed>(*it1).seq.begin() + 1, ditend = ex_to<indexed>(*it1).seq.end();
 749                                 ex dim = ex_to<idx>(*dit).get_dim();
 750                                 ++dit;
 751                                 for (; dit != ditend; ++dit) {
 752                                         dim = minimal_dim(dim, ex_to<idx>(*dit).get_dim());
 753                                 }
 754                                 dit = ex_to<indexed>(*it2).seq.begin() + 1;
 755                                 ditend = ex_to<indexed>(*it2).seq.end();
 756                                 for (; dit != ditend; ++dit) {
 757                                         dim = minimal_dim(dim, ex_to<idx>(*dit).get_dim());
 758                                 }
 759
 760                                 // User-defined scalar product?
 761                                 if (sp.is_defined(*it1, *it2, dim)) {
 762
 763                                         // Yes, substitute it
 764                                         *it1 = sp.evaluate(*it1, *it2, dim);
 765                                         *it2 = _ex1;
 766                                         goto contraction_done;
 767                                 }
 768                         }
 769
 770                         // Try to contract the first one with the second one
 771                         contracted = ex_to<basic>(it1->op(0)).contract_with(it1, it2, v);
 772                         if (!contracted) {
 773
 774                                 // That didn't work; maybe the second object knows how to
 775                                 // contract itself with the first one
 776                                 contracted = ex_to<basic>(it2->op(0)).contract_with(it2, it1, v);
 777                         }
 778                         if (contracted) {
 779 contraction_done:
 780                                 if (first_noncommutative || second_noncommutative
 781                                  || is_exactly_a<add>(*it1) || is_exactly_a<add>(*it2)
 782                                  || is_exactly_a<mul>(*it1) || is_exactly_a<mul>(*it2)
 783                                  || is_exactly_a<ncmul>(*it1) || is_exactly_a<ncmul>(*it2)) {
 784
 785                                         // One of the factors became a sum or product:
 786                                         // re-expand expression and run again
 787                                         // Non-commutative products are always re-expanded to give
 788                                         // eval_ncmul() the chance to re-order and canonicalize
 789                                         // the product
 790                                         ex r = (non_commutative ? ex(ncmul(v, true)) : ex(mul(v)));
 791                                         return simplify_indexed(r, free_indices, dummy_indices, sp);
 792                                 }
 793
 794                                 // Both objects may have new indices now or they might
 795                                 // even not be indexed objects any more, so we have to
 796                                 // start over
 797                                 something_changed = true;
 798                                 goto try_again;
 799                         }
 800                 }
 801         }
 802
 803         // Find free indices (concatenate them all and call find_free_and_dummy())
 804         // and all dummy indices that appear
 805         exvector un, individual_dummy_indices;
 806         for (it1 = v.begin(), itend = v.end(); it1 != itend; ++it1) {
 807                 exvector free_indices_of_factor;
 808                 if (is_a<indexed>(*it1)) {
 809                         exvector dummy_indices_of_factor;
 810                         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);
 811                         individual_dummy_indices.insert(individual_dummy_indices.end(), dummy_indices_of_factor.begin(), dummy_indices_of_factor.end());
 812                 } else
 813                         free_indices_of_factor = it1->get_free_indices();
 814                 un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
 815         }
 816         exvector local_dummy_indices;
 817         find_free_and_dummy(un, free_indices, local_dummy_indices);
 818         local_dummy_indices.insert(local_dummy_indices.end(), individual_dummy_indices.begin(), individual_dummy_indices.end());
 819
 820         // Filter out the dummy indices with variance
 821         exvector variant_dummy_indices;
 822         find_variant_indices(local_dummy_indices, variant_dummy_indices);
 823
 824         // Any indices with variance present at all?
 825         if (!variant_dummy_indices.empty()) {
 826
 827                 // Yes, bring the product into a canonical order that only depends on
 828                 // the base expressions of indexed objects
 829                 if (!non_commutative)
 830                         std::sort(v.begin(), v.end(), ex_base_is_less());
 831
 832                 exvector moved_indices;
 833
 834                 // Iterate over all indexed objects in the product
 835                 for (it1 = v.begin(), itend = v.end(); it1 != itend; ++it1) {
 836                         if (!is_a<indexed>(*it1))
 837                                 continue;
 838
 839                         if (reposition_dummy_indices(*it1, variant_dummy_indices, moved_indices))
 840                                 something_changed = true;
 841                 }
 842         }
 843
 844         ex r;
 845         if (something_changed)
 846                 r = non_commutative ? ex(ncmul(v, true)) : ex(mul(v));
 847         else
 848                 r = e;
 849
 850         // The result should be symmetric with respect to exchange of dummy
 851         // indices, so if the symmetrization vanishes, the whole expression is
 852         // zero. This detects things like eps.i.j.k * p.j * p.k = 0.
 853         if (local_dummy_indices.size() >= 2) {
 854                 exvector dummy_syms;
 855                 dummy_syms.reserve(local_dummy_indices.size());
 856                 for (exvector::const_iterator it = local_dummy_indices.begin(); it != local_dummy_indices.end(); ++it)
 857                         dummy_syms.push_back(it->op(0));
 858                 if (symmetrize(r, dummy_syms).is_zero()) {
 859                         free_indices.clear();
 860                         return _ex0;
 861                 }
 862         }
 863
 864         // Dummy index renaming
 865         r = rename_dummy_indices(r, dummy_indices, local_dummy_indices);
 866
 867         // Product of indexed object with a scalar?
 868         if (is_exactly_a<mul>(r) && r.nops() == 2
 869          && is_exactly_a<numeric>(r.op(1)) && is_a<indexed>(r.op(0)))
 870                 return ex_to<basic>(r.op(0).op(0)).scalar_mul_indexed(r.op(0), ex_to<numeric>(r.op(1)));
 871         else
 872                 return r;
 873 }
 874
 875 /** This structure stores the original and symmetrized versions of terms
 876  *  obtained during the simplification of sums. */
 877 class terminfo {
 878 public:
 879         terminfo(const ex & orig_, const ex & symm_) : orig(orig_), symm(symm_) {}
 880
 881         ex orig; /**< original term */
 882         ex symm; /**< symmtrized term */
 883 };
 884
 885 class terminfo_is_less {
 886 public:
 887         bool operator() (const terminfo & ti1, const terminfo & ti2) const
 888         {
 889                 return (ti1.symm.compare(ti2.symm) < 0);
 890         }
 891 };
 892
 893 /** This structure stores the individual symmetrized terms obtained during
 894  *  the simplification of sums. */
 895 class symminfo {
 896 public:
 897         symminfo() : num(0) {}
 898
 899         symminfo(const ex & symmterm_, const ex & orig_, size_t num_) : orig(orig_), num(num_)
 900         {
 901                 if (is_exactly_a<mul>(symmterm_) && is_exactly_a<numeric>(symmterm_.op(symmterm_.nops()-1))) {
 902                         coeff = symmterm_.op(symmterm_.nops()-1);
 903                         symmterm = symmterm_ / coeff;
 904                 } else {
 905                         coeff = 1;
 906                         symmterm = symmterm_;
 907                 }
 908         }
 909
 910         ex symmterm;  /**< symmetrized term */
 911         ex coeff;     /**< coefficient of symmetrized term */
 912         ex orig;      /**< original term */
 913         size_t num; /**< how many symmetrized terms resulted from the original term */
 914 };
 915
 916 class symminfo_is_less_by_symmterm {
 917 public:
 918         bool operator() (const symminfo & si1, const symminfo & si2) const
 919         {
 920                 return (si1.symmterm.compare(si2.symmterm) < 0);
 921         }
 922 };
 923
 924 class symminfo_is_less_by_orig {
 925 public:
 926         bool operator() (const symminfo & si1, const symminfo & si2) const
 927         {
 928                 return (si1.orig.compare(si2.orig) < 0);
 929         }
 930 };
 931
 932 /** Simplify indexed expression, return list of free indices. */
 933 ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp)
 934 {
 935         // Expand the expression
 936         ex e_expanded = e.expand();
 937
 938         // Simplification of single indexed object: just find the free indices
 939         // and perform dummy index renaming/repositioning
 940         if (is_a<indexed>(e_expanded)) {
 941
 942                 // Find the dummy indices
 943                 const indexed &i = ex_to<indexed>(e_expanded);
 944                 exvector local_dummy_indices;
 945                 find_free_and_dummy(i.seq.begin() + 1, i.seq.end(), free_indices, local_dummy_indices);
 946
 947                 // Filter out the dummy indices with variance
 948                 exvector variant_dummy_indices;
 949                 find_variant_indices(local_dummy_indices, variant_dummy_indices);
 950
 951                 // Any indices with variance present at all?
 952                 if (!variant_dummy_indices.empty()) {
 953
 954                         // Yes, reposition them
 955                         exvector moved_indices;
 956                         reposition_dummy_indices(e_expanded, variant_dummy_indices, moved_indices);
 957                 }
 958
 959                 // Rename the dummy indices
 960                 return rename_dummy_indices(e_expanded, dummy_indices, local_dummy_indices);
 961         }
 962
 963         // Simplification of sum = sum of simplifications, check consistency of
 964         // free indices in each term
 965         if (is_exactly_a<add>(e_expanded)) {
 966                 bool first = true;
 967                 ex sum;
 968                 free_indices.clear();
 969
 970                 for (size_t i=0; i<e_expanded.nops(); i++) {
 971                         exvector free_indices_of_term;
 972                         ex term = simplify_indexed(e_expanded.op(i), free_indices_of_term, dummy_indices, sp);
 973                         if (!term.is_zero()) {
 974                                 if (first) {
 975                                         free_indices = free_indices_of_term;
 976                                         sum = term;
 977                                         first = false;
 978                                 } else {
 979                                         if (!indices_consistent(free_indices, free_indices_of_term)) {
 980                                                 std::ostringstream s;
 981                                                 s << "simplify_indexed: inconsistent indices in sum: ";
 982                                                 s << exprseq(free_indices) << " vs. " << exprseq(free_indices_of_term);
 983                                                 throw (std::runtime_error(s.str()));
 984                                         }
 985                                         if (is_a<indexed>(sum) && is_a<indexed>(term))
 986                                                 sum = ex_to<basic>(sum.op(0)).add_indexed(sum, term);
 987                                         else
 988                                                 sum += term;
 989                                 }
 990                         }
 991                 }
 992
 993                 // If the sum turns out to be zero, we are finished
 994                 if (sum.is_zero()) {
 995                         free_indices.clear();
 996                         return sum;
 997                 }
 998
 999                 // More than one term and more than one dummy index?
1000                 size_t num_terms_orig = (is_exactly_a<add>(sum) ? sum.nops() : 1);
1001                 if (num_terms_orig < 2 || dummy_indices.size() < 2)
1002                         return sum;
1003
1004                 // Yes, construct vector of all dummy index symbols
1005                 exvector dummy_syms;
1006                 dummy_syms.reserve(dummy_indices.size());
1007                 for (exvector::const_iterator it = dummy_indices.begin(); it != dummy_indices.end(); ++it)
1008                         dummy_syms.push_back(it->op(0));
1009
1010                 // Chop the sum into terms and symmetrize each one over the dummy
1011                 // indices
1012                 std::vector<terminfo> terms;
1013                 for (size_t i=0; i<sum.nops(); i++) {
1014                         const ex & term = sum.op(i);
1015                         ex term_symm = symmetrize(term, dummy_syms);
1016                         if (term_symm.is_zero())
1017                                 continue;
1018                         terms.push_back(terminfo(term, term_symm));
1019                 }
1020
1021                 // Sort by symmetrized terms
1022                 std::sort(terms.begin(), terms.end(), terminfo_is_less());
1023
1024                 // Combine equal symmetrized terms
1025                 std::vector<terminfo> terms_pass2;
1026                 for (std::vector<terminfo>::const_iterator i=terms.begin(); i!=terms.end(); ) {
1027                         size_t num = 1;
1028                         std::vector<terminfo>::const_iterator j = i + 1;
1029                         while (j != terms.end() && j->symm == i->symm) {
1030                                 num++;
1031                                 j++;
1032                         }
1033                         terms_pass2.push_back(terminfo(i->orig * num, i->symm * num));
1034                         i = j;
1035                 }
1036
1037                 // If there is only one term left, we are finished
1038                 if (terms_pass2.size() == 1)
1039                         return terms_pass2[0].orig;
1040
1041                 // Chop the symmetrized terms into subterms
1042                 std::vector<symminfo> sy;
1043                 for (std::vector<terminfo>::const_iterator i=terms_pass2.begin(); i!=terms_pass2.end(); ++i) {
1044                         if (is_exactly_a<add>(i->symm)) {
1045                                 size_t num = i->symm.nops();
1046                                 for (size_t j=0; j<num; j++)
1047                                         sy.push_back(symminfo(i->symm.op(j), i->orig, num));
1048                         } else
1049                                 sy.push_back(symminfo(i->symm, i->orig, 1));
1050                 }
1051
1052                 // Sort by symmetrized subterms
1053                 std::sort(sy.begin(), sy.end(), symminfo_is_less_by_symmterm());
1054
1055                 // Combine equal symmetrized subterms
1056                 std::vector<symminfo> sy_pass2;
1057                 exvector result;
1058                 for (std::vector<symminfo>::const_iterator i=sy.begin(); i!=sy.end(); ) {
1059
1060                         // Combine equal terms
1061                         std::vector<symminfo>::const_iterator j = i + 1;
1062                         if (j != sy.end() && j->symmterm == i->symmterm) {
1063
1064                                 // More than one term, collect the coefficients
1065                                 ex coeff = i->coeff;
1066                                 while (j != sy.end() && j->symmterm == i->symmterm) {
1067                                         coeff += j->coeff;
1068                                         j++;
1069                                 }
1070
1071                                 // Add combined term to result
1072                                 if (!coeff.is_zero())
1073                                         result.push_back(coeff * i->symmterm);
1074
1075                         } else {
1076
1077                                 // Single term, store for second pass
1078                                 sy_pass2.push_back(*i);
1079                         }
1080
1081                         i = j;
1082                 }
1083
1084                 // Were there any remaining terms that didn't get combined?
1085                 if (sy_pass2.size() > 0) {
1086
1087                         // Yes, sort by their original terms
1088                         std::sort(sy_pass2.begin(), sy_pass2.end(), symminfo_is_less_by_orig());
1089
1090                         for (std::vector<symminfo>::const_iterator i=sy_pass2.begin(); i!=sy_pass2.end(); ) {
1091
1092                                 // How many symmetrized terms of this original term are left?
1093                                 size_t num = 1;
1094                                 std::vector<symminfo>::const_iterator j = i + 1;
1095                                 while (j != sy_pass2.end() && j->orig == i->orig) {
1096                                         num++;
1097                                         j++;
1098                                 }
1099
1100                                 if (num == i->num) {
1101
1102                                         // All terms left, then add the original term to the result
1103                                         result.push_back(i->orig);
1104
1105                                 } else {
1106
1107                                         // Some terms were combined with others, add up the remaining symmetrized terms
1108                                         std::vector<symminfo>::const_iterator k;
1109                                         for (k=i; k!=j; k++)
1110                                                 result.push_back(k->coeff * k->symmterm);
1111                                 }
1112
1113                                 i = j;
1114                         }
1115                 }
1116
1117                 // Add all resulting terms
1118                 ex sum_symm = (new add(result))->setflag(status_flags::dynallocated);
1119                 if (sum_symm.is_zero())
1120                         free_indices.clear();
1121                 return sum_symm;
1122         }
1123
1124         // Simplification of products
1125         if (is_exactly_a<mul>(e_expanded)
1126          || is_exactly_a<ncmul>(e_expanded)
1127          || (is_exactly_a<power>(e_expanded) && is_a<indexed>(e_expanded.op(0)) && e_expanded.op(1).is_equal(_ex2)))
1128                 return simplify_indexed_product(e_expanded, free_indices, dummy_indices, sp);
1129
1130         // Cannot do anything
1131         free_indices.clear();
1132         return e_expanded;
1133 }
1134
1135 /** Simplify/canonicalize expression containing indexed objects. This
1136  *  performs contraction of dummy indices where possible and checks whether
1137  *  the free indices in sums are consistent.
1138  *
1139  *  @param options Simplification options (currently unused)
1140  *  @return simplified expression */
1141 ex ex::simplify_indexed(unsigned options) const
1142 {
1143         exvector free_indices, dummy_indices;
1144         scalar_products sp;
1145         return GiNaC::simplify_indexed(*this, free_indices, dummy_indices, sp);
1146 }
1147
1148 /** Simplify/canonicalize expression containing indexed objects. This
1149  *  performs contraction of dummy indices where possible, checks whether
1150  *  the free indices in sums are consistent, and automatically replaces
1151  *  scalar products by known values if desired.
1152  *
1153  *  @param sp Scalar products to be replaced automatically
1154  *  @param options Simplification options (currently unused)
1155  *  @return simplified expression */
1156 ex ex::simplify_indexed(const scalar_products & sp, unsigned options) const
1157 {
1158         exvector free_indices, dummy_indices;
1159         return GiNaC::simplify_indexed(*this, free_indices, dummy_indices, sp);
1160 }
1161
1162 /** Symmetrize expression over its free indices. */
1163 ex ex::symmetrize() const
1164 {
1165         return GiNaC::symmetrize(*this, get_free_indices());
1166 }
1167
1168 /** Antisymmetrize expression over its free indices. */
1169 ex ex::antisymmetrize() const
1170 {
1171         return GiNaC::antisymmetrize(*this, get_free_indices());
1172 }
1173
1174 /** Symmetrize expression by cyclic permutation over its free indices. */
1175 ex ex::symmetrize_cyclic() const
1176 {
1177         return GiNaC::symmetrize_cyclic(*this, get_free_indices());
1178 }
1179
1180 //////////
1181 // helper classes
1182 //////////
1183
1184 spmapkey::spmapkey(const ex & v1_, const ex & v2_, const ex & dim_) : dim(dim_)
1185 {
1186         // If indexed, extract base objects
1187         ex s1 = is_a<indexed>(v1_) ? v1_.op(0) : v1_;
1188         ex s2 = is_a<indexed>(v2_) ? v2_.op(0) : v2_;
1189
1190         // Enforce canonical order in pair
1191         if (s1.compare(s2) > 0) {
1192                 v1 = s2;
1193                 v2 = s1;
1194         } else {
1195                 v1 = s1;
1196                 v2 = s2;
1197         }
1198 }
1199
1200 bool spmapkey::operator==(const spmapkey &other) const
1201 {
1202         if (!v1.is_equal(other.v1))
1203                 return false;
1204         if (!v2.is_equal(other.v2))
1205                 return false;
1206         if (is_a<wildcard>(dim) || is_a<wildcard>(other.dim))
1207                 return true;
1208         else
1209                 return dim.is_equal(other.dim);
1210 }
1211
1212 bool spmapkey::operator<(const spmapkey &other) const
1213 {
1214         int cmp = v1.compare(other.v1);
1215         if (cmp)
1216                 return cmp < 0;
1217         cmp = v2.compare(other.v2);
1218         if (cmp)
1219                 return cmp < 0;
1220
1221         // Objects are equal, now check dimensions
1222         if (is_a<wildcard>(dim) || is_a<wildcard>(other.dim))
1223                 return false;
1224         else
1225                 return dim.compare(other.dim) < 0;
1226 }
1227
1228 void spmapkey::debugprint() const
1229 {
1230         std::cerr << "(" << v1 << "," << v2 << "," << dim << ")";
1231 }
1232
1233 void scalar_products::add(const ex & v1, const ex & v2, const ex & sp)
1234 {
1235         spm[spmapkey(v1, v2)] = sp;
1236 }
1237
1238 void scalar_products::add(const ex & v1, const ex & v2, const ex & dim, const ex & sp)
1239 {
1240         spm[spmapkey(v1, v2, dim)] = sp;
1241 }
1242
1243 void scalar_products::add_vectors(const lst & l, const ex & dim)
1244 {
1245         // Add all possible pairs of products
1246         for (lst::const_iterator it1 = l.begin(); it1 != l.end(); ++it1)
1247                 for (lst::const_iterator it2 = l.begin(); it2 != l.end(); ++it2)
1248                         add(*it1, *it2, *it1 * *it2);
1249 }
1250
1251 void scalar_products::clear()
1252 {
1253         spm.clear();
1254 }
1255
1256 /** Check whether scalar product pair is defined. */
1257 bool scalar_products::is_defined(const ex & v1, const ex & v2, const ex & dim) const
1258 {
1259         return spm.find(spmapkey(v1, v2, dim)) != spm.end();
1260 }
1261
1262 /** Return value of defined scalar product pair. */
1263 ex scalar_products::evaluate(const ex & v1, const ex & v2, const ex & dim) const
1264 {
1265         return spm.find(spmapkey(v1, v2, dim))->second;
1266 }
1267
1268 void scalar_products::debugprint() const
1269 {
1270         std::cerr << "map size=" << spm.size() << std::endl;
1271         spmap::const_iterator i = spm.begin(), end = spm.end();
1272         while (i != end) {
1273                 const spmapkey & k = i->first;
1274                 std::cerr << "item key=";
1275                 k.debugprint();
1276                 std::cerr << ", value=" << i->second << std::endl;
1277                 ++i;
1278         }
1279 }
1280
1281 } // namespace GiNaC