ginac/indexed.cpp

   1 /** @file indexed.cpp
   2  *
   3  *  Implementation of GiNaC's indexed expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2001 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 <stdexcept>
  24
  25 #include "indexed.h"
  26 #include "idx.h"
  27 #include "add.h"
  28 #include "mul.h"
  29 #include "ncmul.h"
  30 #include "power.h"
  31 #include "archive.h"
  32 #include "utils.h"
  33 #include "debugmsg.h"
  34
  35 namespace GiNaC {
  36
  37 GINAC_IMPLEMENT_REGISTERED_CLASS(indexed, exprseq)
  38
  39 //////////
  40 // default constructor, destructor, copy constructor assignment operator and helpers
  41 //////////
  42
  43 indexed::indexed() : symmetry(unknown)
  44 {
  45         debugmsg("indexed default constructor", LOGLEVEL_CONSTRUCT);
  46         tinfo_key = TINFO_indexed;
  47 }
  48
  49 void indexed::copy(const indexed & other)
  50 {
  51         inherited::copy(other);
  52         symmetry = other.symmetry;
  53 }
  54
  55 DEFAULT_DESTROY(indexed)
  56
  57 //////////
  58 // other constructors
  59 //////////
  60
  61 indexed::indexed(const ex & b) : inherited(b), symmetry(unknown)
  62 {
  63         debugmsg("indexed constructor from ex", LOGLEVEL_CONSTRUCT);
  64         tinfo_key = TINFO_indexed;
  65         assert_all_indices_of_type_idx();
  66 }
  67
  68 indexed::indexed(const ex & b, const ex & i1) : inherited(b, i1), symmetry(unknown)
  69 {
  70         debugmsg("indexed constructor from ex,ex", LOGLEVEL_CONSTRUCT);
  71         tinfo_key = TINFO_indexed;
  72         assert_all_indices_of_type_idx();
  73 }
  74
  75 indexed::indexed(const ex & b, const ex & i1, const ex & i2) : inherited(b, i1, i2), symmetry(unknown)
  76 {
  77         debugmsg("indexed constructor from ex,ex,ex", LOGLEVEL_CONSTRUCT);
  78         tinfo_key = TINFO_indexed;
  79         assert_all_indices_of_type_idx();
  80 }
  81
  82 indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symmetry(unknown)
  83 {
  84         debugmsg("indexed constructor from ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
  85         tinfo_key = TINFO_indexed;
  86         assert_all_indices_of_type_idx();
  87 }
  88
  89 indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symmetry(unknown)
  90 {
  91         debugmsg("indexed constructor from ex,ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
  92         tinfo_key = TINFO_indexed;
  93         assert_all_indices_of_type_idx();
  94 }
  95
  96 indexed::indexed(const ex & b, symmetry_type symm, const ex & i1, const ex & i2) : inherited(b, i1, i2), symmetry(symm)
  97 {
  98         debugmsg("indexed constructor from ex,symmetry,ex,ex", LOGLEVEL_CONSTRUCT);
  99         tinfo_key = TINFO_indexed;
 100         assert_all_indices_of_type_idx();
 101 }
 102
 103 indexed::indexed(const ex & b, symmetry_type symm, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symmetry(symm)
 104 {
 105         debugmsg("indexed constructor from ex,symmetry,ex,ex,ex", LOGLEVEL_CONSTRUCT);
 106         tinfo_key = TINFO_indexed;
 107         assert_all_indices_of_type_idx();
 108 }
 109
 110 indexed::indexed(const ex & b, symmetry_type symm, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symmetry(symm)
 111 {
 112         debugmsg("indexed constructor from ex,symmetry,ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
 113         tinfo_key = TINFO_indexed;
 114         assert_all_indices_of_type_idx();
 115 }
 116
 117 indexed::indexed(const ex & b, const exvector & v) : inherited(b), symmetry(unknown)
 118 {
 119         debugmsg("indexed constructor from ex,exvector", LOGLEVEL_CONSTRUCT);
 120         seq.insert(seq.end(), v.begin(), v.end());
 121         tinfo_key = TINFO_indexed;
 122         assert_all_indices_of_type_idx();
 123 }
 124
 125 indexed::indexed(const ex & b, symmetry_type symm, const exvector & v) : inherited(b), symmetry(symm)
 126 {
 127         debugmsg("indexed constructor from ex,symmetry,exvector", LOGLEVEL_CONSTRUCT);
 128         seq.insert(seq.end(), v.begin(), v.end());
 129         tinfo_key = TINFO_indexed;
 130         assert_all_indices_of_type_idx();
 131 }
 132
 133 indexed::indexed(symmetry_type symm, const exprseq & es) : inherited(es), symmetry(symm)
 134 {
 135         debugmsg("indexed constructor from symmetry,exprseq", LOGLEVEL_CONSTRUCT);
 136         tinfo_key = TINFO_indexed;
 137         assert_all_indices_of_type_idx();
 138 }
 139
 140 indexed::indexed(symmetry_type symm, const exvector & v, bool discardable) : inherited(v, discardable), symmetry(symm)
 141 {
 142         debugmsg("indexed constructor from symmetry,exvector", LOGLEVEL_CONSTRUCT);
 143         tinfo_key = TINFO_indexed;
 144         assert_all_indices_of_type_idx();
 145 }
 146
 147 indexed::indexed(symmetry_type symm, exvector * vp) : inherited(vp), symmetry(symm)
 148 {
 149         debugmsg("indexed constructor from symmetry,exvector *", LOGLEVEL_CONSTRUCT);
 150         tinfo_key = TINFO_indexed;
 151         assert_all_indices_of_type_idx();
 152 }
 153
 154 //////////
 155 // archiving
 156 //////////
 157
 158 indexed::indexed(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 159 {
 160         debugmsg("indexed constructor from archive_node", LOGLEVEL_CONSTRUCT);
 161         unsigned int symm;
 162         if (!(n.find_unsigned("symmetry", symm)))
 163                 throw (std::runtime_error("unknown indexed symmetry type in archive"));
 164 }
 165
 166 void indexed::archive(archive_node &n) const
 167 {
 168         inherited::archive(n);
 169         n.add_unsigned("symmetry", symmetry);
 170 }
 171
 172 DEFAULT_UNARCHIVE(indexed)
 173
 174 //////////
 175 // functions overriding virtual functions from bases classes
 176 //////////
 177
 178 void indexed::printraw(std::ostream & os) const
 179 {
 180         debugmsg("indexed printraw", LOGLEVEL_PRINT);
 181         GINAC_ASSERT(seq.size() > 0);
 182
 183         os << class_name() << "(";
 184         seq[0].printraw(os);
 185         os << ",indices=";
 186         printrawindices(os);
 187         os << ",hash=" << hashvalue << ",flags=" << flags << ")";
 188 }
 189
 190 void indexed::printtree(std::ostream & os, unsigned indent) const
 191 {
 192         debugmsg("indexed printtree", LOGLEVEL_PRINT);
 193         GINAC_ASSERT(seq.size() > 0);
 194
 195         os << std::string(indent, ' ') << class_name() << ", " << seq.size()-1 << " indices";
 196         os << ",hash=" << hashvalue << ",flags=" << flags << std::endl;
 197         printtreeindices(os, indent);
 198 }
 199
 200 void indexed::print(std::ostream & os, unsigned upper_precedence) const
 201 {
 202         debugmsg("indexed print", LOGLEVEL_PRINT);
 203         GINAC_ASSERT(seq.size() > 0);
 204
 205         const ex & base = seq[0];
 206         bool need_parens = is_ex_exactly_of_type(base, add) || is_ex_exactly_of_type(base, mul)
 207                         || is_ex_exactly_of_type(base, ncmul) || is_ex_exactly_of_type(base, power);
 208         if (need_parens)
 209                 os << "(";
 210         os << base;
 211         if (need_parens)
 212                 os << ")";
 213         printindices(os);
 214 }
 215
 216 bool indexed::info(unsigned inf) const
 217 {
 218         if (inf == info_flags::indexed) return true;
 219         if (inf == info_flags::has_indices) return seq.size() > 1;
 220         return inherited::info(inf);
 221 }
 222
 223 bool indexed::all_index_values_are(unsigned inf) const
 224 {
 225         // No indices? Then no property can be fulfilled
 226         if (seq.size() < 2)
 227                 return false;
 228
 229         // Check all indices
 230         exvector::const_iterator it = seq.begin() + 1, itend = seq.end();
 231         while (it != itend) {
 232                 GINAC_ASSERT(is_ex_of_type(*it, idx));
 233                 if (!ex_to_idx(*it).get_value().info(inf))
 234                         return false;
 235                 it++;
 236         }
 237         return true;
 238 }
 239
 240 int indexed::compare_same_type(const basic & other) const
 241 {
 242         GINAC_ASSERT(is_of_type(other, indexed));
 243         return inherited::compare_same_type(other);
 244 }
 245
 246 // The main difference between sort_index_vector() and canonicalize_indices()
 247 // is that the latter takes the symmetry of the object into account. Once we
 248 // implement mixed symmetries, canonicalize_indices() will only be able to
 249 // reorder index pairs with known symmetry properties, while sort_index_vector()
 250 // always sorts the whole vector.
 251
 252 /** Bring a vector of indices into a canonic order (don't care about the
 253  *  symmetry of the objects carrying the indices). Dummy indices will lie
 254  *  next to each other after the sorting.
 255  *
 256  *  @param v Index vector to be sorted */
 257 static void sort_index_vector(exvector &v)
 258 {
 259         // Nothing to sort if less than 2 elements
 260         if (v.size() < 2)
 261                 return;
 262
 263         // Simple bubble sort algorithm should be sufficient for the small
 264         // number of indices expected
 265         exvector::iterator it1 = v.begin(), itend = v.end(), next_to_last_idx = itend - 1;
 266         while (it1 != next_to_last_idx) {
 267                 exvector::iterator it2 = it1 + 1;
 268                 while (it2 != itend) {
 269                         if (it1->compare(*it2) > 0)
 270                                 it1->swap(*it2);
 271                         it2++;
 272                 }
 273                 it1++;
 274         }
 275 }
 276
 277 /** Bring a vector of indices into a canonic order. This operation only makes
 278  *  sense if the object carrying these indices is either symmetric or totally
 279  *  antisymmetric with respect to the indices.
 280  *
 281  *  @param itbegin Start of index vector
 282  *  @param itend End of index vector
 283  *  @param antisymm Whether the object is antisymmetric
 284  *  @return the sign introduced by the reordering of the indices if the object
 285  *          is antisymmetric (or 0 if two equal indices are encountered). For
 286  *          symmetric objects, this is always +1. If the index vector was
 287  *          already in a canonic order this function returns INT_MAX. */
 288 static int canonicalize_indices(exvector::iterator itbegin, exvector::iterator itend, bool antisymm)
 289 {
 290         bool something_changed = false;
 291         int sig = 1;
 292
 293         // Simple bubble sort algorithm should be sufficient for the small
 294         // number of indices expected
 295         exvector::iterator it1 = itbegin, next_to_last_idx = itend - 1;
 296         while (it1 != next_to_last_idx) {
 297                 exvector::iterator it2 = it1 + 1;
 298                 while (it2 != itend) {
 299                         int cmpval = it1->compare(*it2);
 300                         if (cmpval == 1) {
 301                                 it1->swap(*it2);
 302                                 something_changed = true;
 303                                 if (antisymm)
 304                                         sig = -sig;
 305                         } else if (cmpval == 0 && antisymm) {
 306                                 something_changed = true;
 307                                 sig = 0;
 308                         }
 309                         it2++;
 310                 }
 311                 it1++;
 312         }
 313
 314         return something_changed ? sig : INT_MAX;
 315 }
 316
 317 ex indexed::eval(int level) const
 318 {
 319         // First evaluate children, then we will end up here again
 320         if (level > 1)
 321                 return indexed(symmetry, evalchildren(level));
 322
 323         const ex &base = seq[0];
 324
 325         // If the base object is 0, the whole object is 0
 326         if (base.is_zero())
 327                 return _ex0();
 328
 329         // If the base object is a product, pull out the numeric factor
 330         if (is_ex_exactly_of_type(base, mul) && is_ex_exactly_of_type(base.op(base.nops() - 1), numeric)) {
 331                 exvector v = seq;
 332                 ex f = ex_to_numeric(base.op(base.nops() - 1));
 333                 v[0] = seq[0] / f;
 334                 return f * thisexprseq(v);
 335         }
 336
 337         // Canonicalize indices according to the symmetry properties
 338         if (seq.size() > 2 && (symmetry != unknown && symmetry != mixed)) {
 339                 exvector v = seq;
 340                 int sig = canonicalize_indices(v.begin() + 1, v.end(), symmetry == antisymmetric);
 341                 if (sig != INT_MAX) {
 342                         // Something has changed while sorting indices, more evaluations later
 343                         if (sig == 0)
 344                                 return _ex0();
 345                         return ex(sig) * thisexprseq(v);
 346                 }
 347         }
 348
 349         // Let the class of the base object perform additional evaluations
 350         return base.bp->eval_indexed(*this);
 351 }
 352
 353 ex indexed::thisexprseq(const exvector & v) const
 354 {
 355         return indexed(symmetry, v);
 356 }
 357
 358 ex indexed::thisexprseq(exvector * vp) const
 359 {
 360         return indexed(symmetry, vp);
 361 }
 362
 363 ex indexed::expand(unsigned options) const
 364 {
 365         GINAC_ASSERT(seq.size() > 0);
 366
 367         if ((options & expand_options::expand_indexed) && is_ex_exactly_of_type(seq[0], add)) {
 368
 369                 // expand_indexed expands (a+b).i -> a.i + b.i
 370                 const ex & base = seq[0];
 371                 ex sum = _ex0();
 372                 for (unsigned i=0; i<base.nops(); i++) {
 373                         exvector s = seq;
 374                         s[0] = base.op(i);
 375                         sum += thisexprseq(s).expand();
 376                 }
 377                 return sum;
 378
 379         } else
 380                 return inherited::expand(options);
 381 }
 382
 383 //////////
 384 // virtual functions which can be overridden by derived classes
 385 //////////
 386
 387 // none
 388
 389 //////////
 390 // non-virtual functions in this class
 391 //////////
 392
 393 void indexed::printrawindices(std::ostream & os) const
 394 {
 395         if (seq.size() > 1) {
 396                 exvector::const_iterator it=seq.begin() + 1, itend = seq.end();
 397                 while (it != itend) {
 398                         it->printraw(os);
 399                         it++;
 400                         if (it != itend)
 401                                 os << ",";
 402                 }
 403         }
 404 }
 405
 406 void indexed::printtreeindices(std::ostream & os, unsigned indent) const
 407 {
 408         if (seq.size() > 1) {
 409                 exvector::const_iterator it=seq.begin() + 1, itend = seq.end();
 410                 while (it != itend) {
 411                         os << std::string(indent + delta_indent, ' ');
 412                         it->printraw(os);
 413                         os << std::endl;
 414                         it++;
 415                 }
 416         }
 417 }
 418
 419 void indexed::printindices(std::ostream & os) const
 420 {
 421         if (seq.size() > 1) {
 422                 exvector::const_iterator it=seq.begin() + 1, itend = seq.end();
 423                 while (it != itend) {
 424                         it->print(os);
 425                         it++;
 426                 }
 427         }
 428 }
 429
 430 /** Check whether all indices are of class idx. This function is used
 431  *  internally to make sure that all constructed indexed objects really
 432  *  carry indices and not some other classes. */
 433 void indexed::assert_all_indices_of_type_idx(void) const
 434 {
 435         GINAC_ASSERT(seq.size() > 0);
 436         exvector::const_iterator it = seq.begin() + 1, itend = seq.end();
 437         while (it != itend) {
 438                 if (!is_ex_of_type(*it, idx))
 439                         throw(std::invalid_argument("indices of indexed object must be of type idx"));
 440                 it++;
 441         }
 442 }
 443
 444 //////////
 445 // global functions
 446 //////////
 447
 448 /** Check whether two sorted index vectors are consistent (i.e. equal). */
 449 static bool indices_consistent(const exvector & v1, const exvector & v2)
 450 {
 451         // Number of indices must be the same
 452         if (v1.size() != v2.size())
 453                 return false;
 454
 455         // And also the indices themselves
 456         exvector::const_iterator ait = v1.begin(), aitend = v1.end(),
 457                                  bit = v2.begin(), bitend = v2.end();
 458         while (ait != aitend) {
 459                 if (!ait->is_equal(*bit))
 460                         return false;
 461                 ait++; bit++;
 462         }
 463         return true;
 464 }
 465
 466 exvector indexed::get_indices(void) const
 467 {
 468         GINAC_ASSERT(seq.size() >= 1);
 469         return exvector(seq.begin() + 1, seq.end());
 470 }
 471
 472 exvector indexed::get_dummy_indices(void) const
 473 {
 474         exvector free_indices, dummy_indices;
 475         find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices);
 476         return dummy_indices;
 477 }
 478
 479 exvector indexed::get_dummy_indices(const indexed & other) const
 480 {
 481         exvector indices = get_free_indices();
 482         exvector other_indices = other.get_free_indices();
 483         indices.insert(indices.end(), other_indices.begin(), other_indices.end());
 484         exvector dummy_indices;
 485         find_dummy_indices(indices, dummy_indices);
 486         return dummy_indices;
 487 }
 488
 489 exvector indexed::get_free_indices(void) const
 490 {
 491         exvector free_indices, dummy_indices;
 492         find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices);
 493         return free_indices;
 494 }
 495
 496 exvector add::get_free_indices(void) const
 497 {
 498         exvector free_indices;
 499         for (unsigned i=0; i<nops(); i++) {
 500                 if (i == 0)
 501                         free_indices = op(i).get_free_indices();
 502                 else {
 503                         exvector free_indices_of_term = op(i).get_free_indices();
 504                         if (!indices_consistent(free_indices, free_indices_of_term))
 505                                 throw (std::runtime_error("add::get_free_indices: inconsistent indices in sum"));
 506                 }
 507         }
 508         return free_indices;
 509 }
 510
 511 exvector mul::get_free_indices(void) const
 512 {
 513         // Concatenate free indices of all factors
 514         exvector un;
 515         for (unsigned i=0; i<nops(); i++) {
 516                 exvector free_indices_of_factor = op(i).get_free_indices();
 517                 un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
 518         }
 519
 520         // And remove the dummy indices
 521         exvector free_indices, dummy_indices;
 522         find_free_and_dummy(un, free_indices, dummy_indices);
 523         return free_indices;
 524 }
 525
 526 exvector ncmul::get_free_indices(void) const
 527 {
 528         // Concatenate free indices of all factors
 529         exvector un;
 530         for (unsigned i=0; i<nops(); i++) {
 531                 exvector free_indices_of_factor = op(i).get_free_indices();
 532                 un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
 533         }
 534
 535         // And remove the dummy indices
 536         exvector free_indices, dummy_indices;
 537         find_free_and_dummy(un, free_indices, dummy_indices);
 538         return free_indices;
 539 }
 540
 541 exvector power::get_free_indices(void) const
 542 {
 543         // Return free indices of basis
 544         return basis.get_free_indices();
 545 }
 546
 547 /** Simplify product of indexed expressions (commutative, noncommutative and
 548  *  simple squares), return list of free indices. */
 549 ex simplify_indexed_product(const ex & e, exvector & free_indices, const scalar_products & sp)
 550 {
 551         // Remember whether the product was commutative or noncommutative
 552         // (because we chop it into factors and need to reassemble later)
 553         bool non_commutative = is_ex_exactly_of_type(e, ncmul);
 554
 555         // Collect factors in an exvector, store squares twice
 556         exvector v;
 557         v.reserve(e.nops() * 2);
 558
 559         if (is_ex_exactly_of_type(e, power)) {
 560                 // We only get called for simple squares, split a^2 -> a*a
 561                 GINAC_ASSERT(e.op(1).is_equal(_ex2()));
 562                 v.push_back(e.op(0));
 563                 v.push_back(e.op(0));
 564         } else {
 565                 for (int i=0; i<e.nops(); i++) {
 566                         ex f = e.op(i);
 567                         if (is_ex_exactly_of_type(f, power) && f.op(1).is_equal(_ex2())) {
 568                                 v.push_back(f.op(0));
 569                     v.push_back(f.op(0));
 570                         } else if (is_ex_exactly_of_type(f, ncmul)) {
 571                                 // Noncommutative factor found, split it as well
 572                                 non_commutative = true; // everything becomes noncommutative, ncmul will sort out the commutative factors later
 573                                 for (int j=0; j<f.nops(); j++)
 574                                         v.push_back(f.op(j));
 575                         } else
 576                                 v.push_back(f);
 577                 }
 578         }
 579
 580         // Perform contractions
 581         bool something_changed = false;
 582         GINAC_ASSERT(v.size() > 1);
 583         exvector::iterator it1, itend = v.end(), next_to_last = itend - 1;
 584         for (it1 = v.begin(); it1 != next_to_last; it1++) {
 585
 586 try_again:
 587                 if (!is_ex_of_type(*it1, indexed))
 588                         continue;
 589
 590                 // Indexed factor found, look for contraction candidates
 591                 exvector::iterator it2;
 592                 for (it2 = it1 + 1; it2 != itend; it2++) {
 593
 594                         if (!is_ex_of_type(*it2, indexed))
 595                                 continue;
 596
 597                         // Check whether the two factors share dummy indices
 598                         exvector un(ex_to_indexed(*it1).seq.begin() + 1, ex_to_indexed(*it1).seq.end());
 599                         un.insert(un.end(), ex_to_indexed(*it2).seq.begin() + 1, ex_to_indexed(*it2).seq.end());
 600                         exvector free, dummy;
 601                         find_free_and_dummy(un, free, dummy);
 602                         if (dummy.size() == 0)
 603                                 continue;
 604
 605                         // At least one dummy index, is it a defined scalar product?
 606                         if (free.size() == 0) {
 607                                 if (sp.is_defined(*it1, *it2)) {
 608                                         *it1 = sp.evaluate(*it1, *it2);
 609                                         *it2 = _ex1();
 610                                         something_changed = true;
 611                                         goto try_again;
 612                                 }
 613                         }
 614
 615                         // Contraction of symmetric with antisymmetric object is zero
 616                         if ((ex_to_indexed(*it1).symmetry == indexed::symmetric &&
 617                              ex_to_indexed(*it2).symmetry == indexed::antisymmetric
 618                           || ex_to_indexed(*it1).symmetry == indexed::antisymmetric &&
 619                              ex_to_indexed(*it2).symmetry == indexed::symmetric)
 620                          && dummy.size() > 1) {
 621                                 free_indices.clear();
 622                                 return _ex0();
 623                         }
 624
 625                         // Try to contract the first one with the second one
 626                         bool contracted = it1->op(0).bp->contract_with(it1, it2, v);
 627                         if (!contracted) {
 628
 629                                 // That didn't work; maybe the second object knows how to
 630                                 // contract itself with the first one
 631                                 contracted = it2->op(0).bp->contract_with(it2, it1, v);
 632                         }
 633                         if (contracted) {
 634                                 something_changed = true;
 635
 636                                 // Both objects may have new indices now or they might
 637                                 // even not be indexed objects any more, so we have to
 638                                 // start over
 639                                 goto try_again;
 640                         }
 641                 }
 642         }
 643
 644         // Find free indices (concatenate them all and call find_free_and_dummy())
 645         exvector un, dummy_indices;
 646         it1 = v.begin(); itend = v.end();
 647         while (it1 != itend) {
 648                 if (is_ex_of_type(*it1, indexed)) {
 649                         const indexed & o = ex_to_indexed(*it1);
 650                         un.insert(un.end(), o.seq.begin() + 1, o.seq.end());
 651                 }
 652                 it1++;
 653         }
 654         find_free_and_dummy(un, free_indices, dummy_indices);
 655
 656         ex r;
 657         if (something_changed) {
 658                 if (non_commutative)
 659                         r = ncmul(v);
 660                 else
 661                         r = mul(v);
 662         } else
 663                 r = e;
 664
 665         // Product of indexed object with a scalar?
 666         if (is_ex_exactly_of_type(r, mul) && r.nops() == 2
 667          && is_ex_exactly_of_type(r.op(1), numeric) && is_ex_of_type(r.op(0), indexed))
 668                 return r.op(0).op(0).bp->scalar_mul_indexed(r.op(0), ex_to_numeric(r.op(1)));
 669         else
 670                 return r;
 671 }
 672
 673 /** Simplify indexed expression, return list of free indices. */
 674 ex simplify_indexed(const ex & e, exvector & free_indices, const scalar_products & sp)
 675 {
 676         // Expand the expression
 677         ex e_expanded = e.expand();
 678
 679         // Simplification of single indexed object: just find the free indices
 680         if (is_ex_of_type(e_expanded, indexed)) {
 681                 const indexed &i = ex_to_indexed(e_expanded);
 682                 exvector dummy_indices;
 683                 find_free_and_dummy(i.seq.begin() + 1, i.seq.end(), free_indices, dummy_indices);
 684                 return e_expanded;
 685         }
 686
 687         // Simplification of sum = sum of simplifications, check consistency of
 688         // free indices in each term
 689         if (is_ex_exactly_of_type(e_expanded, add)) {
 690                 bool first = true;
 691                 ex sum = _ex0();
 692                 free_indices.clear();
 693
 694                 for (unsigned i=0; i<e_expanded.nops(); i++) {
 695                         exvector free_indices_of_term;
 696                         ex term = simplify_indexed(e_expanded.op(i), free_indices_of_term, sp);
 697                         if (!term.is_zero()) {
 698                                 if (first) {
 699                                         free_indices = free_indices_of_term;
 700                                         sum = term;
 701                                         first = false;
 702                                 } else {
 703                                         if (!indices_consistent(free_indices, free_indices_of_term))
 704                                                 throw (std::runtime_error("simplify_indexed: inconsistent indices in sum"));
 705                                         if (is_ex_of_type(sum, indexed) && is_ex_of_type(term, indexed))
 706                                                 sum = sum.op(0).bp->add_indexed(sum, term);
 707                                         else
 708                                                 sum += term;
 709                                 }
 710                         }
 711                 }
 712
 713                 return sum;
 714         }
 715
 716         // Simplification of products
 717         if (is_ex_exactly_of_type(e_expanded, mul)
 718          || is_ex_exactly_of_type(e_expanded, ncmul)
 719          || (is_ex_exactly_of_type(e_expanded, power) && is_ex_of_type(e_expanded.op(0), indexed) && e_expanded.op(1).is_equal(_ex2())))
 720                 return simplify_indexed_product(e_expanded, free_indices, sp);
 721
 722         // Cannot do anything
 723         free_indices.clear();
 724         return e_expanded;
 725 }
 726
 727 ex simplify_indexed(const ex & e)
 728 {
 729         exvector free_indices;
 730         scalar_products sp;
 731         return simplify_indexed(e, free_indices, sp);
 732 }
 733
 734 ex simplify_indexed(const ex & e, const scalar_products & sp)
 735 {
 736         exvector free_indices;
 737         return simplify_indexed(e, free_indices, sp);
 738 }
 739
 740 //////////
 741 // helper classes
 742 //////////
 743
 744 void scalar_products::add(const ex & v1, const ex & v2, const ex & sp)
 745 {
 746         spm[make_key(v1, v2)] = sp;
 747 }
 748
 749 void scalar_products::clear(void)
 750 {
 751         spm.clear();
 752 }
 753
 754 /** Check whether scalar product pair is defined. */
 755 bool scalar_products::is_defined(const ex & v1, const ex & v2) const
 756 {
 757         return spm.find(make_key(v1, v2)) != spm.end();
 758 }
 759
 760 /** Return value of defined scalar product pair. */
 761 ex scalar_products::evaluate(const ex & v1, const ex & v2) const
 762 {
 763         return spm.find(make_key(v1, v2))->second;
 764 }
 765
 766 void scalar_products::debugprint(void) const
 767 {
 768         std::cerr << "map size=" << spm.size() << std::endl;
 769         for (spmap::const_iterator cit=spm.begin(); cit!=spm.end(); ++cit) {
 770                 const spmapkey & k = cit->first;
 771                 std::cerr << "item key=(" << k.first << "," << k.second;
 772                 std::cerr << "), value=" << cit->second << std::endl;
 773         }
 774 }
 775
 776 /** Make key from object pair. */
 777 spmapkey scalar_products::make_key(const ex & v1, const ex & v2)
 778 {
 779         // If indexed, extract base objects
 780         ex s1 = is_ex_of_type(v1, indexed) ? v1.op(0) : v1;
 781         ex s2 = is_ex_of_type(v2, indexed) ? v2.op(0) : v2;
 782
 783         // Enforce canonical order in pair
 784         if (s1.compare(s2) > 0)
 785                 return spmapkey(s2, s1);
 786         else
 787                 return spmapkey(s1, s2);
 788 }
 789
 790 } // namespace GiNaC