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 /** Given a vector of indices, split them into two vectors, one containing
 449  *  the free indices, the other containing the dummy indices. */
 450 static void find_free_and_dummy(exvector::const_iterator it, exvector::const_iterator itend, exvector & out_free, exvector & out_dummy)
 451 {
 452         out_free.clear();
 453         out_dummy.clear();
 454
 455         // No indices? Then do nothing
 456         if (it == itend)
 457                 return;
 458
 459         // Only one index? Then it is a free one if it's not numeric
 460         if (itend - it == 1) {
 461                 if (ex_to_idx(*it).is_symbolic())
 462                         out_free.push_back(*it);
 463                 return;
 464         }
 465
 466         // Sort index vector. This will cause dummy indices come to lie next
 467         // to each other (because the sort order is defined to guarantee this).
 468         exvector v(it, itend);
 469         sort_index_vector(v);
 470
 471         // Find dummy pairs and free indices
 472         it = v.begin(); itend = v.end();
 473         exvector::const_iterator last = it++;
 474         while (it != itend) {
 475                 if (is_dummy_pair(*it, *last)) {
 476                         out_dummy.push_back(*last);
 477                         it++;
 478                         if (it == itend)
 479                                 return;
 480                 } else {
 481                         if (!it->is_equal(*last) && ex_to_idx(*last).is_symbolic())
 482                                 out_free.push_back(*last);
 483                 }
 484                 last = it++;
 485         }
 486         if (ex_to_idx(*last).is_symbolic())
 487                 out_free.push_back(*last);
 488 }
 489
 490 /** Check whether two sorted index vectors are consistent (i.e. equal). */
 491 static bool indices_consistent(const exvector & v1, const exvector & v2)
 492 {
 493         // Number of indices must be the same
 494         if (v1.size() != v2.size())
 495                 return false;
 496
 497         // And also the indices themselves
 498         exvector::const_iterator ait = v1.begin(), aitend = v1.end(),
 499                                  bit = v2.begin(), bitend = v2.end();
 500         while (ait != aitend) {
 501                 if (!ait->is_equal(*bit))
 502                         return false;
 503                 ait++; bit++;
 504         }
 505         return true;
 506 }
 507
 508 exvector indexed::get_dummy_indices(void) const
 509 {
 510         exvector free_indices, dummy_indices;
 511         find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices);
 512         return dummy_indices;
 513 }
 514
 515 exvector indexed::get_free_indices(void) const
 516 {
 517         exvector free_indices, dummy_indices;
 518         find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices);
 519         return free_indices;
 520 }
 521
 522 exvector add::get_free_indices(void) const
 523 {
 524         exvector free_indices;
 525         for (unsigned i=0; i<nops(); i++) {
 526                 if (i == 0)
 527                         free_indices = op(i).get_free_indices();
 528                 else {
 529                         exvector free_indices_of_term = op(i).get_free_indices();
 530                         if (!indices_consistent(free_indices, free_indices_of_term))
 531                                 throw (std::runtime_error("add::get_free_indices: inconsistent indices in sum"));
 532                 }
 533         }
 534         return free_indices;
 535 }
 536
 537 exvector mul::get_free_indices(void) const
 538 {
 539         // Concatenate free indices of all factors
 540         exvector un;
 541         for (unsigned i=0; i<nops(); i++) {
 542                 exvector free_indices_of_factor = op(i).get_free_indices();
 543                 un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
 544         }
 545
 546         // And remove the dummy indices
 547         exvector free_indices, dummy_indices;
 548         find_free_and_dummy(un.begin(), un.end(), free_indices, dummy_indices);
 549         return free_indices;
 550 }
 551
 552 exvector ncmul::get_free_indices(void) const
 553 {
 554         // Concatenate free indices of all factors
 555         exvector un;
 556         for (unsigned i=0; i<nops(); i++) {
 557                 exvector free_indices_of_factor = op(i).get_free_indices();
 558                 un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
 559         }
 560
 561         // And remove the dummy indices
 562         exvector free_indices, dummy_indices;
 563         find_free_and_dummy(un.begin(), un.end(), free_indices, dummy_indices);
 564         return free_indices;
 565 }
 566
 567 exvector power::get_free_indices(void) const
 568 {
 569         // Return free indices of basis
 570         return basis.get_free_indices();
 571 }
 572
 573 /** Simplify product of indexed expressions (commutative, noncommutative and
 574  *  simple squares), return list of free indices. */
 575 ex simplify_indexed_product(const ex & e, exvector & free_indices, const scalar_products & sp)
 576 {
 577         // Remember whether the product was commutative or noncommutative
 578         // (because we chop it into factors and need to reassemble later)
 579         bool non_commutative = is_ex_exactly_of_type(e, ncmul);
 580
 581         // Collect factors in an exvector, store squares twice
 582         exvector v;
 583         v.reserve(e.nops() * 2);
 584
 585         if (is_ex_exactly_of_type(e, power)) {
 586                 // We only get called for simple squares, split a^2 -> a*a
 587                 GINAC_ASSERT(e.op(1).is_equal(_ex2()));
 588                 v.push_back(e.op(0));
 589                 v.push_back(e.op(0));
 590         } else {
 591                 for (int i=0; i<e.nops(); i++) {
 592                         ex f = e.op(i);
 593                         if (is_ex_exactly_of_type(f, power) && f.op(1).is_equal(_ex2())) {
 594                                 v.push_back(f.op(0));
 595                     v.push_back(f.op(0));
 596                         } else if (is_ex_exactly_of_type(f, ncmul)) {
 597                                 // Noncommutative factor found, split it as well
 598                                 non_commutative = true; // everything becomes noncommutative, ncmul will sort out the commutative factors later
 599                                 for (int j=0; j<f.nops(); i++)
 600                                         v.push_back(f.op(j));
 601                         } else
 602                                 v.push_back(f);
 603                 }
 604         }
 605
 606         // Perform contractions
 607         bool something_changed = false;
 608         GINAC_ASSERT(v.size() > 1);
 609         exvector::iterator it1, itend = v.end(), next_to_last = itend - 1;
 610         for (it1 = v.begin(); it1 != next_to_last; it1++) {
 611
 612 try_again:
 613                 if (!is_ex_of_type(*it1, indexed))
 614                         continue;
 615
 616                 // Indexed factor found, look for contraction candidates
 617                 exvector::iterator it2;
 618                 for (it2 = it1 + 1; it2 != itend; it2++) {
 619
 620                         if (!is_ex_of_type(*it2, indexed))
 621                                 continue;
 622
 623                         // Check whether the two factors share dummy indices
 624                         exvector un(ex_to_indexed(*it1).seq.begin() + 1, ex_to_indexed(*it1).seq.end());
 625                         un.insert(un.end(), ex_to_indexed(*it2).seq.begin() + 1, ex_to_indexed(*it2).seq.end());
 626                         exvector free, dummy;
 627                         find_free_and_dummy(un.begin(), un.end(), free, dummy);
 628                         if (dummy.size() == 0)
 629                                 continue;
 630
 631                         // At least one dummy index, is it a defined scalar product?
 632                         if (free.size() == 0) {
 633                                 if (sp.is_defined(*it1, *it2)) {
 634                                         *it1 = sp.evaluate(*it1, *it2);
 635                                         *it2 = _ex1();
 636                                         something_changed = true;
 637                                         goto try_again;
 638                                 }
 639                         }
 640
 641                         // Contraction of symmetric with antisymmetric object is zero
 642                         if ((ex_to_indexed(*it1).symmetry == indexed::symmetric &&
 643                              ex_to_indexed(*it2).symmetry == indexed::antisymmetric
 644                           || ex_to_indexed(*it1).symmetry == indexed::antisymmetric &&
 645                              ex_to_indexed(*it2).symmetry == indexed::symmetric)
 646                          && dummy.size() > 1) {
 647                                 free_indices.clear();
 648                                 return _ex0();
 649                         }
 650
 651                         // Try to contract the first one with the second one
 652                         bool contracted = it1->op(0).bp->contract_with(it1, it2, v);
 653                         if (!contracted) {
 654
 655                                 // That didn't work; maybe the second object knows how to
 656                                 // contract itself with the first one
 657                                 contracted = it2->op(0).bp->contract_with(it2, it1, v);
 658                         }
 659                         if (contracted) {
 660                                 something_changed = true;
 661
 662                                 // Both objects may have new indices now or they might
 663                                 // even not be indexed objects any more, so we have to
 664                                 // start over
 665                                 goto try_again;
 666                         }
 667                 }
 668         }
 669
 670         // Find free indices (concatenate them all and call find_free_and_dummy())
 671         exvector un, dummy_indices;
 672         it1 = v.begin(); itend = v.end();
 673         while (it1 != itend) {
 674                 if (is_ex_of_type(*it1, indexed)) {
 675                         const indexed & o = ex_to_indexed(*it1);
 676                         un.insert(un.end(), o.seq.begin() + 1, o.seq.end());
 677                 }
 678                 it1++;
 679         }
 680         find_free_and_dummy(un.begin(), un.end(), free_indices, dummy_indices);
 681
 682         ex r;
 683         if (something_changed) {
 684                 if (non_commutative)
 685                         r = ncmul(v);
 686                 else
 687                         r = mul(v);
 688         } else
 689                 r = e;
 690
 691         // Product of indexed object with a scalar?
 692         if (is_ex_exactly_of_type(r, mul) && r.nops() == 2
 693          && is_ex_exactly_of_type(r.op(1), numeric) && is_ex_of_type(r.op(0), indexed))
 694                 return r.op(0).op(0).bp->scalar_mul_indexed(r.op(0), ex_to_numeric(r.op(1)));
 695         else
 696                 return r;
 697 }
 698
 699 /** Simplify indexed expression, return list of free indices. */
 700 ex simplify_indexed(const ex & e, exvector & free_indices, const scalar_products & sp)
 701 {
 702         // Expand the expression
 703         ex e_expanded = e.expand();
 704
 705         // Simplification of single indexed object: just find the free indices
 706         if (is_ex_of_type(e_expanded, indexed)) {
 707                 const indexed &i = ex_to_indexed(e_expanded);
 708                 exvector dummy_indices;
 709                 find_free_and_dummy(i.seq.begin() + 1, i.seq.end(), free_indices, dummy_indices);
 710                 return e_expanded;
 711         }
 712
 713         // Simplification of sum = sum of simplifications, check consistency of
 714         // free indices in each term
 715         if (is_ex_exactly_of_type(e_expanded, add)) {
 716                 bool first = true;
 717                 ex sum = _ex0();
 718                 free_indices.clear();
 719
 720                 for (unsigned i=0; i<e_expanded.nops(); i++) {
 721                         exvector free_indices_of_term;
 722                         ex term = simplify_indexed(e_expanded.op(i), free_indices_of_term, sp);
 723                         if (!term.is_zero()) {
 724                                 if (first) {
 725                                         free_indices = free_indices_of_term;
 726                                         sum = term;
 727                                         first = false;
 728                                 } else {
 729                                         if (!indices_consistent(free_indices, free_indices_of_term))
 730                                                 throw (std::runtime_error("simplify_indexed: inconsistent indices in sum"));
 731                                         if (is_ex_of_type(sum, indexed) && is_ex_of_type(term, indexed))
 732                                                 sum = sum.op(0).bp->add_indexed(sum, term);
 733                                         else
 734                                                 sum += term;
 735                                 }
 736                         }
 737                 }
 738
 739                 return sum;
 740         }
 741
 742         // Simplification of products
 743         if (is_ex_exactly_of_type(e_expanded, mul)
 744          || is_ex_exactly_of_type(e_expanded, ncmul)
 745          || (is_ex_exactly_of_type(e_expanded, power) && is_ex_of_type(e_expanded.op(0), indexed) && e_expanded.op(1).is_equal(_ex2())))
 746                 return simplify_indexed_product(e_expanded, free_indices, sp);
 747
 748         // Cannot do anything
 749         free_indices.clear();
 750         return e_expanded;
 751 }
 752
 753 ex simplify_indexed(const ex & e)
 754 {
 755         exvector free_indices;
 756         scalar_products sp;
 757         return simplify_indexed(e, free_indices, sp);
 758 }
 759
 760 ex simplify_indexed(const ex & e, const scalar_products & sp)
 761 {
 762         exvector free_indices;
 763         return simplify_indexed(e, free_indices, sp);
 764 }
 765
 766 //////////
 767 // helper classes
 768 //////////
 769
 770 void scalar_products::add(const ex & v1, const ex & v2, const ex & sp)
 771 {
 772         spm[make_key(v1, v2)] = sp;
 773 }
 774
 775 void scalar_products::clear(void)
 776 {
 777         spm.clear();
 778 }
 779
 780 /** Check whether scalar product pair is defined. */
 781 bool scalar_products::is_defined(const ex & v1, const ex & v2) const
 782 {
 783         return spm.find(make_key(v1, v2)) != spm.end();
 784 }
 785
 786 /** Return value of defined scalar product pair. */
 787 ex scalar_products::evaluate(const ex & v1, const ex & v2) const
 788 {
 789         return spm.find(make_key(v1, v2))->second;
 790 }
 791
 792 void scalar_products::debugprint(void) const
 793 {
 794         std::cerr << "map size=" << spm.size() << std::endl;
 795         for (spmap::const_iterator cit=spm.begin(); cit!=spm.end(); ++cit) {
 796                 const spmapkey & k = cit->first;
 797                 std::cerr << "item key=(" << k.first << "," << k.second;
 798                 std::cerr << "), value=" << cit->second << std::endl;
 799         }
 800 }
 801
 802 /** Make key from object pair. */
 803 spmapkey scalar_products::make_key(const ex & v1, const ex & v2)
 804 {
 805         // If indexed, extract base objects
 806         ex s1 = is_ex_of_type(v1, indexed) ? v1.op(0) : v1;
 807         ex s2 = is_ex_of_type(v2, indexed) ? v2.op(0) : v2;
 808
 809         // Enforce canonical order in pair
 810         if (s1.compare(s2) > 0)
 811                 return spmapkey(s2, s1);
 812         else
 813                 return spmapkey(s1, s2);
 814 }
 815
 816 } // namespace GiNaC