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