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 #include <algorithm>
  25
  26 #include "indexed.h"
  27 #include "idx.h"
  28 #include "add.h"
  29 #include "mul.h"
  30 #include "ncmul.h"
  31 #include "power.h"
  32 #include "symmetry.h"
  33 #include "lst.h"
  34 #include "print.h"
  35 #include "archive.h"
  36 #include "utils.h"
  37 #include "debugmsg.h"
  38
  39 namespace GiNaC {
  40
  41 GINAC_IMPLEMENT_REGISTERED_CLASS(indexed, exprseq)
  42
  43 //////////
  44 // default constructor, destructor, copy constructor assignment operator and helpers
  45 //////////
  46
  47 indexed::indexed() : symtree(sy_none())
  48 {
  49         debugmsg("indexed default constructor", LOGLEVEL_CONSTRUCT);
  50         tinfo_key = TINFO_indexed;
  51 }
  52
  53 void indexed::copy(const indexed & other)
  54 {
  55         inherited::copy(other);
  56         symtree = other.symtree;
  57 }
  58
  59 DEFAULT_DESTROY(indexed)
  60
  61 //////////
  62 // other constructors
  63 //////////
  64
  65 indexed::indexed(const ex & b) : inherited(b), symtree(sy_none())
  66 {
  67         debugmsg("indexed constructor from ex", LOGLEVEL_CONSTRUCT);
  68         tinfo_key = TINFO_indexed;
  69         validate();
  70 }
  71
  72 indexed::indexed(const ex & b, const ex & i1) : inherited(b, i1), symtree(sy_none())
  73 {
  74         debugmsg("indexed constructor from ex,ex", LOGLEVEL_CONSTRUCT);
  75         tinfo_key = TINFO_indexed;
  76         validate();
  77 }
  78
  79 indexed::indexed(const ex & b, const ex & i1, const ex & i2) : inherited(b, i1, i2), symtree(sy_none())
  80 {
  81         debugmsg("indexed constructor from ex,ex,ex", LOGLEVEL_CONSTRUCT);
  82         tinfo_key = TINFO_indexed;
  83         validate();
  84 }
  85
  86 indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symtree(sy_none())
  87 {
  88         debugmsg("indexed constructor from ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
  89         tinfo_key = TINFO_indexed;
  90         validate();
  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), symtree(sy_none())
  94 {
  95         debugmsg("indexed constructor from ex,ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
  96         tinfo_key = TINFO_indexed;
  97         validate();
  98 }
  99
 100 indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2) : inherited(b, i1, i2), symtree(symm)
 101 {
 102         debugmsg("indexed constructor from ex,symmetry,ex,ex", LOGLEVEL_CONSTRUCT);
 103         tinfo_key = TINFO_indexed;
 104         validate();
 105 }
 106
 107 indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symtree(symm)
 108 {
 109         debugmsg("indexed constructor from ex,symmetry,ex,ex,ex", LOGLEVEL_CONSTRUCT);
 110         tinfo_key = TINFO_indexed;
 111         validate();
 112 }
 113
 114 indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symtree(symm)
 115 {
 116         debugmsg("indexed constructor from ex,symmetry,ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
 117         tinfo_key = TINFO_indexed;
 118         validate();
 119 }
 120
 121 indexed::indexed(const ex & b, const exvector & v) : inherited(b), symtree(sy_none())
 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         validate();
 127 }
 128
 129 indexed::indexed(const ex & b, const symmetry & symm, const exvector & v) : inherited(b), symtree(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         validate();
 135 }
 136
 137 indexed::indexed(const symmetry & symm, const exprseq & es) : inherited(es), symtree(symm)
 138 {
 139         debugmsg("indexed constructor from symmetry,exprseq", LOGLEVEL_CONSTRUCT);
 140         tinfo_key = TINFO_indexed;
 141 }
 142
 143 indexed::indexed(const symmetry & symm, const exvector & v, bool discardable) : inherited(v, discardable), symtree(symm)
 144 {
 145         debugmsg("indexed constructor from symmetry,exvector", LOGLEVEL_CONSTRUCT);
 146         tinfo_key = TINFO_indexed;
 147 }
 148
 149 indexed::indexed(const symmetry & symm, exvector * vp) : inherited(vp), symtree(symm)
 150 {
 151         debugmsg("indexed constructor from symmetry,exvector *", LOGLEVEL_CONSTRUCT);
 152         tinfo_key = TINFO_indexed;
 153 }
 154
 155 //////////
 156 // archiving
 157 //////////
 158
 159 indexed::indexed(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 160 {
 161         debugmsg("indexed constructor from archive_node", LOGLEVEL_CONSTRUCT);
 162         if (!n.find_ex("symmetry", symtree, sym_lst)) {
 163                 // GiNaC versions <= 0.9.0 had an unsigned "symmetry" property
 164                 unsigned symm = 0;
 165                 n.find_unsigned("symmetry", symm);
 166                 switch (symm) {
 167                         case 1:
 168                                 symtree = sy_symm();
 169                                 break;
 170                         case 2:
 171                                 symtree = sy_anti();
 172                                 break;
 173                         default:
 174                                 symtree = sy_none();
 175                                 break;
 176                 }
 177                 ex_to_nonconst_symmetry(symtree).validate(seq.size() - 1);
 178         }
 179 }
 180
 181 void indexed::archive(archive_node &n) const
 182 {
 183         inherited::archive(n);
 184         n.add_ex("symmetry", symtree);
 185 }
 186
 187 DEFAULT_UNARCHIVE(indexed)
 188
 189 //////////
 190 // functions overriding virtual functions from bases classes
 191 //////////
 192
 193 void indexed::print(const print_context & c, unsigned level) const
 194 {
 195         debugmsg("indexed print", LOGLEVEL_PRINT);
 196         GINAC_ASSERT(seq.size() > 0);
 197
 198         if (is_of_type(c, print_tree)) {
 199
 200                 c.s << std::string(level, ' ') << class_name()
 201                     << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 202                     << ", " << seq.size()-1 << " indices"
 203                     << ", symmetry=" << symtree << std::endl;
 204                 c.s << std::endl;
 205                 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
 206                 seq[0].print(c, level + delta_indent);
 207                 printindices(c, level + delta_indent);
 208
 209         } else {
 210
 211                 bool is_tex = is_of_type(c, print_latex);
 212                 const ex & base = seq[0];
 213                 bool need_parens = is_ex_exactly_of_type(base, add) || is_ex_exactly_of_type(base, mul)
 214                                 || is_ex_exactly_of_type(base, ncmul) || is_ex_exactly_of_type(base, power)
 215                                 || is_ex_of_type(base, indexed);
 216                 if (is_tex)
 217                         c.s << "{";
 218                 if (need_parens)
 219                         c.s << "(";
 220                 base.print(c);
 221                 if (need_parens)
 222                         c.s << ")";
 223                 if (is_tex)
 224                         c.s << "}";
 225                 printindices(c, level);
 226         }
 227 }
 228
 229 bool indexed::info(unsigned inf) const
 230 {
 231         if (inf == info_flags::indexed) return true;
 232         if (inf == info_flags::has_indices) return seq.size() > 1;
 233         return inherited::info(inf);
 234 }
 235
 236 struct idx_is_not : public std::binary_function<ex, unsigned, bool> {
 237         bool operator() (const ex & e, unsigned inf) const {
 238                 return !(ex_to<idx>(e).get_value().info(inf));
 239         }
 240 };
 241
 242 bool indexed::all_index_values_are(unsigned inf) const
 243 {
 244         // No indices? Then no property can be fulfilled
 245         if (seq.size() < 2)
 246                 return false;
 247
 248         // Check all indices
 249         return find_if(seq.begin() + 1, seq.end(), bind2nd(idx_is_not(), inf)) == seq.end();
 250 }
 251
 252 int indexed::compare_same_type(const basic & other) const
 253 {
 254         GINAC_ASSERT(is_of_type(other, indexed));
 255         return inherited::compare_same_type(other);
 256 }
 257
 258 ex indexed::eval(int level) const
 259 {
 260         // First evaluate children, then we will end up here again
 261         if (level > 1)
 262                 return indexed(ex_to<symmetry>(symtree), evalchildren(level));
 263
 264         const ex &base = seq[0];
 265
 266         // If the base object is 0, the whole object is 0
 267         if (base.is_zero())
 268                 return _ex0();
 269
 270         // If the base object is a product, pull out the numeric factor
 271         if (is_ex_exactly_of_type(base, mul) && is_ex_exactly_of_type(base.op(base.nops() - 1), numeric)) {
 272                 exvector v(seq);
 273                 ex f = ex_to<numeric>(base.op(base.nops() - 1));
 274                 v[0] = seq[0] / f;
 275                 return f * thisexprseq(v);
 276         }
 277
 278         // Canonicalize indices according to the symmetry properties
 279         if (seq.size() > 2) {
 280                 exvector v = seq;
 281                 GINAC_ASSERT(is_ex_exactly_of_type(symtree, symmetry));
 282                 int sig = canonicalize(v.begin() + 1, ex_to<symmetry>(symtree));
 283                 if (sig != INT_MAX) {
 284                         // Something has changed while sorting indices, more evaluations later
 285                         if (sig == 0)
 286                                 return _ex0();
 287                         return ex(sig) * thisexprseq(v);
 288                 }
 289         }
 290
 291         // Let the class of the base object perform additional evaluations
 292         return base.bp->eval_indexed(*this);
 293 }
 294
 295 int indexed::degree(const ex & s) const
 296 {
 297         return is_equal(*s.bp) ? 1 : 0;
 298 }
 299
 300 int indexed::ldegree(const ex & s) const
 301 {
 302         return is_equal(*s.bp) ? 1 : 0;
 303 }
 304
 305 ex indexed::coeff(const ex & s, int n) const
 306 {
 307         if (is_equal(*s.bp))
 308                 return n==1 ? _ex1() : _ex0();
 309         else
 310                 return n==0 ? ex(*this) : _ex0();
 311 }
 312
 313 ex indexed::thisexprseq(const exvector & v) const
 314 {
 315         return indexed(ex_to<symmetry>(symtree), v);
 316 }
 317
 318 ex indexed::thisexprseq(exvector * vp) const
 319 {
 320         return indexed(ex_to<symmetry>(symtree), vp);
 321 }
 322
 323 ex indexed::expand(unsigned options) const
 324 {
 325         GINAC_ASSERT(seq.size() > 0);
 326
 327         if ((options & expand_options::expand_indexed) && is_ex_exactly_of_type(seq[0], add)) {
 328
 329                 // expand_indexed expands (a+b).i -> a.i + b.i
 330                 const ex & base = seq[0];
 331                 ex sum = _ex0();
 332                 for (unsigned i=0; i<base.nops(); i++) {
 333                         exvector s = seq;
 334                         s[0] = base.op(i);
 335                         sum += thisexprseq(s).expand();
 336                 }
 337                 return sum;
 338
 339         } else
 340                 return inherited::expand(options);
 341 }
 342
 343 //////////
 344 // virtual functions which can be overridden by derived classes
 345 //////////
 346
 347 // none
 348
 349 //////////
 350 // non-virtual functions in this class
 351 //////////
 352
 353 void indexed::printindices(const print_context & c, unsigned level) const
 354 {
 355         if (seq.size() > 1) {
 356
 357                 exvector::const_iterator it=seq.begin() + 1, itend = seq.end();
 358
 359                 if (is_of_type(c, print_latex)) {
 360
 361                         // TeX output: group by variance
 362                         bool first = true;
 363                         bool covariant = true;
 364
 365                         while (it != itend) {
 366                                 bool cur_covariant = (is_ex_of_type(*it, varidx) ? ex_to<varidx>(*it).is_covariant() : true);
 367                                 if (first || cur_covariant != covariant) {
 368                                         if (!first)
 369                                                 c.s << "}";
 370                                         covariant = cur_covariant;
 371                                         if (covariant)
 372                                                 c.s << "_{";
 373                                         else
 374                                                 c.s << "^{";
 375                                 }
 376                                 it->print(c, level);
 377                                 c.s << " ";
 378                                 first = false;
 379                                 it++;
 380                         }
 381                         c.s << "}";
 382
 383                 } else {
 384
 385                         // Ordinary output
 386                         while (it != itend) {
 387                                 it->print(c, level);
 388                                 it++;
 389                         }
 390                 }
 391         }
 392 }
 393
 394 /** Check whether all indices are of class idx and validate the symmetry
 395  *  tree. This function is used internally to make sure that all constructed
 396  *  indexed objects really carry indices and not some other classes. */
 397 void indexed::validate(void) const
 398 {
 399         GINAC_ASSERT(seq.size() > 0);
 400         exvector::const_iterator it = seq.begin() + 1, itend = seq.end();
 401         while (it != itend) {
 402                 if (!is_ex_of_type(*it, idx))
 403                         throw(std::invalid_argument("indices of indexed object must be of type idx"));
 404                 it++;
 405         }
 406
 407         if (!symtree.is_zero()) {
 408                 if (!is_ex_exactly_of_type(symtree, symmetry))
 409                         throw(std::invalid_argument("symmetry of indexed object must be of type symmetry"));
 410                 ex_to_nonconst_symmetry(symtree).validate(seq.size() - 1);
 411         }
 412 }
 413
 414 /** Implementation of ex::diff() for an indexed object always returns 0.
 415  *
 416  *  @see ex::diff */
 417 ex indexed::derivative(const symbol & s) const
 418 {
 419         return _ex0();
 420 }
 421
 422 //////////
 423 // global functions
 424 //////////
 425
 426 /** Check whether two sorted index vectors are consistent (i.e. equal). */
 427 static bool indices_consistent(const exvector & v1, const exvector & v2)
 428 {
 429         // Number of indices must be the same
 430         if (v1.size() != v2.size())
 431                 return false;
 432
 433         return equal(v1.begin(), v1.end(), v2.begin(), ex_is_equal());
 434 }
 435
 436 exvector indexed::get_indices(void) const
 437 {
 438         GINAC_ASSERT(seq.size() >= 1);
 439         return exvector(seq.begin() + 1, seq.end());
 440 }
 441
 442 exvector indexed::get_dummy_indices(void) const
 443 {
 444         exvector free_indices, dummy_indices;
 445         find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices);
 446         return dummy_indices;
 447 }
 448
 449 exvector indexed::get_dummy_indices(const indexed & other) const
 450 {
 451         exvector indices = get_free_indices();
 452         exvector other_indices = other.get_free_indices();
 453         indices.insert(indices.end(), other_indices.begin(), other_indices.end());
 454         exvector dummy_indices;
 455         find_dummy_indices(indices, dummy_indices);
 456         return dummy_indices;
 457 }
 458
 459 bool indexed::has_dummy_index_for(const ex & i) const
 460 {
 461         exvector::const_iterator it = seq.begin() + 1, itend = seq.end();
 462         while (it != itend) {
 463                 if (is_dummy_pair(*it, i))
 464                         return true;
 465                 it++;
 466         }
 467         return false;
 468 }
 469
 470 exvector indexed::get_free_indices(void) const
 471 {
 472         exvector free_indices, dummy_indices;
 473         find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices);
 474         return free_indices;
 475 }
 476
 477 exvector add::get_free_indices(void) const
 478 {
 479         exvector free_indices;
 480         for (unsigned i=0; i<nops(); i++) {
 481                 if (i == 0)
 482                         free_indices = op(i).get_free_indices();
 483                 else {
 484                         exvector free_indices_of_term = op(i).get_free_indices();
 485                         if (!indices_consistent(free_indices, free_indices_of_term))
 486                                 throw (std::runtime_error("add::get_free_indices: inconsistent indices in sum"));
 487                 }
 488         }
 489         return free_indices;
 490 }
 491
 492 exvector mul::get_free_indices(void) const
 493 {
 494         // Concatenate free indices of all factors
 495         exvector un;
 496         for (unsigned i=0; i<nops(); i++) {
 497                 exvector free_indices_of_factor = op(i).get_free_indices();
 498                 un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
 499         }
 500
 501         // And remove the dummy indices
 502         exvector free_indices, dummy_indices;
 503         find_free_and_dummy(un, free_indices, dummy_indices);
 504         return free_indices;
 505 }
 506
 507 exvector ncmul::get_free_indices(void) const
 508 {
 509         // Concatenate free indices of all factors
 510         exvector un;
 511         for (unsigned i=0; i<nops(); i++) {
 512                 exvector free_indices_of_factor = op(i).get_free_indices();
 513                 un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
 514         }
 515
 516         // And remove the dummy indices
 517         exvector free_indices, dummy_indices;
 518         find_free_and_dummy(un, free_indices, dummy_indices);
 519         return free_indices;
 520 }
 521
 522 exvector power::get_free_indices(void) const
 523 {
 524         // Return free indices of basis
 525         return basis.get_free_indices();
 526 }
 527
 528 /** Rename dummy indices in an expression.
 529  *
 530  *  @param e Expression to be worked on
 531  *  @param local_dummy_indices The set of dummy indices that appear in the
 532  *    expression "e"
 533  *  @param global_dummy_indices The set of dummy indices that have appeared
 534  *    before and which we would like to use in "e", too. This gets updated
 535  *    by the function */
 536 static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, exvector & local_dummy_indices)
 537 {
 538         int global_size = global_dummy_indices.size(),
 539             local_size = local_dummy_indices.size();
 540
 541         // Any local dummy indices at all?
 542         if (local_size == 0)
 543                 return e;
 544
 545         if (global_size < local_size) {
 546
 547                 // More local indices than we encountered before, add the new ones
 548                 // to the global set
 549                 int remaining = local_size - global_size;
 550                 exvector::const_iterator it = local_dummy_indices.begin(), itend = local_dummy_indices.end();
 551                 while (it != itend && remaining > 0) {
 552                         if (find_if(global_dummy_indices.begin(), global_dummy_indices.end(), bind2nd(ex_is_equal(), *it)) == global_dummy_indices.end()) {
 553                                 global_dummy_indices.push_back(*it);
 554                                 global_size++;
 555                                 remaining--;
 556                         }
 557                         it++;
 558                 }
 559         }
 560
 561         // Replace index symbols in expression
 562         GINAC_ASSERT(local_size <= global_size);
 563         bool all_equal = true;
 564         lst local_syms, global_syms;
 565         for (unsigned i=0; i<local_size; i++) {
 566                 ex loc_sym = local_dummy_indices[i].op(0);
 567                 ex glob_sym = global_dummy_indices[i].op(0);
 568                 if (!loc_sym.is_equal(glob_sym)
 569                  && ex_to<idx>(local_dummy_indices[i]).get_dim().is_equal(ex_to<idx>(global_dummy_indices[i]).get_dim())) {
 570                         all_equal = false;
 571                         local_syms.append(loc_sym);
 572                         global_syms.append(glob_sym);
 573                 }
 574         }
 575         if (all_equal)
 576                 return e;
 577         else
 578                 return e.subs(local_syms, global_syms);
 579 }
 580
 581 /** Simplify product of indexed expressions (commutative, noncommutative and
 582  *  simple squares), return list of free indices. */
 583 ex simplify_indexed_product(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp)
 584 {
 585         // Remember whether the product was commutative or noncommutative
 586         // (because we chop it into factors and need to reassemble later)
 587         bool non_commutative = is_ex_exactly_of_type(e, ncmul);
 588
 589         // Collect factors in an exvector, store squares twice
 590         exvector v;
 591         v.reserve(e.nops() * 2);
 592
 593         if (is_ex_exactly_of_type(e, power)) {
 594                 // We only get called for simple squares, split a^2 -> a*a
 595                 GINAC_ASSERT(e.op(1).is_equal(_ex2()));
 596                 v.push_back(e.op(0));
 597                 v.push_back(e.op(0));
 598         } else {
 599                 for (int i=0; i<e.nops(); i++) {
 600                         ex f = e.op(i);
 601                         if (is_ex_exactly_of_type(f, power) && f.op(1).is_equal(_ex2())) {
 602                                 v.push_back(f.op(0));
 603                     v.push_back(f.op(0));
 604                         } else if (is_ex_exactly_of_type(f, ncmul)) {
 605                                 // Noncommutative factor found, split it as well
 606                                 non_commutative = true; // everything becomes noncommutative, ncmul will sort out the commutative factors later
 607                                 for (int j=0; j<f.nops(); j++)
 608                                         v.push_back(f.op(j));
 609                         } else
 610                                 v.push_back(f);
 611                 }
 612         }
 613
 614         // Perform contractions
 615         bool something_changed = false;
 616         GINAC_ASSERT(v.size() > 1);
 617         exvector::iterator it1, itend = v.end(), next_to_last = itend - 1;
 618         for (it1 = v.begin(); it1 != next_to_last; it1++) {
 619
 620 try_again:
 621                 if (!is_ex_of_type(*it1, indexed))
 622                         continue;
 623
 624                 bool first_noncommutative = (it1->return_type() != return_types::commutative);
 625
 626                 // Indexed factor found, get free indices and look for contraction
 627                 // candidates
 628                 exvector free1, dummy1;
 629                 find_free_and_dummy(ex_to<indexed>(*it1).seq.begin() + 1, ex_to<indexed>(*it1).seq.end(), free1, dummy1);
 630
 631                 exvector::iterator it2;
 632                 for (it2 = it1 + 1; it2 != itend; it2++) {
 633
 634                         if (!is_ex_of_type(*it2, indexed))
 635                                 continue;
 636
 637                         bool second_noncommutative = (it2->return_type() != return_types::commutative);
 638
 639                         // Find free indices of second factor and merge them with free
 640                         // indices of first factor
 641                         exvector un;
 642                         find_free_and_dummy(ex_to<indexed>(*it2).seq.begin() + 1, ex_to<indexed>(*it2).seq.end(), un, dummy1);
 643                         un.insert(un.end(), free1.begin(), free1.end());
 644
 645                         // Check whether the two factors share dummy indices
 646                         exvector free, dummy;
 647                         find_free_and_dummy(un, free, dummy);
 648                         if (dummy.size() == 0)
 649                                 continue;
 650
 651                         // At least one dummy index, is it a defined scalar product?
 652                         bool contracted = false;
 653                         if (free.size() == 0) {
 654                                 if (sp.is_defined(*it1, *it2)) {
 655                                         *it1 = sp.evaluate(*it1, *it2);
 656                                         *it2 = _ex1();
 657                                         goto contraction_done;
 658                                 }
 659                         }
 660
 661                         // Contraction of symmetric with antisymmetric object is zero
 662                         if (dummy.size() > 1
 663                          && ex_to<symmetry>(ex_to<indexed>(*it1).symtree).has_symmetry()
 664                          && ex_to<symmetry>(ex_to<indexed>(*it2).symtree).has_symmetry()) {
 665
 666                                 // Check all pairs of dummy indices
 667                                 for (unsigned idx1=0; idx1<dummy.size()-1; idx1++) {
 668                                         for (unsigned idx2=idx1+1; idx2<dummy.size(); idx2++) {
 669
 670                                                 // Try and swap the index pair and check whether the
 671                                                 // relative sign changed
 672                                                 lst subs_lst(dummy[idx1].op(0), dummy[idx2].op(0)), repl_lst(dummy[idx2].op(0), dummy[idx1].op(0));
 673                                                 ex swapped1 = it1->subs(subs_lst, repl_lst);
 674                                                 ex swapped2 = it2->subs(subs_lst, repl_lst);
 675                                                 if (it1->is_equal(swapped1) && it2->is_equal(-swapped2)
 676                                                  || it1->is_equal(-swapped1) && it2->is_equal(swapped2)) {
 677                                                         free_indices.clear();
 678                                                         return _ex0();
 679                                                 }
 680                                         }
 681                                 }
 682                         }
 683
 684                         // Try to contract the first one with the second one
 685                         contracted = it1->op(0).bp->contract_with(it1, it2, v);
 686                         if (!contracted) {
 687
 688                                 // That didn't work; maybe the second object knows how to
 689                                 // contract itself with the first one
 690                                 contracted = it2->op(0).bp->contract_with(it2, it1, v);
 691                         }
 692                         if (contracted) {
 693 contraction_done:
 694                                 if (first_noncommutative || second_noncommutative
 695                                  || is_ex_exactly_of_type(*it1, add) || is_ex_exactly_of_type(*it2, add)
 696                                  || is_ex_exactly_of_type(*it1, mul) || is_ex_exactly_of_type(*it2, mul)
 697                                  || is_ex_exactly_of_type(*it1, ncmul) || is_ex_exactly_of_type(*it2, ncmul)) {
 698
 699                                         // One of the factors became a sum or product:
 700                                         // re-expand expression and run again
 701                                         // Non-commutative products are always re-expanded to give
 702                                         // simplify_ncmul() the chance to re-order and canonicalize
 703                                         // the product
 704                                         ex r = (non_commutative ? ex(ncmul(v, true)) : ex(mul(v)));
 705                                         return simplify_indexed(r, free_indices, dummy_indices, sp);
 706                                 }
 707
 708                                 // Both objects may have new indices now or they might
 709                                 // even not be indexed objects any more, so we have to
 710                                 // start over
 711                                 something_changed = true;
 712                                 goto try_again;
 713                         }
 714                 }
 715         }
 716
 717         // Find free indices (concatenate them all and call find_free_and_dummy())
 718         // and all dummy indices that appear
 719         exvector un, individual_dummy_indices;
 720         it1 = v.begin(); itend = v.end();
 721         while (it1 != itend) {
 722                 exvector free_indices_of_factor;
 723                 if (is_ex_of_type(*it1, indexed)) {
 724                         exvector dummy_indices_of_factor;
 725                         find_free_and_dummy(ex_to<indexed>(*it1).seq.begin() + 1, ex_to<indexed>(*it1).seq.end(), free_indices_of_factor, dummy_indices_of_factor);
 726                         individual_dummy_indices.insert(individual_dummy_indices.end(), dummy_indices_of_factor.begin(), dummy_indices_of_factor.end());
 727                 } else
 728                         free_indices_of_factor = it1->get_free_indices();
 729                 un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
 730                 it1++;
 731         }
 732         exvector local_dummy_indices;
 733         find_free_and_dummy(un, free_indices, local_dummy_indices);
 734         local_dummy_indices.insert(local_dummy_indices.end(), individual_dummy_indices.begin(), individual_dummy_indices.end());
 735
 736         ex r;
 737         if (something_changed)
 738                 r = non_commutative ? ex(ncmul(v, true)) : ex(mul(v));
 739         else
 740                 r = e;
 741
 742         // Dummy index renaming
 743         r = rename_dummy_indices(r, dummy_indices, local_dummy_indices);
 744
 745         // Product of indexed object with a scalar?
 746         if (is_ex_exactly_of_type(r, mul) && r.nops() == 2
 747          && is_ex_exactly_of_type(r.op(1), numeric) && is_ex_of_type(r.op(0), indexed))
 748                 return r.op(0).op(0).bp->scalar_mul_indexed(r.op(0), ex_to<numeric>(r.op(1)));
 749         else
 750                 return r;
 751 }
 752
 753 /** Simplify indexed expression, return list of free indices. */
 754 ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp)
 755 {
 756         // Expand the expression
 757         ex e_expanded = e.expand();
 758
 759         // Simplification of single indexed object: just find the free indices
 760         // and perform dummy index renaming
 761         if (is_ex_of_type(e_expanded, indexed)) {
 762                 const indexed &i = ex_to<indexed>(e_expanded);
 763                 exvector local_dummy_indices;
 764                 find_free_and_dummy(i.seq.begin() + 1, i.seq.end(), free_indices, local_dummy_indices);
 765                 return rename_dummy_indices(e_expanded, dummy_indices, local_dummy_indices);
 766         }
 767
 768         // Simplification of sum = sum of simplifications, check consistency of
 769         // free indices in each term
 770         if (is_ex_exactly_of_type(e_expanded, add)) {
 771                 bool first = true;
 772                 ex sum = _ex0();
 773                 free_indices.clear();
 774
 775                 for (unsigned i=0; i<e_expanded.nops(); i++) {
 776                         exvector free_indices_of_term;
 777                         ex term = simplify_indexed(e_expanded.op(i), free_indices_of_term, dummy_indices, sp);
 778                         if (!term.is_zero()) {
 779                                 if (first) {
 780                                         free_indices = free_indices_of_term;
 781                                         sum = term;
 782                                         first = false;
 783                                 } else {
 784                                         if (!indices_consistent(free_indices, free_indices_of_term))
 785                                                 throw (std::runtime_error("simplify_indexed: inconsistent indices in sum"));
 786                                         if (is_ex_of_type(sum, indexed) && is_ex_of_type(term, indexed))
 787                                                 sum = sum.op(0).bp->add_indexed(sum, term);
 788                                         else
 789                                                 sum += term;
 790                                 }
 791                         }
 792                 }
 793
 794                 return sum;
 795         }
 796
 797         // Simplification of products
 798         if (is_ex_exactly_of_type(e_expanded, mul)
 799          || is_ex_exactly_of_type(e_expanded, ncmul)
 800          || (is_ex_exactly_of_type(e_expanded, power) && is_ex_of_type(e_expanded.op(0), indexed) && e_expanded.op(1).is_equal(_ex2())))
 801                 return simplify_indexed_product(e_expanded, free_indices, dummy_indices, sp);
 802
 803         // Cannot do anything
 804         free_indices.clear();
 805         return e_expanded;
 806 }
 807
 808 /** Simplify/canonicalize expression containing indexed objects. This
 809  *  performs contraction of dummy indices where possible and checks whether
 810  *  the free indices in sums are consistent.
 811  *
 812  *  @return simplified expression */
 813 ex ex::simplify_indexed(void) const
 814 {
 815         exvector free_indices, dummy_indices;
 816         scalar_products sp;
 817         return GiNaC::simplify_indexed(*this, free_indices, dummy_indices, sp);
 818 }
 819
 820 /** Simplify/canonicalize expression containing indexed objects. This
 821  *  performs contraction of dummy indices where possible, checks whether
 822  *  the free indices in sums are consistent, and automatically replaces
 823  *  scalar products by known values if desired.
 824  *
 825  *  @param sp Scalar products to be replaced automatically
 826  *  @return simplified expression */
 827 ex ex::simplify_indexed(const scalar_products & sp) const
 828 {
 829         exvector free_indices, dummy_indices;
 830         return GiNaC::simplify_indexed(*this, free_indices, dummy_indices, sp);
 831 }
 832
 833 /** Symmetrize expression over its free indices. */
 834 ex ex::symmetrize(void) const
 835 {
 836         return GiNaC::symmetrize(*this, get_free_indices());
 837 }
 838
 839 /** Antisymmetrize expression over its free indices. */
 840 ex ex::antisymmetrize(void) const
 841 {
 842         return GiNaC::antisymmetrize(*this, get_free_indices());
 843 }
 844
 845 /** Symmetrize expression by cyclic permutation over its free indices. */
 846 ex ex::symmetrize_cyclic(void) const
 847 {
 848         return GiNaC::symmetrize_cyclic(*this, get_free_indices());
 849 }
 850
 851 //////////
 852 // helper classes
 853 //////////
 854
 855 void scalar_products::add(const ex & v1, const ex & v2, const ex & sp)
 856 {
 857         spm[make_key(v1, v2)] = sp;
 858 }
 859
 860 void scalar_products::add_vectors(const lst & l)
 861 {
 862         // Add all possible pairs of products
 863         unsigned num = l.nops();
 864         for (unsigned i=0; i<num; i++) {
 865                 ex a = l.op(i);
 866                 for (unsigned j=0; j<num; j++) {
 867                         ex b = l.op(j);
 868                         add(a, b, a*b);
 869                 }
 870         }
 871 }
 872
 873 void scalar_products::clear(void)
 874 {
 875         spm.clear();
 876 }
 877
 878 /** Check whether scalar product pair is defined. */
 879 bool scalar_products::is_defined(const ex & v1, const ex & v2) const
 880 {
 881         return spm.find(make_key(v1, v2)) != spm.end();
 882 }
 883
 884 /** Return value of defined scalar product pair. */
 885 ex scalar_products::evaluate(const ex & v1, const ex & v2) const
 886 {
 887         return spm.find(make_key(v1, v2))->second;
 888 }
 889
 890 void scalar_products::debugprint(void) const
 891 {
 892         std::cerr << "map size=" << spm.size() << std::endl;
 893         for (spmap::const_iterator cit=spm.begin(); cit!=spm.end(); ++cit) {
 894                 const spmapkey & k = cit->first;
 895                 std::cerr << "item key=(" << k.first << "," << k.second;
 896                 std::cerr << "), value=" << cit->second << std::endl;
 897         }
 898 }
 899
 900 /** Make key from object pair. */
 901 spmapkey scalar_products::make_key(const ex & v1, const ex & v2)
 902 {
 903         // If indexed, extract base objects
 904         ex s1 = is_ex_of_type(v1, indexed) ? v1.op(0) : v1;
 905         ex s2 = is_ex_of_type(v2, indexed) ? v2.op(0) : v2;
 906
 907         // Enforce canonical order in pair
 908         if (s1.compare(s2) > 0)
 909                 return spmapkey(s2, s1);
 910         else
 911                 return spmapkey(s1, s2);
 912 }
 913
 914 } // namespace GiNaC