c3fe1d9a26e6d49ca311b0e793913d6050ef402f
[ginac.git] / 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, v);
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, v);
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