- added skeleton implementation of color and clifford classes (don't bother
[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 DEFAULT_DESTROY(indexed)
56
57 //////////
58 // other constructors
59 //////////
60
61 indexed::indexed(const ex & b) : inherited(b), symmetry(unknown)
62 {
63         debugmsg("indexed constructor from ex", LOGLEVEL_CONSTRUCT);
64         tinfo_key = TINFO_indexed;
65         assert_all_indices_of_type_idx();
66 }
67
68 indexed::indexed(const ex & b, const ex & i1) : inherited(b, i1), symmetry(unknown)
69 {
70         debugmsg("indexed constructor from ex,ex", LOGLEVEL_CONSTRUCT);
71         tinfo_key = TINFO_indexed;
72         assert_all_indices_of_type_idx();
73 }
74
75 indexed::indexed(const ex & b, const ex & i1, const ex & i2) : inherited(b, i1, i2), symmetry(unknown)
76 {
77         debugmsg("indexed constructor from ex,ex,ex", LOGLEVEL_CONSTRUCT);
78         tinfo_key = TINFO_indexed;
79         assert_all_indices_of_type_idx();
80 }
81
82 indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symmetry(unknown)
83 {
84         debugmsg("indexed constructor from ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
85         tinfo_key = TINFO_indexed;
86         assert_all_indices_of_type_idx();
87 }
88
89 indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symmetry(unknown)
90 {
91         debugmsg("indexed constructor from ex,ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
92         tinfo_key = TINFO_indexed;
93         assert_all_indices_of_type_idx();
94 }
95
96 indexed::indexed(const ex & b, symmetry_type symm, const ex & i1, const ex & i2) : inherited(b, i1, i2), symmetry(symm)
97 {
98         debugmsg("indexed constructor from ex,symmetry,ex,ex", LOGLEVEL_CONSTRUCT);
99         tinfo_key = TINFO_indexed;
100         assert_all_indices_of_type_idx();
101 }
102
103 indexed::indexed(const ex & b, symmetry_type symm, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symmetry(symm)
104 {
105         debugmsg("indexed constructor from ex,symmetry,ex,ex,ex", LOGLEVEL_CONSTRUCT);
106         tinfo_key = TINFO_indexed;
107         assert_all_indices_of_type_idx();
108 }
109
110 indexed::indexed(const ex & b, symmetry_type symm, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symmetry(symm)
111 {
112         debugmsg("indexed constructor from ex,symmetry,ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
113         tinfo_key = TINFO_indexed;
114         assert_all_indices_of_type_idx();
115 }
116
117 indexed::indexed(const ex & b, const exvector & v) : inherited(b), symmetry(unknown)
118 {
119         debugmsg("indexed constructor from ex,exvector", LOGLEVEL_CONSTRUCT);
120         seq.insert(seq.end(), v.begin(), v.end());
121         tinfo_key = TINFO_indexed;
122         assert_all_indices_of_type_idx();
123 }
124
125 indexed::indexed(const ex & b, symmetry_type symm, const exvector & v) : inherited(b), symmetry(symm)
126 {
127         debugmsg("indexed constructor from ex,symmetry,exvector", LOGLEVEL_CONSTRUCT);
128         seq.insert(seq.end(), v.begin(), v.end());
129         tinfo_key = TINFO_indexed;
130         assert_all_indices_of_type_idx();
131 }
132
133 indexed::indexed(symmetry_type symm, const exprseq & es) : inherited(es), symmetry(symm)
134 {
135         debugmsg("indexed constructor from symmetry,exprseq", LOGLEVEL_CONSTRUCT);
136         tinfo_key = TINFO_indexed;
137         assert_all_indices_of_type_idx();
138 }
139
140 indexed::indexed(symmetry_type symm, const exvector & v, bool discardable) : inherited(v, discardable), symmetry(symm)
141 {
142         debugmsg("indexed constructor from symmetry,exvector", LOGLEVEL_CONSTRUCT);
143         tinfo_key = TINFO_indexed;
144         assert_all_indices_of_type_idx();
145 }
146
147 indexed::indexed(symmetry_type symm, exvector * vp) : inherited(vp), symmetry(symm)
148 {
149         debugmsg("indexed constructor from symmetry,exvector *", LOGLEVEL_CONSTRUCT);
150         tinfo_key = TINFO_indexed;
151         assert_all_indices_of_type_idx();
152 }
153
154 //////////
155 // archiving
156 //////////
157
158 indexed::indexed(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
159 {
160         debugmsg("indexed constructor from archive_node", LOGLEVEL_CONSTRUCT);
161         unsigned int symm;
162         if (!(n.find_unsigned("symmetry", symm)))
163                 throw (std::runtime_error("unknown indexed symmetry type in archive"));
164 }
165
166 void indexed::archive(archive_node &n) const
167 {
168         inherited::archive(n);
169         n.add_unsigned("symmetry", symmetry);
170 }
171
172 DEFAULT_UNARCHIVE(indexed)
173
174 //////////
175 // functions overriding virtual functions from bases classes
176 //////////
177
178 void indexed::printraw(std::ostream & os) const
179 {
180         debugmsg("indexed printraw", LOGLEVEL_PRINT);
181         GINAC_ASSERT(seq.size() > 0);
182
183         os << class_name() << "(";
184         seq[0].printraw(os);
185         os << ",indices=";
186         printrawindices(os);
187         os << ",hash=" << hashvalue << ",flags=" << flags << ")";
188 }
189
190 void indexed::printtree(std::ostream & os, unsigned indent) const
191 {
192         debugmsg("indexed printtree", LOGLEVEL_PRINT);
193         GINAC_ASSERT(seq.size() > 0);
194
195         os << std::string(indent, ' ') << class_name() << ", " << seq.size()-1 << " indices";
196         os << ",hash=" << hashvalue << ",flags=" << flags << std::endl;
197         printtreeindices(os, indent);
198 }
199
200 void indexed::print(std::ostream & os, unsigned upper_precedence) const
201 {
202         debugmsg("indexed print", LOGLEVEL_PRINT);
203         GINAC_ASSERT(seq.size() > 0);
204
205         const ex & base = seq[0];
206         bool need_parens = is_ex_exactly_of_type(base, add) || is_ex_exactly_of_type(base, mul)
207                         || is_ex_exactly_of_type(base, ncmul) || is_ex_exactly_of_type(base, power);
208         if (need_parens)
209                 os << "(";
210         os << base;
211         if (need_parens)
212                 os << ")";
213         printindices(os);
214 }
215
216 bool indexed::info(unsigned inf) const
217 {
218         if (inf == info_flags::indexed) return true;
219         if (inf == info_flags::has_indices) return seq.size() > 1;
220         return inherited::info(inf);
221 }
222
223 bool indexed::all_index_values_are(unsigned inf) const
224 {
225         // No indices? Then no property can be fulfilled
226         if (seq.size() < 2)
227                 return false;
228
229         // Check all indices
230         exvector::const_iterator it = seq.begin() + 1, itend = seq.end();
231         while (it != itend) {
232                 GINAC_ASSERT(is_ex_of_type(*it, idx));
233                 if (!ex_to_idx(*it).get_value().info(inf))
234                         return false;
235                 it++;
236         }
237         return true;
238 }
239
240 int indexed::compare_same_type(const basic & other) const
241 {
242         GINAC_ASSERT(is_of_type(other, indexed));
243         return inherited::compare_same_type(other);
244 }
245
246 // The main difference between sort_index_vector() and canonicalize_indices()
247 // is that the latter takes the symmetry of the object into account. Once we
248 // implement mixed symmetries, canonicalize_indices() will only be able to
249 // reorder index pairs with known symmetry properties, while sort_index_vector()
250 // always sorts the whole vector.
251
252 /** Bring a vector of indices into a canonic order (don't care about the
253  *  symmetry of the objects carrying the indices). Dummy indices will lie
254  *  next to each other after the sorting.
255  *
256  *  @param v Index vector to be sorted */
257 static void sort_index_vector(exvector &v)
258 {
259         // Nothing to sort if less than 2 elements
260         if (v.size() < 2)
261                 return;
262
263         // Simple bubble sort algorithm should be sufficient for the small
264         // number of indices expected
265         exvector::iterator it1 = v.begin(), itend = v.end(), next_to_last_idx = itend - 1;
266         while (it1 != next_to_last_idx) {
267                 exvector::iterator it2 = it1 + 1;
268                 while (it2 != itend) {
269                         if (it1->compare(*it2) > 0)
270                                 it1->swap(*it2);
271                         it2++;
272                 }
273                 it1++;
274         }
275 }
276
277 /** Bring a vector of indices into a canonic order. This operation only makes
278  *  sense if the object carrying these indices is either symmetric or totally
279  *  antisymmetric with respect to the indices.
280  *
281  *  @param itbegin Start of index vector
282  *  @param itend End of index vector
283  *  @param antisymm Whether the object is antisymmetric
284  *  @return the sign introduced by the reordering of the indices if the object
285  *          is antisymmetric (or 0 if two equal indices are encountered). For
286  *          symmetric objects, this is always +1. If the index vector was
287  *          already in a canonic order this function returns INT_MAX. */
288 static int canonicalize_indices(exvector::iterator itbegin, exvector::iterator itend, bool antisymm)
289 {
290         bool something_changed = false;
291         int sig = 1;
292
293         // Simple bubble sort algorithm should be sufficient for the small
294         // number of indices expected
295         exvector::iterator it1 = itbegin, next_to_last_idx = itend - 1;
296         while (it1 != next_to_last_idx) {
297                 exvector::iterator it2 = it1 + 1;
298                 while (it2 != itend) {
299                         int cmpval = it1->compare(*it2);
300                         if (cmpval == 1) {
301                                 it1->swap(*it2);
302                                 something_changed = true;
303                                 if (antisymm)
304                                         sig = -sig;
305                         } else if (cmpval == 0 && antisymm) {
306                                 something_changed = true;
307                                 sig = 0;
308                         }
309                         it2++;
310                 }
311                 it1++;
312         }
313
314         return something_changed ? sig : INT_MAX;
315 }
316
317 ex indexed::eval(int level) const
318 {
319         // First evaluate children, then we will end up here again
320         if (level > 1)
321                 return indexed(symmetry, evalchildren(level));
322
323         const ex &base = seq[0];
324
325         // If the base object is 0, the whole object is 0
326         if (base.is_zero())
327                 return _ex0();
328
329         // If the base object is a product, pull out the numeric factor
330         if (is_ex_exactly_of_type(base, mul) && is_ex_exactly_of_type(base.op(base.nops() - 1), numeric)) {
331                 exvector v = seq;
332                 ex f = ex_to_numeric(base.op(base.nops() - 1));
333                 v[0] = seq[0] / f;
334                 return f * thisexprseq(v);
335         }
336
337         // Canonicalize indices according to the symmetry properties
338         if (seq.size() > 2 && (symmetry != unknown && symmetry != mixed)) {
339                 exvector v = seq;
340                 int sig = canonicalize_indices(v.begin() + 1, v.end(), symmetry == antisymmetric);
341                 if (sig != INT_MAX) {
342                         // Something has changed while sorting indices, more evaluations later
343                         if (sig == 0)
344                                 return _ex0();
345                         return ex(sig) * thisexprseq(v);
346                 }
347         }
348
349         // Let the class of the base object perform additional evaluations
350         return base.bp->eval_indexed(*this);
351 }
352
353 ex indexed::thisexprseq(const exvector & v) const
354 {
355         return indexed(symmetry, v);
356 }
357
358 ex indexed::thisexprseq(exvector * vp) const
359 {
360         return indexed(symmetry, vp);
361 }
362
363 ex indexed::expand(unsigned options) const
364 {
365         GINAC_ASSERT(seq.size() > 0);
366
367         if ((options & expand_options::expand_indexed) && is_ex_exactly_of_type(seq[0], add)) {
368
369                 // expand_indexed expands (a+b).i -> a.i + b.i
370                 const ex & base = seq[0];
371                 ex sum = _ex0();
372                 for (unsigned i=0; i<base.nops(); i++) {
373                         exvector s = seq;
374                         s[0] = base.op(i);
375                         sum += thisexprseq(s).expand();
376                 }
377                 return sum;
378
379         } else
380                 return inherited::expand(options);
381 }
382
383 //////////
384 // virtual functions which can be overridden by derived classes
385 //////////
386
387 // none
388
389 //////////
390 // non-virtual functions in this class
391 //////////
392
393 void indexed::printrawindices(std::ostream & os) const
394 {
395         if (seq.size() > 1) {
396                 exvector::const_iterator it=seq.begin() + 1, itend = seq.end();
397                 while (it != itend) {
398                         it->printraw(os);
399                         it++;
400                         if (it != itend)
401                                 os << ",";
402                 }
403         }
404 }
405
406 void indexed::printtreeindices(std::ostream & os, unsigned indent) const
407 {
408         if (seq.size() > 1) {
409                 exvector::const_iterator it=seq.begin() + 1, itend = seq.end();
410                 while (it != itend) {
411                         os << std::string(indent + delta_indent, ' ');
412                         it->printraw(os);
413                         os << std::endl;
414                         it++;
415                 }
416         }
417 }
418
419 void indexed::printindices(std::ostream & os) const
420 {
421         if (seq.size() > 1) {
422                 exvector::const_iterator it=seq.begin() + 1, itend = seq.end();
423                 while (it != itend) {
424                         it->print(os);
425                         it++;
426                 }
427         }
428 }
429
430 /** Check whether all indices are of class idx. This function is used
431  *  internally to make sure that all constructed indexed objects really
432  *  carry indices and not some other classes. */
433 void indexed::assert_all_indices_of_type_idx(void) const
434 {
435         GINAC_ASSERT(seq.size() > 0);
436         exvector::const_iterator it = seq.begin() + 1, itend = seq.end();
437         while (it != itend) {
438                 if (!is_ex_of_type(*it, idx))
439                         throw(std::invalid_argument("indices of indexed object must be of type idx"));
440                 it++;
441         }
442 }
443
444 //////////
445 // global functions
446 //////////
447
448 /** Given a vector of indices, split them into two vectors, one containing
449  *  the free indices, the other containing the dummy indices. */
450 static void find_free_and_dummy(exvector::const_iterator it, exvector::const_iterator itend, exvector & out_free, exvector & out_dummy)
451 {
452         out_free.clear();
453         out_dummy.clear();
454
455         // No indices? Then do nothing
456         if (it == itend)
457                 return;
458
459         // Only one index? Then it is a free one if it's not numeric
460         if (itend - it == 1) {
461                 if (ex_to_idx(*it).is_symbolic())
462                         out_free.push_back(*it);
463                 return;
464         }
465
466         // Sort index vector. This will cause dummy indices come to lie next
467         // to each other (because the sort order is defined to guarantee this).
468         exvector v(it, itend);
469         sort_index_vector(v);
470
471         // Find dummy pairs and free indices
472         it = v.begin(); itend = v.end();
473         exvector::const_iterator last = it++;
474         while (it != itend) {
475                 if (is_dummy_pair(*it, *last)) {
476                         out_dummy.push_back(*last);
477                         it++;
478                         if (it == itend)
479                                 return;
480                 } else {
481                         if (!it->is_equal(*last) && ex_to_idx(*last).is_symbolic())
482                                 out_free.push_back(*last);
483                 }
484                 last = it++;
485         }
486         if (ex_to_idx(*last).is_symbolic())
487                 out_free.push_back(*last);
488 }
489
490 /** Check whether two sorted index vectors are consistent (i.e. equal). */
491 static bool indices_consistent(const exvector & v1, const exvector & v2)
492 {
493         // Number of indices must be the same
494         if (v1.size() != v2.size())
495                 return false;
496
497         // And also the indices themselves
498         exvector::const_iterator ait = v1.begin(), aitend = v1.end(),
499                                  bit = v2.begin(), bitend = v2.end();
500         while (ait != aitend) {
501                 if (!ait->is_equal(*bit))
502                         return false;
503                 ait++; bit++;
504         }
505         return true;
506 }
507
508 exvector indexed::get_dummy_indices(void) const
509 {
510         exvector free_indices, dummy_indices;
511         find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices);
512         return dummy_indices;
513 }
514
515 exvector indexed::get_free_indices(void) const
516 {
517         exvector free_indices, dummy_indices;
518         find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices);
519         return free_indices;
520 }
521
522 exvector add::get_free_indices(void) const
523 {
524         exvector free_indices;
525         for (unsigned i=0; i<nops(); i++) {
526                 if (i == 0)
527                         free_indices = op(i).get_free_indices();
528                 else {
529                         exvector free_indices_of_term = op(i).get_free_indices();
530                         if (!indices_consistent(free_indices, free_indices_of_term))
531                                 throw (std::runtime_error("add::get_free_indices: inconsistent indices in sum"));
532                 }
533         }
534         return free_indices;
535 }
536
537 exvector mul::get_free_indices(void) const
538 {
539         // Concatenate free indices of all factors
540         exvector un;
541         for (unsigned i=0; i<nops(); i++) {
542                 exvector free_indices_of_factor = op(i).get_free_indices();
543                 un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
544         }
545
546         // And remove the dummy indices
547         exvector free_indices, dummy_indices;
548         find_free_and_dummy(un.begin(), un.end(), free_indices, dummy_indices);
549         return free_indices;
550 }
551
552 exvector ncmul::get_free_indices(void) const
553 {
554         // Concatenate free indices of all factors
555         exvector un;
556         for (unsigned i=0; i<nops(); i++) {
557                 exvector free_indices_of_factor = op(i).get_free_indices();
558                 un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
559         }
560
561         // And remove the dummy indices
562         exvector free_indices, dummy_indices;
563         find_free_and_dummy(un.begin(), un.end(), free_indices, dummy_indices);
564         return free_indices;
565 }
566
567 exvector power::get_free_indices(void) const
568 {
569         // Return free indices of basis
570         return basis.get_free_indices();
571 }
572
573 /** Simplify product of indexed expressions (commutative, noncommutative and
574  *  simple squares), return list of free indices. */
575 ex simplify_indexed_product(const ex & e, exvector & free_indices, const scalar_products & sp)
576 {
577         // Remember whether the product was commutative or noncommutative
578         // (because we chop it into factors and need to reassemble later)
579         bool non_commutative = is_ex_exactly_of_type(e, ncmul);
580
581         // Collect factors in an exvector, store squares twice
582         exvector v;
583         v.reserve(e.nops() * 2);
584
585         if (is_ex_exactly_of_type(e, power)) {
586                 // We only get called for simple squares, split a^2 -> a*a
587                 GINAC_ASSERT(e.op(1).is_equal(_ex2()));
588                 v.push_back(e.op(0));
589                 v.push_back(e.op(0));
590         } else {
591                 for (int i=0; i<e.nops(); i++) {
592                         ex f = e.op(i);
593                         if (is_ex_exactly_of_type(f, power) && f.op(1).is_equal(_ex2())) {
594                                 v.push_back(f.op(0));
595                     v.push_back(f.op(0));
596                         } else if (is_ex_exactly_of_type(f, ncmul)) {
597                                 // Noncommutative factor found, split it as well
598                                 non_commutative = true; // everything becomes noncommutative, ncmul will sort out the commutative factors later
599                                 for (int j=0; j<f.nops(); i++)
600                                         v.push_back(f.op(j));
601                         } else
602                                 v.push_back(f);
603                 }
604         }
605
606         // Perform contractions
607         bool something_changed = false;
608         GINAC_ASSERT(v.size() > 1);
609         exvector::iterator it1, itend = v.end(), next_to_last = itend - 1;
610         for (it1 = v.begin(); it1 != next_to_last; it1++) {
611
612 try_again:
613                 if (!is_ex_of_type(*it1, indexed))
614                         continue;
615
616                 // Indexed factor found, look for contraction candidates
617                 exvector::iterator it2;
618                 for (it2 = it1 + 1; it2 != itend; it2++) {
619
620                         if (!is_ex_of_type(*it2, indexed))
621                                 continue;
622
623                         // Check whether the two factors share dummy indices
624                         exvector un(ex_to_indexed(*it1).seq.begin() + 1, ex_to_indexed(*it1).seq.end());
625                         un.insert(un.end(), ex_to_indexed(*it2).seq.begin() + 1, ex_to_indexed(*it2).seq.end());
626                         exvector free, dummy;
627                         find_free_and_dummy(un.begin(), un.end(), free, dummy);
628                         if (dummy.size() == 0)
629                                 continue;
630
631                         // At least one dummy index, is it a defined scalar product?
632                         if (free.size() == 0) {
633                                 if (sp.is_defined(*it1, *it2)) {
634                                         *it1 = sp.evaluate(*it1, *it2);
635                                         *it2 = _ex1();
636                                         something_changed = true;
637                                         goto try_again;
638                                 }
639                         }
640
641                         // Contraction of symmetric with antisymmetric object is zero
642                         if ((ex_to_indexed(*it1).symmetry == indexed::symmetric &&
643                              ex_to_indexed(*it2).symmetry == indexed::antisymmetric
644                           || ex_to_indexed(*it1).symmetry == indexed::antisymmetric &&
645                              ex_to_indexed(*it2).symmetry == indexed::symmetric)
646                          && dummy.size() > 1) {
647                                 free_indices.clear();
648                                 return _ex0();
649                         }
650
651                         // Try to contract the first one with the second one
652                         bool contracted = it1->op(0).bp->contract_with(it1, it2, v);
653                         if (!contracted) {
654
655                                 // That didn't work; maybe the second object knows how to
656                                 // contract itself with the first one
657                                 contracted = it2->op(0).bp->contract_with(it2, it1, v);
658                         }
659                         if (contracted) {
660                                 something_changed = true;
661
662                                 // Both objects may have new indices now or they might
663                                 // even not be indexed objects any more, so we have to
664                                 // start over
665                                 goto try_again;
666                         }
667                 }
668         }
669
670         // Find free indices (concatenate them all and call find_free_and_dummy())
671         exvector un, dummy_indices;
672         it1 = v.begin(); itend = v.end();
673         while (it1 != itend) {
674                 if (is_ex_of_type(*it1, indexed)) {
675                         const indexed & o = ex_to_indexed(*it1);
676                         un.insert(un.end(), o.seq.begin() + 1, o.seq.end());
677                 }
678                 it1++;
679         }
680         find_free_and_dummy(un.begin(), un.end(), free_indices, dummy_indices);
681
682         ex r;
683         if (something_changed) {
684                 if (non_commutative)
685                         r = ncmul(v);
686                 else
687                         r = mul(v);
688         } else
689                 r = e;
690
691         // Product of indexed object with a scalar?
692         if (is_ex_exactly_of_type(r, mul) && r.nops() == 2
693          && is_ex_exactly_of_type(r.op(1), numeric) && is_ex_of_type(r.op(0), indexed))
694                 return r.op(0).op(0).bp->scalar_mul_indexed(r.op(0), ex_to_numeric(r.op(1)));
695         else
696                 return r;
697 }
698
699 /** Simplify indexed expression, return list of free indices. */
700 ex simplify_indexed(const ex & e, exvector & free_indices, const scalar_products & sp)
701 {
702         // Expand the expression
703         ex e_expanded = e.expand();
704
705         // Simplification of single indexed object: just find the free indices
706         if (is_ex_of_type(e_expanded, indexed)) {
707                 const indexed &i = ex_to_indexed(e_expanded);
708                 exvector dummy_indices;
709                 find_free_and_dummy(i.seq.begin() + 1, i.seq.end(), free_indices, dummy_indices);
710                 return e_expanded;
711         }
712
713         // Simplification of sum = sum of simplifications, check consistency of
714         // free indices in each term
715         if (is_ex_exactly_of_type(e_expanded, add)) {
716                 bool first = true;
717                 ex sum = _ex0();
718                 free_indices.clear();
719
720                 for (unsigned i=0; i<e_expanded.nops(); i++) {
721                         exvector free_indices_of_term;
722                         ex term = simplify_indexed(e_expanded.op(i), free_indices_of_term, sp);
723                         if (!term.is_zero()) {
724                                 if (first) {
725                                         free_indices = free_indices_of_term;
726                                         sum = term;
727                                         first = false;
728                                 } else {
729                                         if (!indices_consistent(free_indices, free_indices_of_term))
730                                                 throw (std::runtime_error("simplify_indexed: inconsistent indices in sum"));
731                                         if (is_ex_of_type(sum, indexed) && is_ex_of_type(term, indexed))
732                                                 sum = sum.op(0).bp->add_indexed(sum, term);
733                                         else
734                                                 sum += term;
735                                 }
736                         }
737                 }
738
739                 return sum;
740         }
741
742         // Simplification of products
743         if (is_ex_exactly_of_type(e_expanded, mul)
744          || is_ex_exactly_of_type(e_expanded, ncmul)
745          || (is_ex_exactly_of_type(e_expanded, power) && is_ex_of_type(e_expanded.op(0), indexed) && e_expanded.op(1).is_equal(_ex2())))
746                 return simplify_indexed_product(e_expanded, free_indices, sp);
747
748         // Cannot do anything
749         free_indices.clear();
750         return e_expanded;
751 }
752
753 ex simplify_indexed(const ex & e)
754 {
755         exvector free_indices;
756         scalar_products sp;
757         return simplify_indexed(e, free_indices, sp);
758 }
759
760 ex simplify_indexed(const ex & e, const scalar_products & sp)
761 {
762         exvector free_indices;
763         return simplify_indexed(e, free_indices, sp);
764 }
765
766 //////////
767 // helper classes
768 //////////
769
770 void scalar_products::add(const ex & v1, const ex & v2, const ex & sp)
771 {
772         spm[make_key(v1, v2)] = sp;
773 }
774
775 void scalar_products::clear(void)
776 {
777         spm.clear();
778 }
779
780 /** Check whether scalar product pair is defined. */
781 bool scalar_products::is_defined(const ex & v1, const ex & v2) const
782 {
783         return spm.find(make_key(v1, v2)) != spm.end();
784 }
785
786 /** Return value of defined scalar product pair. */
787 ex scalar_products::evaluate(const ex & v1, const ex & v2) const
788 {
789         return spm.find(make_key(v1, v2))->second;
790 }
791
792 void scalar_products::debugprint(void) const
793 {
794         std::cerr << "map size=" << spm.size() << std::endl;
795         for (spmap::const_iterator cit=spm.begin(); cit!=spm.end(); ++cit) {
796                 const spmapkey & k = cit->first;
797                 std::cerr << "item key=(" << k.first << "," << k.second;
798                 std::cerr << "), value=" << cit->second << std::endl;
799         }
800 }
801
802 /** Make key from object pair. */
803 spmapkey scalar_products::make_key(const ex & v1, const ex & v2)
804 {
805         // If indexed, extract base objects
806         ex s1 = is_ex_of_type(v1, indexed) ? v1.op(0) : v1;
807         ex s2 = is_ex_of_type(v2, indexed) ? v2.op(0) : v2;
808
809         // Enforce canonical order in pair
810         if (s1.compare(s2) > 0)
811                 return spmapkey(s2, s1);
812         else
813                 return spmapkey(s1, s2);
814 }
815
816 } // namespace GiNaC