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[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 /** Check whether two sorted index vectors are consistent (i.e. equal). */
449 static bool indices_consistent(const exvector & v1, const exvector & v2)
450 {
451         // Number of indices must be the same
452         if (v1.size() != v2.size())
453                 return false;
454
455         // And also the indices themselves
456         exvector::const_iterator ait = v1.begin(), aitend = v1.end(),
457                                  bit = v2.begin(), bitend = v2.end();
458         while (ait != aitend) {
459                 if (!ait->is_equal(*bit))
460                         return false;
461                 ait++; bit++;
462         }
463         return true;
464 }
465
466 exvector indexed::get_indices(void) const
467 {
468         GINAC_ASSERT(seq.size() >= 1);
469         return exvector(seq.begin() + 1, seq.end());
470 }
471
472 exvector indexed::get_dummy_indices(void) const
473 {
474         exvector free_indices, dummy_indices;
475         find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices);
476         return dummy_indices;
477 }
478
479 exvector indexed::get_dummy_indices(const indexed & other) const
480 {
481         exvector indices = get_free_indices();
482         exvector other_indices = other.get_free_indices();
483         indices.insert(indices.end(), other_indices.begin(), other_indices.end());
484         exvector dummy_indices;
485         find_dummy_indices(indices, dummy_indices);
486         return dummy_indices;
487 }
488
489 exvector indexed::get_free_indices(void) const
490 {
491         exvector free_indices, dummy_indices;
492         find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices);
493         return free_indices;
494 }
495
496 exvector add::get_free_indices(void) const
497 {
498         exvector free_indices;
499         for (unsigned i=0; i<nops(); i++) {
500                 if (i == 0)
501                         free_indices = op(i).get_free_indices();
502                 else {
503                         exvector free_indices_of_term = op(i).get_free_indices();
504                         if (!indices_consistent(free_indices, free_indices_of_term))
505                                 throw (std::runtime_error("add::get_free_indices: inconsistent indices in sum"));
506                 }
507         }
508         return free_indices;
509 }
510
511 exvector mul::get_free_indices(void) const
512 {
513         // Concatenate free indices of all factors
514         exvector un;
515         for (unsigned i=0; i<nops(); i++) {
516                 exvector free_indices_of_factor = op(i).get_free_indices();
517                 un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
518         }
519
520         // And remove the dummy indices
521         exvector free_indices, dummy_indices;
522         find_free_and_dummy(un, free_indices, dummy_indices);
523         return free_indices;
524 }
525
526 exvector ncmul::get_free_indices(void) const
527 {
528         // Concatenate free indices of all factors
529         exvector un;
530         for (unsigned i=0; i<nops(); i++) {
531                 exvector free_indices_of_factor = op(i).get_free_indices();
532                 un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
533         }
534
535         // And remove the dummy indices
536         exvector free_indices, dummy_indices;
537         find_free_and_dummy(un, free_indices, dummy_indices);
538         return free_indices;
539 }
540
541 exvector power::get_free_indices(void) const
542 {
543         // Return free indices of basis
544         return basis.get_free_indices();
545 }
546
547 /** Simplify product of indexed expressions (commutative, noncommutative and
548  *  simple squares), return list of free indices. */
549 ex simplify_indexed_product(const ex & e, exvector & free_indices, const scalar_products & sp)
550 {
551         // Remember whether the product was commutative or noncommutative
552         // (because we chop it into factors and need to reassemble later)
553         bool non_commutative = is_ex_exactly_of_type(e, ncmul);
554
555         // Collect factors in an exvector, store squares twice
556         exvector v;
557         v.reserve(e.nops() * 2);
558
559         if (is_ex_exactly_of_type(e, power)) {
560                 // We only get called for simple squares, split a^2 -> a*a
561                 GINAC_ASSERT(e.op(1).is_equal(_ex2()));
562                 v.push_back(e.op(0));
563                 v.push_back(e.op(0));
564         } else {
565                 for (int i=0; i<e.nops(); i++) {
566                         ex f = e.op(i);
567                         if (is_ex_exactly_of_type(f, power) && f.op(1).is_equal(_ex2())) {
568                                 v.push_back(f.op(0));
569                     v.push_back(f.op(0));
570                         } else if (is_ex_exactly_of_type(f, ncmul)) {
571                                 // Noncommutative factor found, split it as well
572                                 non_commutative = true; // everything becomes noncommutative, ncmul will sort out the commutative factors later
573                                 for (int j=0; j<f.nops(); j++)
574                                         v.push_back(f.op(j));
575                         } else
576                                 v.push_back(f);
577                 }
578         }
579
580         // Perform contractions
581         bool something_changed = false;
582         GINAC_ASSERT(v.size() > 1);
583         exvector::iterator it1, itend = v.end(), next_to_last = itend - 1;
584         for (it1 = v.begin(); it1 != next_to_last; it1++) {
585
586 try_again:
587                 if (!is_ex_of_type(*it1, indexed))
588                         continue;
589
590                 // Indexed factor found, get free indices and look for contraction
591                 // candidates
592                 exvector free1, dummy1;
593                 find_free_and_dummy(ex_to_indexed(*it1).seq.begin() + 1, ex_to_indexed(*it1).seq.end(), free1, dummy1);
594
595                 exvector::iterator it2;
596                 for (it2 = it1 + 1; it2 != itend; it2++) {
597
598                         if (!is_ex_of_type(*it2, indexed))
599                                 continue;
600
601                         // Find free indices of second factor and merge them with free
602                         // indices of first factor
603                         exvector un;
604                         find_free_and_dummy(ex_to_indexed(*it2).seq.begin() + 1, ex_to_indexed(*it2).seq.end(), un, dummy1);
605                         un.insert(un.end(), free1.begin(), free1.end());
606
607                         // Check whether the two factors share dummy indices
608                         exvector free, dummy;
609                         find_free_and_dummy(un, free, dummy);
610                         if (dummy.size() == 0)
611                                 continue;
612
613                         // At least one dummy index, is it a defined scalar product?
614                         if (free.size() == 0) {
615                                 if (sp.is_defined(*it1, *it2)) {
616                                         *it1 = sp.evaluate(*it1, *it2);
617                                         *it2 = _ex1();
618                                         something_changed = true;
619                                         goto try_again;
620                                 }
621                         }
622
623                         // Contraction of symmetric with antisymmetric object is zero
624                         if ((ex_to_indexed(*it1).symmetry == indexed::symmetric &&
625                              ex_to_indexed(*it2).symmetry == indexed::antisymmetric
626                           || ex_to_indexed(*it1).symmetry == indexed::antisymmetric &&
627                              ex_to_indexed(*it2).symmetry == indexed::symmetric)
628                          && dummy.size() > 1) {
629                                 free_indices.clear();
630                                 return _ex0();
631                         }
632
633                         // Try to contract the first one with the second one
634                         bool contracted = it1->op(0).bp->contract_with(it1, it2, v);
635                         if (!contracted) {
636
637                                 // That didn't work; maybe the second object knows how to
638                                 // contract itself with the first one
639                                 contracted = it2->op(0).bp->contract_with(it2, it1, v);
640                         }
641                         if (contracted) {
642                                 something_changed = true;
643
644                                 // Both objects may have new indices now or they might
645                                 // even not be indexed objects any more, so we have to
646                                 // start over
647                                 goto try_again;
648                         }
649                 }
650         }
651
652         // Find free indices (concatenate them all and call find_free_and_dummy())
653         exvector un, dummy_indices;
654         it1 = v.begin(); itend = v.end();
655         while (it1 != itend) {
656                 if (is_ex_of_type(*it1, indexed)) {
657                         const indexed & o = ex_to_indexed(*it1);
658                         un.insert(un.end(), o.seq.begin() + 1, o.seq.end());
659                 }
660                 it1++;
661         }
662         find_free_and_dummy(un, free_indices, dummy_indices);
663
664         ex r;
665         if (something_changed) {
666                 if (non_commutative)
667                         r = ncmul(v);
668                 else
669                         r = mul(v);
670         } else
671                 r = e;
672
673         // Product of indexed object with a scalar?
674         if (is_ex_exactly_of_type(r, mul) && r.nops() == 2
675          && is_ex_exactly_of_type(r.op(1), numeric) && is_ex_of_type(r.op(0), indexed))
676                 return r.op(0).op(0).bp->scalar_mul_indexed(r.op(0), ex_to_numeric(r.op(1)));
677         else
678                 return r;
679 }
680
681 /** Simplify indexed expression, return list of free indices. */
682 ex simplify_indexed(const ex & e, exvector & free_indices, const scalar_products & sp)
683 {
684         // Expand the expression
685         ex e_expanded = e.expand();
686
687         // Simplification of single indexed object: just find the free indices
688         if (is_ex_of_type(e_expanded, indexed)) {
689                 const indexed &i = ex_to_indexed(e_expanded);
690                 exvector dummy_indices;
691                 find_free_and_dummy(i.seq.begin() + 1, i.seq.end(), free_indices, dummy_indices);
692                 return e_expanded;
693         }
694
695         // Simplification of sum = sum of simplifications, check consistency of
696         // free indices in each term
697         if (is_ex_exactly_of_type(e_expanded, add)) {
698                 bool first = true;
699                 ex sum = _ex0();
700                 free_indices.clear();
701
702                 for (unsigned i=0; i<e_expanded.nops(); i++) {
703                         exvector free_indices_of_term;
704                         ex term = simplify_indexed(e_expanded.op(i), free_indices_of_term, sp);
705                         if (!term.is_zero()) {
706                                 if (first) {
707                                         free_indices = free_indices_of_term;
708                                         sum = term;
709                                         first = false;
710                                 } else {
711                                         if (!indices_consistent(free_indices, free_indices_of_term))
712                                                 throw (std::runtime_error("simplify_indexed: inconsistent indices in sum"));
713                                         if (is_ex_of_type(sum, indexed) && is_ex_of_type(term, indexed))
714                                                 sum = sum.op(0).bp->add_indexed(sum, term);
715                                         else
716                                                 sum += term;
717                                 }
718                         }
719                 }
720
721                 return sum;
722         }
723
724         // Simplification of products
725         if (is_ex_exactly_of_type(e_expanded, mul)
726          || is_ex_exactly_of_type(e_expanded, ncmul)
727          || (is_ex_exactly_of_type(e_expanded, power) && is_ex_of_type(e_expanded.op(0), indexed) && e_expanded.op(1).is_equal(_ex2())))
728                 return simplify_indexed_product(e_expanded, free_indices, sp);
729
730         // Cannot do anything
731         free_indices.clear();
732         return e_expanded;
733 }
734
735 ex simplify_indexed(const ex & e)
736 {
737         exvector free_indices;
738         scalar_products sp;
739         return simplify_indexed(e, free_indices, sp);
740 }
741
742 ex simplify_indexed(const ex & e, const scalar_products & sp)
743 {
744         exvector free_indices;
745         return simplify_indexed(e, free_indices, sp);
746 }
747
748 //////////
749 // helper classes
750 //////////
751
752 void scalar_products::add(const ex & v1, const ex & v2, const ex & sp)
753 {
754         spm[make_key(v1, v2)] = sp;
755 }
756
757 void scalar_products::clear(void)
758 {
759         spm.clear();
760 }
761
762 /** Check whether scalar product pair is defined. */
763 bool scalar_products::is_defined(const ex & v1, const ex & v2) const
764 {
765         return spm.find(make_key(v1, v2)) != spm.end();
766 }
767
768 /** Return value of defined scalar product pair. */
769 ex scalar_products::evaluate(const ex & v1, const ex & v2) const
770 {
771         return spm.find(make_key(v1, v2))->second;
772 }
773
774 void scalar_products::debugprint(void) const
775 {
776         std::cerr << "map size=" << spm.size() << std::endl;
777         for (spmap::const_iterator cit=spm.begin(); cit!=spm.end(); ++cit) {
778                 const spmapkey & k = cit->first;
779                 std::cerr << "item key=(" << k.first << "," << k.second;
780                 std::cerr << "), value=" << cit->second << std::endl;
781         }
782 }
783
784 /** Make key from object pair. */
785 spmapkey scalar_products::make_key(const ex & v1, const ex & v2)
786 {
787         // If indexed, extract base objects
788         ex s1 = is_ex_of_type(v1, indexed) ? v1.op(0) : v1;
789         ex s2 = is_ex_of_type(v2, indexed) ? v2.op(0) : v2;
790
791         // Enforce canonical order in pair
792         if (s1.compare(s2) > 0)
793                 return spmapkey(s2, s1);
794         else
795                 return spmapkey(s1, s2);
796 }
797
798 } // namespace GiNaC