* Happy New Year(s)!
[ginac.git] / ginac / tensor.cpp
1 /** @file tensor.cpp
2  *
3  *  Implementation of GiNaC's special tensors. */
4
5 /*
6  *  GiNaC Copyright (C) 1999-2007 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., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
21  */
22
23 #include <iostream>
24 #include <stdexcept>
25 #include <vector>
26
27 #include "tensor.h"
28 #include "idx.h"
29 #include "indexed.h"
30 #include "symmetry.h"
31 #include "relational.h"
32 #include "operators.h"
33 #include "lst.h"
34 #include "numeric.h"
35 #include "matrix.h"
36 #include "archive.h"
37 #include "utils.h"
38
39 namespace GiNaC {
40
41 GINAC_IMPLEMENT_REGISTERED_CLASS(tensor, basic)
42
43 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(tensdelta, tensor,
44   print_func<print_dflt>(&tensdelta::do_print).
45   print_func<print_latex>(&tensdelta::do_print_latex))
46
47 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(tensmetric, tensor,
48   print_func<print_dflt>(&tensmetric::do_print).
49   print_func<print_latex>(&tensmetric::do_print))
50
51 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(minkmetric, tensmetric,
52   print_func<print_dflt>(&minkmetric::do_print).
53   print_func<print_latex>(&minkmetric::do_print_latex))
54
55 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(spinmetric, tensmetric,
56   print_func<print_dflt>(&spinmetric::do_print).
57   print_func<print_latex>(&spinmetric::do_print_latex))
58
59 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(tensepsilon, tensor,
60   print_func<print_dflt>(&tensepsilon::do_print).
61   print_func<print_latex>(&tensepsilon::do_print_latex))
62
63 //////////
64 // constructors
65 //////////
66
67 tensor::tensor() : inherited(&tensor::tinfo_static)
68 {
69         setflag(status_flags::evaluated | status_flags::expanded);
70 }
71
72 DEFAULT_CTOR(tensdelta)
73 DEFAULT_CTOR(tensmetric)
74
75 minkmetric::minkmetric() : pos_sig(false)
76 {
77         tinfo_key = &minkmetric::tinfo_static;
78 }
79
80 spinmetric::spinmetric()
81 {
82         tinfo_key = &spinmetric::tinfo_static;
83 }
84
85 minkmetric::minkmetric(bool ps) : pos_sig(ps)
86 {
87         tinfo_key = &minkmetric::tinfo_static;
88 }
89
90 tensepsilon::tensepsilon() : minkowski(false), pos_sig(false)
91 {
92         tinfo_key = &tensepsilon::tinfo_static;
93 }
94
95 tensepsilon::tensepsilon(bool mink, bool ps) : minkowski(mink), pos_sig(ps)
96 {
97         tinfo_key = &tensepsilon::tinfo_static;
98 }
99
100 //////////
101 // archiving
102 //////////
103
104 DEFAULT_ARCHIVING(tensor)
105 DEFAULT_ARCHIVING(tensdelta)
106 DEFAULT_ARCHIVING(tensmetric)
107 DEFAULT_ARCHIVING(spinmetric)
108 DEFAULT_UNARCHIVE(minkmetric)
109 DEFAULT_UNARCHIVE(tensepsilon)
110
111 minkmetric::minkmetric(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
112 {
113         n.find_bool("pos_sig", pos_sig);
114 }
115
116 void minkmetric::archive(archive_node &n) const
117 {
118         inherited::archive(n);
119         n.add_bool("pos_sig", pos_sig);
120 }
121
122 tensepsilon::tensepsilon(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
123 {
124         n.find_bool("minkowski", minkowski);
125         n.find_bool("pos_sig", pos_sig);
126 }
127
128 void tensepsilon::archive(archive_node &n) const
129 {
130         inherited::archive(n);
131         n.add_bool("minkowski", minkowski);
132         n.add_bool("pos_sig", pos_sig);
133 }
134
135 //////////
136 // functions overriding virtual functions from base classes
137 //////////
138
139 DEFAULT_COMPARE(tensor)
140 DEFAULT_COMPARE(tensdelta)
141 DEFAULT_COMPARE(tensmetric)
142 DEFAULT_COMPARE(spinmetric)
143
144 bool tensdelta::info(unsigned inf) const
145 {
146         if(inf == info_flags::real)
147                 return true;
148
149         return false;
150 }
151
152 bool tensmetric::info(unsigned inf) const
153 {
154         if(inf == info_flags::real)
155                 return true;
156
157         return false;
158 }
159
160 int minkmetric::compare_same_type(const basic & other) const
161 {
162         GINAC_ASSERT(is_a<minkmetric>(other));
163         const minkmetric &o = static_cast<const minkmetric &>(other);
164
165         if (pos_sig != o.pos_sig)
166                 return pos_sig ? -1 : 1;
167         else
168                 return inherited::compare_same_type(other);
169 }
170
171 bool minkmetric::info(unsigned inf) const
172 {
173         if(inf == info_flags::real)
174                 return true;
175
176         return false;
177 }
178
179 int tensepsilon::compare_same_type(const basic & other) const
180 {
181         GINAC_ASSERT(is_a<tensepsilon>(other));
182         const tensepsilon &o = static_cast<const tensepsilon &>(other);
183
184         if (minkowski != o.minkowski)
185                 return minkowski ? -1 : 1;
186         else if (pos_sig != o.pos_sig)
187                 return pos_sig ? -1 : 1;
188         else
189                 return inherited::compare_same_type(other);
190 }
191
192 bool tensepsilon::info(unsigned inf) const
193 {
194         if(inf == info_flags::real)
195                 return true;
196
197         return false;
198 }
199
200 bool spinmetric::info(unsigned inf) const
201 {
202         if(inf == info_flags::real)
203                 return true;
204
205         return false;
206 }
207
208 DEFAULT_PRINT_LATEX(tensdelta, "delta", "\\delta")
209 DEFAULT_PRINT(tensmetric, "g")
210 DEFAULT_PRINT_LATEX(minkmetric, "eta", "\\eta")
211 DEFAULT_PRINT_LATEX(spinmetric, "eps", "\\varepsilon")
212 DEFAULT_PRINT_LATEX(tensepsilon, "eps", "\\varepsilon")
213
214 /** Automatic symbolic evaluation of an indexed delta tensor. */
215 ex tensdelta::eval_indexed(const basic & i) const
216 {
217         GINAC_ASSERT(is_a<indexed>(i));
218         GINAC_ASSERT(i.nops() == 3);
219         GINAC_ASSERT(is_a<tensdelta>(i.op(0)));
220
221         const idx & i1 = ex_to<idx>(i.op(1));
222         const idx & i2 = ex_to<idx>(i.op(2));
223
224         // The dimension of the indices must be equal, otherwise we use the minimal
225         // dimension
226         if (!i1.get_dim().is_equal(i2.get_dim())) {
227                 ex min_dim = i1.minimal_dim(i2);
228                 exmap m;
229                 m[i1] = i1.replace_dim(min_dim);
230                 m[i2] = i2.replace_dim(min_dim);
231                 return i.subs(m, subs_options::no_pattern);
232         }
233
234         // Trace of delta tensor is the (effective) dimension of the space
235         if (is_dummy_pair(i1, i2)) {
236                 try {
237                         return i1.minimal_dim(i2);
238                 } catch (std::exception &e) {
239                         return i.hold();
240                 }
241         }
242
243         // Numeric evaluation
244         if (static_cast<const indexed &>(i).all_index_values_are(info_flags::integer)) {
245                 int n1 = ex_to<numeric>(i1.get_value()).to_int(), n2 = ex_to<numeric>(i2.get_value()).to_int();
246                 if (n1 == n2)
247                         return _ex1;
248                 else
249                         return _ex0;
250         }
251
252         // No further simplifications
253         return i.hold();
254 }
255
256 /** Automatic symbolic evaluation of an indexed metric tensor. */
257 ex tensmetric::eval_indexed(const basic & i) const
258 {
259         GINAC_ASSERT(is_a<indexed>(i));
260         GINAC_ASSERT(i.nops() == 3);
261         GINAC_ASSERT(is_a<tensmetric>(i.op(0)));
262         GINAC_ASSERT(is_a<varidx>(i.op(1)));
263         GINAC_ASSERT(is_a<varidx>(i.op(2)));
264
265         const varidx & i1 = ex_to<varidx>(i.op(1));
266         const varidx & i2 = ex_to<varidx>(i.op(2));
267
268         // The dimension of the indices must be equal, otherwise we use the minimal
269         // dimension
270         if (!i1.get_dim().is_equal(i2.get_dim())) {
271                 ex min_dim = i1.minimal_dim(i2);
272                 exmap m;
273                 m[i1] = i1.replace_dim(min_dim);
274                 m[i2] = i2.replace_dim(min_dim);
275                 return i.subs(m, subs_options::no_pattern);
276         }
277
278         // A metric tensor with one covariant and one contravariant index gets
279         // replaced by a delta tensor
280         if (i1.is_covariant() != i2.is_covariant())
281                 return delta_tensor(i1, i2);
282
283         // No further simplifications
284         return i.hold();
285 }
286
287 /** Automatic symbolic evaluation of an indexed Lorentz metric tensor. */
288 ex minkmetric::eval_indexed(const basic & i) const
289 {
290         GINAC_ASSERT(is_a<indexed>(i));
291         GINAC_ASSERT(i.nops() == 3);
292         GINAC_ASSERT(is_a<minkmetric>(i.op(0)));
293         GINAC_ASSERT(is_a<varidx>(i.op(1)));
294         GINAC_ASSERT(is_a<varidx>(i.op(2)));
295
296         const varidx & i1 = ex_to<varidx>(i.op(1));
297         const varidx & i2 = ex_to<varidx>(i.op(2));
298
299         // Numeric evaluation
300         if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
301                 int n1 = ex_to<numeric>(i1.get_value()).to_int(), n2 = ex_to<numeric>(i2.get_value()).to_int();
302                 if (n1 != n2)
303                         return _ex0;
304                 else if (n1 == 0)
305                         return pos_sig ? _ex_1 : _ex1;
306                 else
307                         return pos_sig ? _ex1 : _ex_1;
308         }
309
310         // Perform the usual evaluations of a metric tensor
311         return inherited::eval_indexed(i);
312 }
313
314 /** Automatic symbolic evaluation of an indexed metric tensor. */
315 ex spinmetric::eval_indexed(const basic & i) const
316 {
317         GINAC_ASSERT(is_a<indexed>(i));
318         GINAC_ASSERT(i.nops() == 3);
319         GINAC_ASSERT(is_a<spinmetric>(i.op(0)));
320         GINAC_ASSERT(is_a<spinidx>(i.op(1)));
321         GINAC_ASSERT(is_a<spinidx>(i.op(2)));
322
323         const spinidx & i1 = ex_to<spinidx>(i.op(1));
324         const spinidx & i2 = ex_to<spinidx>(i.op(2));
325
326         // Convolutions are zero
327         if (!(static_cast<const indexed &>(i).get_dummy_indices().empty()))
328                 return _ex0;
329
330         // Numeric evaluation
331         if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
332                 int n1 = ex_to<numeric>(i1.get_value()).to_int(), n2 = ex_to<numeric>(i2.get_value()).to_int();
333                 if (n1 == n2)
334                         return _ex0;
335                 else if (n1 < n2)
336                         return _ex1;
337                 else
338                         return _ex_1;
339         }
340
341         // No further simplifications
342         return i.hold();
343 }
344
345 /** Automatic symbolic evaluation of an indexed epsilon tensor. */
346 ex tensepsilon::eval_indexed(const basic & i) const
347 {
348         GINAC_ASSERT(is_a<indexed>(i));
349         GINAC_ASSERT(i.nops() > 1);
350         GINAC_ASSERT(is_a<tensepsilon>(i.op(0)));
351
352         // Convolutions are zero
353         if (!(static_cast<const indexed &>(i).get_dummy_indices().empty()))
354                 return _ex0;
355
356         // Numeric evaluation
357         if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
358
359                 // Get sign of index permutation (the indices should already be in
360                 // a canonic order but we can't assume what exactly that order is)
361                 std::vector<int> v;
362                 v.reserve(i.nops() - 1);
363                 for (size_t j=1; j<i.nops(); j++)
364                         v.push_back(ex_to<numeric>(ex_to<idx>(i.op(j)).get_value()).to_int());
365                 int sign = permutation_sign(v.begin(), v.end());
366
367                 // In a Minkowski space, check for covariant indices
368                 if (minkowski) {
369                         for (size_t j=1; j<i.nops(); j++) {
370                                 const ex & x = i.op(j);
371                                 if (!is_a<varidx>(x))
372                                         throw(std::runtime_error("indices of epsilon tensor in Minkowski space must be of type varidx"));
373                                 if (ex_to<varidx>(x).is_covariant())
374                                         if (ex_to<idx>(x).get_value().is_zero())
375                                                 sign = (pos_sig ? -sign : sign);
376                                         else
377                                                 sign = (pos_sig ? sign : -sign);
378                         }
379                 }
380
381                 return sign;
382         }
383
384         // No further simplifications
385         return i.hold();
386 }
387
388 bool tensor::replace_contr_index(exvector::iterator self, exvector::iterator other) const
389 {
390         // Try to contract the first index
391         const idx *self_idx = &ex_to<idx>(self->op(1));
392         const idx *free_idx = &ex_to<idx>(self->op(2));
393         bool first_index_tried = false;
394
395 again:
396         if (self_idx->is_symbolic()) {
397                 for (size_t i=1; i<other->nops(); i++) {
398                         if (! is_a<idx>(other->op(i)))
399                                 continue;
400                         const idx &other_idx = ex_to<idx>(other->op(i));
401                         if (is_dummy_pair(*self_idx, other_idx)) {
402
403                                 // Contraction found, remove this tensor and substitute the
404                                 // index in the second object
405                                 try {
406                                         // minimal_dim() throws an exception when index dimensions are not comparable
407                                         ex min_dim = self_idx->minimal_dim(other_idx);
408                                         *other = other->subs(other_idx == free_idx->replace_dim(min_dim));
409                                         *self = _ex1; // *other is assigned first because assigning *self invalidates free_idx
410                                         return true;
411                                 } catch (std::exception &e) {
412                                         return false;
413                                 }
414                         }
415                 }
416         }
417
418         if (!first_index_tried) {
419
420                 // No contraction with the first index found, try the second index
421                 self_idx = &ex_to<idx>(self->op(2));
422                 free_idx = &ex_to<idx>(self->op(1));
423                 first_index_tried = true;
424                 goto again;
425         }
426
427         return false;
428 }
429
430 /** Contraction of an indexed delta tensor with something else. */
431 bool tensdelta::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
432 {
433         GINAC_ASSERT(is_a<indexed>(*self));
434         GINAC_ASSERT(is_a<indexed>(*other));
435         GINAC_ASSERT(self->nops() == 3);
436         GINAC_ASSERT(is_a<tensdelta>(self->op(0)));
437
438         // Replace the dummy index with this tensor's other index and remove
439         // the tensor (this is valid for contractions with all other tensors)
440         return replace_contr_index(self, other);
441 }
442
443 /** Contraction of an indexed metric tensor with something else. */
444 bool tensmetric::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
445 {
446         GINAC_ASSERT(is_a<indexed>(*self));
447         GINAC_ASSERT(is_a<indexed>(*other));
448         GINAC_ASSERT(self->nops() == 3);
449         GINAC_ASSERT(is_a<tensmetric>(self->op(0)));
450
451         // If contracting with the delta tensor, let the delta do it
452         // (don't raise/lower delta indices)
453         if (is_a<tensdelta>(other->op(0)))
454                 return false;
455
456         // Replace the dummy index with this tensor's other index and remove
457         // the tensor
458         return replace_contr_index(self, other);
459 }
460
461 /** Contraction of an indexed spinor metric with something else. */
462 bool spinmetric::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
463 {
464         GINAC_ASSERT(is_a<indexed>(*self));
465         GINAC_ASSERT(is_a<indexed>(*other));
466         GINAC_ASSERT(self->nops() == 3);
467         GINAC_ASSERT(is_a<spinmetric>(self->op(0)));
468
469         // Contractions between spinor metrics
470         if (is_a<spinmetric>(other->op(0))) {
471                 const idx &self_i1 = ex_to<idx>(self->op(1));
472                 const idx &self_i2 = ex_to<idx>(self->op(2));
473                 const idx &other_i1 = ex_to<idx>(other->op(1));
474                 const idx &other_i2 = ex_to<idx>(other->op(2));
475
476                 if (is_dummy_pair(self_i1, other_i1)) {
477                         if (is_dummy_pair(self_i2, other_i2))
478                                 *self = _ex2;
479                         else
480                                 *self = delta_tensor(self_i2, other_i2);
481                         *other = _ex1;
482                         return true;
483                 } else if (is_dummy_pair(self_i1, other_i2)) {
484                         if (is_dummy_pair(self_i2, other_i1))
485                                 *self = _ex_2;
486                         else
487                                 *self = -delta_tensor(self_i2, other_i1);
488                         *other = _ex1;
489                         return true;
490                 } else if (is_dummy_pair(self_i2, other_i1)) {
491                         *self = -delta_tensor(self_i1, other_i2);
492                         *other = _ex1;
493                         return true;
494                 } else if (is_dummy_pair(self_i2, other_i2)) {
495                         *self = delta_tensor(self_i1, other_i1);
496                         *other = _ex1;
497                         return true;
498                 }
499         }
500
501         // If contracting with the delta tensor, let the delta do it
502         // (don't raise/lower delta indices)
503         if (is_a<tensdelta>(other->op(0)))
504                 return false;
505
506         // Try to contract first index
507         const idx *self_idx = &ex_to<idx>(self->op(1));
508         const idx *free_idx = &ex_to<idx>(self->op(2));
509         bool first_index_tried = false;
510         int sign = 1;
511
512 again:
513         if (self_idx->is_symbolic()) {
514                 for (size_t i=1; i<other->nops(); i++) {
515                         const idx &other_idx = ex_to<idx>(other->op(i));
516                         if (is_dummy_pair(*self_idx, other_idx)) {
517
518                                 // Contraction found, remove metric tensor and substitute
519                                 // index in second object (assign *self last because this
520                                 // invalidates free_idx)
521                                 *other = other->subs(other_idx == *free_idx);
522                                 *self = (static_cast<const spinidx *>(self_idx)->is_covariant() ? sign : -sign);
523                                 return true;
524                         }
525                 }
526         }
527
528         if (!first_index_tried) {
529
530                 // No contraction with first index found, try second index
531                 self_idx = &ex_to<idx>(self->op(2));
532                 free_idx = &ex_to<idx>(self->op(1));
533                 first_index_tried = true;
534                 sign = -sign;
535                 goto again;
536         }
537
538         return false;
539 }
540
541 /** Contraction of epsilon tensor with something else. */
542 bool tensepsilon::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
543 {
544         GINAC_ASSERT(is_a<indexed>(*self));
545         GINAC_ASSERT(is_a<indexed>(*other));
546         GINAC_ASSERT(is_a<tensepsilon>(self->op(0)));
547         size_t num = self->nops() - 1;
548
549         if (is_exactly_a<tensepsilon>(other->op(0)) && num+1 == other->nops()) {
550
551                 // Contraction of two epsilon tensors is a determinant
552                 bool variance = is_a<varidx>(self->op(1));
553                 matrix M(num, num);
554                 for (size_t i=0; i<num; i++) {
555                         for (size_t j=0; j<num; j++) {
556                                 if (minkowski)
557                                         M(i, j) = lorentz_g(self->op(i+1), other->op(j+1), pos_sig);
558                                 else if (variance)
559                                         M(i, j) = metric_tensor(self->op(i+1), other->op(j+1));
560                                 else
561                                         M(i, j) = delta_tensor(self->op(i+1), other->op(j+1));
562                         }
563                 }
564                 int sign = minkowski ? -1 : 1;
565                 *self = sign * M.determinant().simplify_indexed();
566                 *other = _ex1;
567                 return true;
568         }
569
570         return false;
571 }
572
573 //////////
574 // global functions
575 //////////
576
577 ex delta_tensor(const ex & i1, const ex & i2)
578 {
579         static ex delta = (new tensdelta)->setflag(status_flags::dynallocated);
580
581         if (!is_a<idx>(i1) || !is_a<idx>(i2))
582                 throw(std::invalid_argument("indices of delta tensor must be of type idx"));
583
584         return indexed(delta, symmetric2(), i1, i2);
585 }
586
587 ex metric_tensor(const ex & i1, const ex & i2)
588 {
589         static ex metric = (new tensmetric)->setflag(status_flags::dynallocated);
590
591         if (!is_a<varidx>(i1) || !is_a<varidx>(i2))
592                 throw(std::invalid_argument("indices of metric tensor must be of type varidx"));
593
594         return indexed(metric, symmetric2(), i1, i2);
595 }
596
597 ex lorentz_g(const ex & i1, const ex & i2, bool pos_sig)
598 {
599         static ex metric_neg = (new minkmetric(false))->setflag(status_flags::dynallocated);
600         static ex metric_pos = (new minkmetric(true))->setflag(status_flags::dynallocated);
601
602         if (!is_a<varidx>(i1) || !is_a<varidx>(i2))
603                 throw(std::invalid_argument("indices of metric tensor must be of type varidx"));
604
605         return indexed(pos_sig ? metric_pos : metric_neg, symmetric2(), i1, i2);
606 }
607
608 ex spinor_metric(const ex & i1, const ex & i2)
609 {
610         static ex metric = (new spinmetric)->setflag(status_flags::dynallocated);
611
612         if (!is_a<spinidx>(i1) || !is_a<spinidx>(i2))
613                 throw(std::invalid_argument("indices of spinor metric must be of type spinidx"));
614         if (!ex_to<idx>(i1).get_dim().is_equal(2) || !ex_to<idx>(i2).get_dim().is_equal(2))
615                 throw(std::runtime_error("index dimension for spinor metric must be 2"));
616
617         return indexed(metric, antisymmetric2(), i1, i2);
618 }
619
620 ex epsilon_tensor(const ex & i1, const ex & i2)
621 {
622         static ex epsilon = (new tensepsilon)->setflag(status_flags::dynallocated);
623
624         if (!is_a<idx>(i1) || !is_a<idx>(i2))
625                 throw(std::invalid_argument("indices of epsilon tensor must be of type idx"));
626
627         ex dim = ex_to<idx>(i1).get_dim();
628         if (!dim.is_equal(ex_to<idx>(i2).get_dim()))
629                 throw(std::invalid_argument("all indices of epsilon tensor must have the same dimension"));
630         if (!ex_to<idx>(i1).get_dim().is_equal(_ex2))
631                 throw(std::runtime_error("index dimension of epsilon tensor must match number of indices"));
632
633         if(is_a<wildcard>(i1.op(0))||is_a<wildcard>(i2.op(0)))
634                 return indexed(epsilon, antisymmetric2(), i1, i2).hold();
635
636         return indexed(epsilon, antisymmetric2(), i1, i2);
637 }
638
639 ex epsilon_tensor(const ex & i1, const ex & i2, const ex & i3)
640 {
641         static ex epsilon = (new tensepsilon)->setflag(status_flags::dynallocated);
642
643         if (!is_a<idx>(i1) || !is_a<idx>(i2) || !is_a<idx>(i3))
644                 throw(std::invalid_argument("indices of epsilon tensor must be of type idx"));
645
646         ex dim = ex_to<idx>(i1).get_dim();
647         if (!dim.is_equal(ex_to<idx>(i2).get_dim()) || !dim.is_equal(ex_to<idx>(i3).get_dim()))
648                 throw(std::invalid_argument("all indices of epsilon tensor must have the same dimension"));
649         if (!ex_to<idx>(i1).get_dim().is_equal(_ex3))
650                 throw(std::runtime_error("index dimension of epsilon tensor must match number of indices"));
651
652         if(is_a<wildcard>(i1.op(0))||is_a<wildcard>(i2.op(0))||is_a<wildcard>(i3.op(0)))
653                 return indexed(epsilon, antisymmetric3(), i1, i2, i3).hold();
654
655         return indexed(epsilon, antisymmetric3(), i1, i2, i3);
656 }
657
658 ex lorentz_eps(const ex & i1, const ex & i2, const ex & i3, const ex & i4, bool pos_sig)
659 {
660         static ex epsilon_neg = (new tensepsilon(true, false))->setflag(status_flags::dynallocated);
661         static ex epsilon_pos = (new tensepsilon(true, true))->setflag(status_flags::dynallocated);
662
663         if (!is_a<varidx>(i1) || !is_a<varidx>(i2) || !is_a<varidx>(i3) || !is_a<varidx>(i4))
664                 throw(std::invalid_argument("indices of Lorentz epsilon tensor must be of type varidx"));
665
666         ex dim = ex_to<idx>(i1).get_dim();
667         if (!dim.is_equal(ex_to<idx>(i2).get_dim()) || !dim.is_equal(ex_to<idx>(i3).get_dim()) || !dim.is_equal(ex_to<idx>(i4).get_dim()))
668                 throw(std::invalid_argument("all indices of epsilon tensor must have the same dimension"));
669         if (!ex_to<idx>(i1).get_dim().is_equal(_ex4))
670                 throw(std::runtime_error("index dimension of epsilon tensor must match number of indices"));
671
672         if(is_a<wildcard>(i1.op(0))||is_a<wildcard>(i2.op(0))||is_a<wildcard>(i3.op(0))||is_a<wildcard>(i4.op(0)))
673                 return indexed(pos_sig ? epsilon_pos : epsilon_neg, antisymmetric4(), i1, i2, i3, i4).hold();
674
675         return indexed(pos_sig ? epsilon_pos : epsilon_neg, antisymmetric4(), i1, i2, i3, i4);
676 }
677
678 } // namespace GiNaC