3 * Implementation of GiNaC's special tensors. */
6 * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
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.
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.
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
29 #include "relational.h"
39 GINAC_IMPLEMENT_REGISTERED_CLASS(tensor, basic)
40 GINAC_IMPLEMENT_REGISTERED_CLASS(tensdelta, tensor)
41 GINAC_IMPLEMENT_REGISTERED_CLASS(tensmetric, tensor)
42 GINAC_IMPLEMENT_REGISTERED_CLASS(minkmetric, tensmetric)
43 GINAC_IMPLEMENT_REGISTERED_CLASS(tensepsilon, tensor)
46 // default constructor, destructor, copy constructor assignment operator and helpers
49 tensor::tensor(unsigned ti) : inherited(ti)
51 debugmsg("tensor constructor from unsigned", LOGLEVEL_CONSTRUCT); \
55 DEFAULT_CTORS(tensdelta)
56 DEFAULT_CTORS(tensmetric)
57 DEFAULT_DESTROY(minkmetric)
58 DEFAULT_DESTROY(tensepsilon)
60 minkmetric::minkmetric() : pos_sig(false)
62 debugmsg("minkmetric default constructor", LOGLEVEL_CONSTRUCT);
63 tinfo_key = TINFO_minkmetric;
66 minkmetric::minkmetric(bool ps) : pos_sig(ps)
68 debugmsg("minkmetric constructor from bool", LOGLEVEL_CONSTRUCT);
69 tinfo_key = TINFO_minkmetric;
72 void minkmetric::copy(const minkmetric & other)
74 inherited::copy(other);
75 pos_sig = other.pos_sig;
78 tensepsilon::tensepsilon() : minkowski(false), pos_sig(false)
80 debugmsg("tensepsilon default constructor", LOGLEVEL_CONSTRUCT);
81 tinfo_key = TINFO_tensepsilon;
84 tensepsilon::tensepsilon(bool mink, bool ps) : minkowski(mink), pos_sig(ps)
86 debugmsg("tensepsilon constructor from bool,bool", LOGLEVEL_CONSTRUCT);
87 tinfo_key = TINFO_tensepsilon;
90 void tensepsilon::copy(const tensepsilon & other)
92 inherited::copy(other);
93 minkowski = other.minkowski;
94 pos_sig = other.pos_sig;
101 DEFAULT_ARCHIVING(tensor)
102 DEFAULT_ARCHIVING(tensdelta)
103 DEFAULT_ARCHIVING(tensmetric)
104 DEFAULT_UNARCHIVE(minkmetric)
105 DEFAULT_UNARCHIVE(tensepsilon)
107 minkmetric::minkmetric(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
109 debugmsg("minkmetric constructor from archive_node", LOGLEVEL_CONSTRUCT);
110 n.find_bool("pos_sig", pos_sig);
113 void minkmetric::archive(archive_node &n) const
115 inherited::archive(n);
116 n.add_bool("pos_sig", pos_sig);
119 tensepsilon::tensepsilon(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
121 debugmsg("tensepsilon constructor from archive_node", LOGLEVEL_CONSTRUCT);
122 n.find_bool("minkowski", minkowski);
123 n.find_bool("pos_sig", pos_sig);
126 void tensepsilon::archive(archive_node &n) const
128 inherited::archive(n);
129 n.add_bool("minkowski", minkowski);
130 n.add_bool("pos_sig", pos_sig);
134 // functions overriding virtual functions from bases classes
137 DEFAULT_COMPARE(tensor)
138 DEFAULT_COMPARE(tensdelta)
139 DEFAULT_COMPARE(tensmetric)
141 int minkmetric::compare_same_type(const basic & other) const
143 GINAC_ASSERT(is_of_type(other, minkmetric));
144 const minkmetric &o = static_cast<const minkmetric &>(other);
146 if (pos_sig != o.pos_sig)
147 return pos_sig ? -1 : 1;
149 return inherited::compare_same_type(other);
152 int tensepsilon::compare_same_type(const basic & other) const
154 GINAC_ASSERT(is_of_type(other, tensepsilon));
155 const tensepsilon &o = static_cast<const tensepsilon &>(other);
157 if (minkowski != o.minkowski)
158 return minkowski ? -1 : 1;
159 else if (pos_sig != o.pos_sig)
160 return pos_sig ? -1 : 1;
162 return inherited::compare_same_type(other);
165 DEFAULT_PRINT_LATEX(tensdelta, "delta", "\\delta")
166 DEFAULT_PRINT(tensmetric, "g")
167 DEFAULT_PRINT_LATEX(minkmetric, "eta", "\\eta")
168 DEFAULT_PRINT_LATEX(tensepsilon, "eps", "\\epsilon")
170 /** Automatic symbolic evaluation of an indexed delta tensor. */
171 ex tensdelta::eval_indexed(const basic & i) const
173 GINAC_ASSERT(is_of_type(i, indexed));
174 GINAC_ASSERT(i.nops() == 3);
175 GINAC_ASSERT(is_ex_of_type(i.op(0), tensdelta));
177 const idx & i1 = ex_to_idx(i.op(1));
178 const idx & i2 = ex_to_idx(i.op(2));
180 // Trace of delta tensor is the dimension of the space
181 if (is_dummy_pair(i1, i2))
184 // Numeric evaluation
185 if (static_cast<const indexed &>(i).all_index_values_are(info_flags::integer)) {
186 int n1 = ex_to_numeric(i1.get_value()).to_int(), n2 = ex_to_numeric(i2.get_value()).to_int();
193 // No further simplifications
197 /** Automatic symbolic evaluation of an indexed metric tensor. */
198 ex tensmetric::eval_indexed(const basic & i) const
200 GINAC_ASSERT(is_of_type(i, indexed));
201 GINAC_ASSERT(i.nops() == 3);
202 GINAC_ASSERT(is_ex_of_type(i.op(0), tensmetric));
203 GINAC_ASSERT(is_ex_of_type(i.op(1), varidx));
204 GINAC_ASSERT(is_ex_of_type(i.op(2), varidx));
206 const varidx & i1 = ex_to_varidx(i.op(1));
207 const varidx & i2 = ex_to_varidx(i.op(2));
209 // A metric tensor with one covariant and one contravariant index gets
210 // replaced by a delta tensor
211 if (i1.is_covariant() != i2.is_covariant())
212 return delta_tensor(i1, i2);
214 // No further simplifications
218 /** Automatic symbolic evaluation of an indexed Lorentz metric tensor. */
219 ex minkmetric::eval_indexed(const basic & i) const
221 GINAC_ASSERT(is_of_type(i, indexed));
222 GINAC_ASSERT(i.nops() == 3);
223 GINAC_ASSERT(is_ex_of_type(i.op(0), minkmetric));
224 GINAC_ASSERT(is_ex_of_type(i.op(1), varidx));
225 GINAC_ASSERT(is_ex_of_type(i.op(2), varidx));
227 const varidx & i1 = ex_to_varidx(i.op(1));
228 const varidx & i2 = ex_to_varidx(i.op(2));
230 // Numeric evaluation
231 if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
232 int n1 = ex_to_numeric(i1.get_value()).to_int(), n2 = ex_to_numeric(i2.get_value()).to_int();
236 return pos_sig ? _ex_1() : _ex1();
238 return pos_sig ? _ex1() : _ex_1();
241 // Perform the usual evaluations of a metric tensor
242 return inherited::eval_indexed(i);
245 /** Automatic symbolic evaluation of an indexed epsilon tensor. */
246 ex tensepsilon::eval_indexed(const basic & i) const
248 GINAC_ASSERT(is_of_type(i, indexed));
249 GINAC_ASSERT(i.nops() > 1);
250 GINAC_ASSERT(is_ex_of_type(i.op(0), tensepsilon));
252 // Convolutions are zero
253 if (static_cast<const indexed &>(i).get_dummy_indices().size() != 0)
256 // Numeric evaluation
257 if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
259 // Get sign of index permutation (the indices should already be in
260 // a canonic order but we can't assume what exactly that order is)
262 v.reserve(i.nops() - 1);
263 for (unsigned j=1; j<i.nops(); j++)
264 v.push_back(ex_to_numeric(ex_to_idx(i.op(j)).get_value()).to_int());
265 int sign = permutation_sign(v);
267 // In a Minkowski space, check for covariant indices
269 for (unsigned j=1; j<i.nops(); j++) {
270 const ex & x = i.op(j);
271 if (!is_ex_of_type(x, varidx))
272 throw(std::runtime_error("indices of epsilon tensor in Minkowski space must be of type varidx"));
273 if (ex_to_varidx(x).is_covariant())
274 if (ex_to_idx(x).get_value().is_zero())
275 sign = (pos_sig ? -sign : sign);
277 sign = (pos_sig ? sign : -sign);
284 // No further simplifications
288 /** Contraction of an indexed delta tensor with something else. */
289 bool tensdelta::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
291 GINAC_ASSERT(is_ex_of_type(*self, indexed));
292 GINAC_ASSERT(is_ex_of_type(*other, indexed));
293 GINAC_ASSERT(self->nops() == 3);
294 GINAC_ASSERT(is_ex_of_type(self->op(0), tensdelta));
296 // Try to contract first index
297 const idx *self_idx = &ex_to_idx(self->op(1));
298 const idx *free_idx = &ex_to_idx(self->op(2));
299 bool first_index_tried = false;
302 if (self_idx->is_symbolic()) {
303 for (int i=1; i<other->nops(); i++) {
304 const idx &other_idx = ex_to_idx(other->op(i));
305 if (is_dummy_pair(*self_idx, other_idx)) {
307 // Contraction found, remove delta tensor and substitute
308 // index in second object
310 *other = other->subs(other_idx == *free_idx);
316 if (!first_index_tried) {
318 // No contraction with first index found, try second index
319 self_idx = &ex_to_idx(self->op(2));
320 free_idx = &ex_to_idx(self->op(1));
321 first_index_tried = true;
328 /** Contraction of an indexed metric tensor with something else. */
329 bool tensmetric::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
331 GINAC_ASSERT(is_ex_of_type(*self, indexed));
332 GINAC_ASSERT(is_ex_of_type(*other, indexed));
333 GINAC_ASSERT(self->nops() == 3);
334 GINAC_ASSERT(is_ex_of_type(self->op(0), tensmetric));
336 // If contracting with the delta tensor, let the delta do it
337 // (don't raise/lower delta indices)
338 if (is_ex_of_type(other->op(0), tensdelta))
341 // Try to contract first index
342 const idx *self_idx = &ex_to_idx(self->op(1));
343 const idx *free_idx = &ex_to_idx(self->op(2));
344 bool first_index_tried = false;
347 if (self_idx->is_symbolic()) {
348 for (int i=1; i<other->nops(); i++) {
349 const idx &other_idx = ex_to_idx(other->op(i));
350 if (is_dummy_pair(*self_idx, other_idx)) {
352 // Contraction found, remove metric tensor and substitute
353 // index in second object
355 *other = other->subs(other_idx == *free_idx);
361 if (!first_index_tried) {
363 // No contraction with first index found, try second index
364 self_idx = &ex_to_idx(self->op(2));
365 free_idx = &ex_to_idx(self->op(1));
366 first_index_tried = true;
377 ex delta_tensor(const ex & i1, const ex & i2)
379 if (!is_ex_of_type(i1, idx) || !is_ex_of_type(i2, idx))
380 throw(std::invalid_argument("indices of delta tensor must be of type idx"));
382 return indexed(tensdelta(), indexed::symmetric, i1, i2);
385 ex metric_tensor(const ex & i1, const ex & i2)
387 if (!is_ex_of_type(i1, varidx) || !is_ex_of_type(i2, varidx))
388 throw(std::invalid_argument("indices of metric tensor must be of type varidx"));
390 return indexed(tensmetric(), indexed::symmetric, i1, i2);
393 ex lorentz_g(const ex & i1, const ex & i2, bool pos_sig)
395 if (!is_ex_of_type(i1, varidx) || !is_ex_of_type(i2, varidx))
396 throw(std::invalid_argument("indices of metric tensor must be of type varidx"));
398 return indexed(minkmetric(pos_sig), indexed::symmetric, i1, i2);
401 ex epsilon_tensor(const ex & i1, const ex & i2)
403 if (!is_ex_of_type(i1, idx) || !is_ex_of_type(i2, idx))
404 throw(std::invalid_argument("indices of epsilon tensor must be of type idx"));
406 ex dim = ex_to_idx(i1).get_dim();
407 if (!dim.is_equal(ex_to_idx(i2).get_dim()))
408 throw(std::invalid_argument("all indices of epsilon tensor must have the same dimension"));
409 if (!ex_to_idx(i1).get_dim().is_equal(_ex2()))
410 throw(std::runtime_error("index dimension of epsilon tensor must match number of indices"));
412 return indexed(tensepsilon(), indexed::antisymmetric, i1, i2);
415 ex epsilon_tensor(const ex & i1, const ex & i2, const ex & i3)
417 if (!is_ex_of_type(i1, idx) || !is_ex_of_type(i2, idx) || !is_ex_of_type(i3, idx))
418 throw(std::invalid_argument("indices of epsilon tensor must be of type idx"));
420 ex dim = ex_to_idx(i1).get_dim();
421 if (!dim.is_equal(ex_to_idx(i2).get_dim()) || !dim.is_equal(ex_to_idx(i3).get_dim()))
422 throw(std::invalid_argument("all indices of epsilon tensor must have the same dimension"));
423 if (!ex_to_idx(i1).get_dim().is_equal(_ex3()))
424 throw(std::runtime_error("index dimension of epsilon tensor must match number of indices"));
426 return indexed(tensepsilon(), indexed::antisymmetric, i1, i2, i3);
429 ex lorentz_eps(const ex & i1, const ex & i2, const ex & i3, const ex & i4, bool pos_sig)
431 if (!is_ex_of_type(i1, varidx) || !is_ex_of_type(i2, varidx) || !is_ex_of_type(i3, varidx) || !is_ex_of_type(i4, varidx))
432 throw(std::invalid_argument("indices of Lorentz epsilon tensor must be of type varidx"));
434 ex dim = ex_to_idx(i1).get_dim();
435 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()))
436 throw(std::invalid_argument("all indices of epsilon tensor must have the same dimension"));
437 if (!ex_to_idx(i1).get_dim().is_equal(_ex4()))
438 throw(std::runtime_error("index dimension of epsilon tensor must match number of indices"));
440 return indexed(tensepsilon(true, pos_sig), indexed::antisymmetric, i1, i2, i3, i4);
443 ex eps0123(const ex & i1, const ex & i2, const ex & i3, const ex & i4, bool pos_sig)
445 if (!is_ex_of_type(i1, varidx) || !is_ex_of_type(i2, varidx) || !is_ex_of_type(i3, varidx) || !is_ex_of_type(i4, varidx))
446 throw(std::invalid_argument("indices of epsilon tensor must be of type varidx"));
448 ex dim = ex_to_idx(i1).get_dim();
450 return lorentz_eps(i1, i2, i3, i4, pos_sig);
452 return indexed(tensepsilon(true, pos_sig), indexed::antisymmetric, i1, i2, i3, i4);