3 * Interface to 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
23 #ifndef __GINAC_TENSOR_H__
24 #define __GINAC_TENSOR_H__
31 /** This class holds one of GiNaC's predefined special tensors such as the
32 * delta and the metric tensors. They are represented without indices.
33 * To attach indices to them, wrap them in an object of class indexed. */
34 class tensor : public basic
36 GINAC_DECLARE_REGISTERED_CLASS(tensor, basic)
42 // functions overriding virtual functions from bases classes
44 unsigned return_type(void) const { return return_types::noncommutative_composite; }
48 /** This class represents the delta tensor. If indexed, it must have exactly
49 * two indices of the same type. */
50 class tensdelta : public tensor
52 GINAC_DECLARE_REGISTERED_CLASS(tensdelta, tensor)
54 // functions overriding virtual functions from bases classes
56 void print(std::ostream & os, unsigned upper_precedence=0) const;
57 ex eval_indexed(const basic & i) const;
58 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
62 /** This class represents a general metric tensor which can be used to
63 * raise/lower indices. If indexed, it must have exactly two indices of the
64 * same type which must be of class varidx or a subclass. */
65 class tensmetric : public tensor
67 GINAC_DECLARE_REGISTERED_CLASS(tensmetric, tensor)
69 // functions overriding virtual functions from bases classes
71 void print(std::ostream & os, unsigned upper_precedence=0) const;
72 ex eval_indexed(const basic & i) const;
73 bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;
77 /** This class represents a Minkowski metric tensor. It has all the
78 * properties of a metric tensor and is (as a matrix) equal to
79 * diag(1,-1,-1,...) or diag(-1,1,1,...). */
80 class minkmetric : public tensmetric
82 GINAC_DECLARE_REGISTERED_CLASS(minkmetric, tensmetric)
86 /** Construct Lorentz metric tensor with given signature. */
87 minkmetric(bool pos_sig);
89 // functions overriding virtual functions from bases classes
91 void print(std::ostream & os, unsigned upper_precedence=0) const;
92 ex eval_indexed(const basic & i) const;
96 bool pos_sig; /**< If true, the metric is diag(-1,1,1...). Otherwise it is diag(1,-1,-1,...). */
100 /** This class represents the totally antisymmetric epsilon tensor. If
101 * indexed, all indices must be of the same type and their number must
102 * be equal to the dimension of the index space. */
103 class tensepsilon : public tensor
105 GINAC_DECLARE_REGISTERED_CLASS(tensepsilon, tensor)
107 // other constructors
109 tensepsilon(bool minkowski, bool pos_sig);
111 // functions overriding virtual functions from bases classes
113 void print(std::ostream & os, unsigned upper_precedence=0) const;
114 ex eval_indexed(const basic & i) const;
118 bool minkowski; /**< If true, tensor is in Minkowski-type space. Otherwise it is in a Euclidean space. */
119 bool pos_sig; /**< If true, the metric is assumed to be diag(-1,1,1...). Otherwise it is diag(1,-1,-1,...). This is only relevant if minkowski = true. */
124 inline const tensor &ex_to_tensor(const ex &e)
126 return static_cast<const tensor &>(*e.bp);
129 /** Create a delta tensor with specified indices. The indices must be of class
130 * idx or a subclass. The delta tensor is always symmetric and its trace is
131 * the dimension of the index space.
133 * @param i1 First index
134 * @param i2 Second index
135 * @return newly constructed delta tensor */
136 ex delta_tensor(const ex & i1, const ex & i2);
138 /** Create a symmetric metric tensor with specified indices. The indices
139 * must be of class varidx or a subclass. A metric tensor with one
140 * covariant and one contravariant index is equivalent to the delta tensor.
142 * @param i1 First index
143 * @param i2 Second index
144 * @return newly constructed metric tensor */
145 ex metric_tensor(const ex & i1, const ex & i2);
147 /** Create a Minkowski metric tensor with specified indices. The indices
148 * must be of class varidx or a subclass. The Lorentz metric is a symmetric
149 * tensor with a matrix representation of diag(1,-1,-1,...) (negative
150 * signature, the default) or diag(-1,1,1,...) (positive signature).
152 * @param i1 First index
153 * @param i2 Second index
154 * @param pos_sig Whether the signature is positive
155 * @return newly constructed Lorentz metric tensor */
156 ex lorentz_g(const ex & i1, const ex & i2, bool pos_sig = false);
158 /** Create an epsilon tensor in a Euclidean space with two indices. The
159 * indices must be of class idx or a subclass, and have a dimension of 2.
161 * @param i1 First index
162 * @param i2 Second index
163 * @return newly constructed epsilon tensor */
164 ex epsilon_tensor(const ex & i1, const ex & i2);
166 /** Create an epsilon tensor in a Euclidean space with three indices. The
167 * indices must be of class idx or a subclass, and have a dimension of 3.
169 * @param i1 First index
170 * @param i2 Second index
171 * @param i3 Third index
172 * @return newly constructed epsilon tensor */
173 ex epsilon_tensor(const ex & i1, const ex & i2, const ex & i3);
175 /** Create an epsilon tensor in a Minkowski space with four indices. The
176 * indices must be of class varidx or a subclass, and have a dimension of 4.
178 * @param i1 First index
179 * @param i2 Second index
180 * @param i3 Third index
181 * @param i4 Fourth index
182 * @param pos_sig Whether the signature of the metric is positive
183 * @return newly constructed epsilon tensor */
184 ex lorentz_eps(const ex & i1, const ex & i2, const ex & i3, const ex & i4, bool pos_sig = false);
188 #endif // ndef __GINAC_TENSOR_H__