3 * Interface to GiNaC's indices. */
6 * GiNaC Copyright (C) 1999-2008 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
23 #ifndef __GINAC_IDX_H__
24 #define __GINAC_IDX_H__
32 /** This class holds one index of an indexed object. Indices can
33 * theoretically consist of any symbolic expression but they are usually
34 * only just a symbol (e.g. "mu", "i") or numeric (integer). Indices belong
35 * to a space with a certain numeric or symbolic dimension. */
36 class idx : public basic
38 GINAC_DECLARE_REGISTERED_CLASS(idx, basic)
42 /** Construct index with given value and dimension.
44 * @param v Value of index (numeric or symbolic)
45 * @param dim Dimension of index space (numeric or symbolic)
46 * @return newly constructed index */
47 explicit idx(const ex & v, const ex & dim);
49 // functions overriding virtual functions from base classes
51 bool info(unsigned inf) const;
53 ex op(size_t i) const;
54 ex map(map_function & f) const;
55 ex evalf(int level = 0) const;
56 ex subs(const exmap & m, unsigned options = 0) const;
57 void archive(archive_node& n) const;
58 void read_archive(const archive_node& n, lst& syms);
60 ex derivative(const symbol & s) const;
61 bool match_same_type(const basic & other) const;
62 unsigned calchash() const;
64 // new virtual functions in this class
66 /** Check whether the index forms a dummy index pair with another index
67 * of the same type. */
68 virtual bool is_dummy_pair_same_type(const basic & other) const;
70 // non-virtual functions in this class
72 /** Get value of index. */
73 ex get_value() const {return value;}
75 /** Check whether the index is numeric. */
76 bool is_numeric() const {return is_exactly_a<numeric>(value);}
78 /** Check whether the index is symbolic. */
79 bool is_symbolic() const {return !is_exactly_a<numeric>(value);}
81 /** Get dimension of index space. */
82 ex get_dim() const {return dim;}
84 /** Check whether the dimension is numeric. */
85 bool is_dim_numeric() const {return is_exactly_a<numeric>(dim);}
87 /** Check whether the dimension is symbolic. */
88 bool is_dim_symbolic() const {return !is_exactly_a<numeric>(dim);}
90 /** Make a new index with the same value but a different dimension. */
91 ex replace_dim(const ex & new_dim) const;
93 /** Return the minimum of the dimensions of this and another index.
94 * If this is undecidable, throw an exception. */
95 ex minimal_dim(const idx & other) const;
98 void print_index(const print_context & c, unsigned level) const;
99 void do_print(const print_context & c, unsigned level) const;
100 void do_print_csrc(const print_csrc & c, unsigned level) const;
101 void do_print_latex(const print_latex & c, unsigned level) const;
102 void do_print_tree(const print_tree & c, unsigned level) const;
105 ex value; /**< Expression that constitutes the index (numeric or symbolic name) */
106 ex dim; /**< Dimension of space (can be symbolic or numeric) */
108 GINAC_DECLARE_UNARCHIVER(idx);
111 /** This class holds an index with a variance (co- or contravariant). There
112 * is an associated metric tensor that can be used to raise/lower indices. */
113 class varidx : public idx
115 GINAC_DECLARE_REGISTERED_CLASS(varidx, idx)
117 // other constructors
119 /** Construct index with given value, dimension and variance.
121 * @param v Value of index (numeric or symbolic)
122 * @param dim Dimension of index space (numeric or symbolic)
123 * @param covariant Make covariant index (default is contravariant)
124 * @return newly constructed index */
125 varidx(const ex & v, const ex & dim, bool covariant = false);
127 // functions overriding virtual functions from base classes
129 bool is_dummy_pair_same_type(const basic & other) const;
130 void archive(archive_node& n) const;
131 void read_archive(const archive_node& n, lst& syms);
133 bool match_same_type(const basic & other) const;
135 // non-virtual functions in this class
137 /** Check whether the index is covariant. */
138 bool is_covariant() const {return covariant;}
140 /** Check whether the index is contravariant (not covariant). */
141 bool is_contravariant() const {return !covariant;}
143 /** Make a new index with the same value but the opposite variance. */
144 ex toggle_variance() const;
147 void do_print(const print_context & c, unsigned level) const;
148 void do_print_tree(const print_tree & c, unsigned level) const;
152 bool covariant; /**< x.mu, default is contravariant: x~mu */
154 GINAC_DECLARE_UNARCHIVER(varidx);
157 /** This class holds a spinor index that can be dotted or undotted and that
158 * also has a variance. This is used in the Weyl-van-der-Waerden formalism
159 * where the dot indicates complex conjugation. There is an associated
160 * (asymmetric) metric tensor that can be used to raise/lower spinor
162 class spinidx : public varidx
164 GINAC_DECLARE_REGISTERED_CLASS(spinidx, varidx)
166 // other constructors
168 /** Construct index with given value, dimension, variance and dot.
170 * @param v Value of index (numeric or symbolic)
171 * @param dim Dimension of index space (numeric or symbolic)
172 * @param covariant Make covariant index (default is contravariant)
173 * @param dotted Make covariant dotted (default is undotted)
174 * @return newly constructed index */
175 spinidx(const ex & v, const ex & dim = 2, bool covariant = false, bool dotted = false);
177 // functions overriding virtual functions from base classes
179 bool is_dummy_pair_same_type(const basic & other) const;
180 // complex conjugation
181 ex conjugate() const { return toggle_dot(); }
182 void archive(archive_node& n) const;
183 void read_archive(const archive_node& n, lst& syms);
185 bool match_same_type(const basic & other) const;
187 // non-virtual functions in this class
189 /** Check whether the index is dotted. */
190 bool is_dotted() const {return dotted;}
192 /** Check whether the index is not dotted. */
193 bool is_undotted() const {return !dotted;}
195 /** Make a new index with the same value and variance but the opposite
197 ex toggle_dot() const;
199 /** Make a new index with the same value but opposite variance and
201 ex toggle_variance_dot() const;
204 void do_print(const print_context & c, unsigned level) const;
205 void do_print_latex(const print_latex & c, unsigned level) const;
206 void do_print_tree(const print_tree & c, unsigned level) const;
212 GINAC_DECLARE_UNARCHIVER(spinidx);
217 /** Check whether two indices form a dummy pair. */
218 bool is_dummy_pair(const idx & i1, const idx & i2);
220 /** Check whether two expressions form a dummy index pair. */
221 bool is_dummy_pair(const ex & e1, const ex & e2);
223 /** Given a vector of indices, split them into two vectors, one containing
224 * the free indices, the other containing the dummy indices (numeric
225 * indices are neither free nor dummy ones).
227 * @param it Pointer to start of index vector
228 * @param itend Pointer to end of index vector
229 * @param out_free Vector of free indices (returned, sorted)
230 * @param out_dummy Vector of dummy indices (returned, sorted) */
231 void find_free_and_dummy(exvector::const_iterator it, exvector::const_iterator itend, exvector & out_free, exvector & out_dummy);
233 /** Given a vector of indices, split them into two vectors, one containing
234 * the free indices, the other containing the dummy indices (numeric
235 * indices are neither free nor dummy ones).
237 * @param v Index vector
238 * @param out_free Vector of free indices (returned, sorted)
239 * @param out_dummy Vector of dummy indices (returned, sorted) */
240 inline void find_free_and_dummy(const exvector & v, exvector & out_free, exvector & out_dummy)
242 find_free_and_dummy(v.begin(), v.end(), out_free, out_dummy);
245 /** Given a vector of indices, find the dummy indices.
247 * @param v Index vector
248 * @param out_dummy Vector of dummy indices (returned, sorted) */
249 inline void find_dummy_indices(const exvector & v, exvector & out_dummy)
251 exvector free_indices;
252 find_free_and_dummy(v.begin(), v.end(), free_indices, out_dummy);
255 /** Count the number of dummy index pairs in an index vector. */
256 inline size_t count_dummy_indices(const exvector & v)
258 exvector free_indices, dummy_indices;
259 find_free_and_dummy(v.begin(), v.end(), free_indices, dummy_indices);
260 return dummy_indices.size();
263 /** Count the number of dummy index pairs in an index vector. */
264 inline size_t count_free_indices(const exvector & v)
266 exvector free_indices, dummy_indices;
267 find_free_and_dummy(v.begin(), v.end(), free_indices, dummy_indices);
268 return free_indices.size();
271 /** Return the minimum of two index dimensions. If this is undecidable,
272 * throw an exception. Numeric dimensions are always considered "smaller"
273 * than symbolic dimensions. */
274 ex minimal_dim(const ex & dim1, const ex & dim2);
278 #endif // ndef __GINAC_IDX_H__