3 * Interface to GiNaC's indices. */
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_IDX_H__
24 #define __GINAC_IDX_H__
31 /** This class holds one index of an indexed object. Indices can
32 * theoretically consist of any symbolic expression but they are usually
33 * only just a symbol (e.g. "mu", "i") or numeric (integer). Indices belong
34 * to a space with a certain numeric or symbolic dimension. */
35 class idx : public basic
37 GINAC_DECLARE_REGISTERED_CLASS(idx, basic)
41 /** Construct index with given value and dimension.
43 * @param v Value of index (numeric or symbolic)
44 * @param dim Dimension of index space (numeric or symbolic)
45 * @return newly constructed index */
46 explicit idx(const ex & v, const ex & dim);
48 // functions overriding virtual functions from bases classes
50 void print(const print_context & c, unsigned level = 0) const;
51 bool info(unsigned inf) const;
52 unsigned nops() const;
54 ex evalf(int level = 0) const;
55 bool match(const ex & pattern, lst & repl_lst) const;
56 ex subs(const lst & ls, const lst & lr, bool no_pattern = false) const;
59 ex derivative(const symbol & s) const;
61 // new virtual functions in this class
63 /** Check whether the index forms a dummy index pair with another index
64 * of the same type. */
65 virtual bool is_dummy_pair_same_type(const basic & other) const;
67 // non-virtual functions in this class
69 /** Get value of index. */
70 ex get_value(void) const {return value;}
72 /** Check whether the index is numeric. */
73 bool is_numeric(void) const {return is_ex_exactly_of_type(value, numeric);}
75 /** Check whether the index is symbolic. */
76 bool is_symbolic(void) const {return !is_ex_exactly_of_type(value, numeric);}
78 /** Get dimension of index space. */
79 ex get_dim(void) const {return dim;}
81 /** Check whether the dimension is numeric. */
82 bool is_dim_numeric(void) const {return is_ex_exactly_of_type(dim, numeric);}
84 /** Check whether the dimension is symbolic. */
85 bool is_dim_symbolic(void) const {return !is_ex_exactly_of_type(dim, numeric);}
88 ex value; /**< Expression that constitutes the index (numeric or symbolic name) */
89 ex dim; /**< Dimension of space (can be symbolic or numeric) */
93 /** This class holds an index with a variance (co- or contravariant). There
94 * is an associated metric tensor that can be used to raise/lower indices. */
95 class varidx : public idx
97 GINAC_DECLARE_REGISTERED_CLASS(varidx, idx)
101 /** Construct index with given value, dimension and variance.
103 * @param v Value of index (numeric or symbolic)
104 * @param dim Dimension of index space (numeric or symbolic)
105 * @param covariant Make covariant index (default is contravariant)
106 * @return newly constructed index */
107 varidx(const ex & v, const ex & dim, bool covariant = false);
109 // functions overriding virtual functions from bases classes
111 void print(const print_context & c, unsigned level = 0) const;
112 bool match(const ex & pattern, lst & repl_lst) const;
113 bool is_dummy_pair_same_type(const basic & other) const;
115 // non-virtual functions in this class
117 /** Check whether the index is covariant. */
118 bool is_covariant(void) const {return covariant;}
120 /** Check whether the index is contravariant (not covariant). */
121 bool is_contravariant(void) const {return !covariant;}
123 /** Make a new index with the same value but the opposite variance. */
124 ex toggle_variance(void) const;
128 bool covariant; /**< x.mu, default is contravariant: x~mu */
132 /** This class holds a spinor index that can be dotted or undotted and that
133 * also has a variance. This is used in the Weyl-van-der-Waerden formalism
134 * where the dot indicates complex conjugation. There is an associated
135 * (asymmetric) metric tensor that can be used to raise/lower spinor
137 class spinidx : public varidx
139 GINAC_DECLARE_REGISTERED_CLASS(spinidx, varidx)
141 // other constructors
143 /** Construct index with given value, dimension, variance and dot.
145 * @param v Value of index (numeric or symbolic)
146 * @param dim Dimension of index space (numeric or symbolic)
147 * @param covariant Make covariant index (default is contravariant)
148 * @param dotted Make covariant dotted (default is undotted)
149 * @return newly constructed index */
150 spinidx(const ex & v, const ex & dim = 2, bool covariant = false, bool dotted = false);
152 // functions overriding virtual functions from bases classes
154 void print(const print_context & c, unsigned level = 0) const;
155 bool match(const ex & pattern, lst & repl_lst) const;
156 bool is_dummy_pair_same_type(const basic & other) const;
158 // non-virtual functions in this class
160 /** Check whether the index is dotted. */
161 bool is_dotted(void) const {return dotted;}
163 /** Check whether the index is not dotted. */
164 bool is_undotted(void) const {return !dotted;}
166 /** Make a new index with the same value and variance but the opposite
168 ex toggle_dot(void) const;
170 /** Make a new index with the same value but opposite variance and
172 ex toggle_variance_dot(void) const;
182 /** Return the idx object handled by an ex. Deprecated: use ex_to<idx>().
183 * This is unsafe: you need to check the type first. */
184 inline const idx &ex_to_idx(const ex & e)
186 return static_cast<const idx &>(*e.bp);
189 /** Return the varidx object handled by an ex. Deprecated: use ex_to<varidx>().
190 * This is unsafe: you need to check the type first. */
191 inline const varidx &ex_to_varidx(const ex & e)
193 return static_cast<const varidx &>(*e.bp);
196 /** Return the spinidx object handled by an ex. Deprecated: use ex_to<spinidx>().
197 * This is unsafe: you need to check the type first. */
198 inline const spinidx &ex_to_spinidx(const ex & e)
200 return static_cast<const spinidx &>(*e.bp);
203 /** Specialization of is_exactly_a<idx>(obj) for idx objects. */
204 template<> inline bool is_exactly_a<idx>(const basic & obj)
206 return obj.tinfo()==TINFO_idx;
209 /** Specialization of is_exactly_a<varidx>(obj) for varidx objects. */
210 template<> inline bool is_exactly_a<varidx>(const basic & obj)
212 return obj.tinfo()==TINFO_varidx;
215 /** Specialization of is_exactly_a<spinidx>(obj) for spinidx objects. */
216 template<> inline bool is_exactly_a<spinidx>(const basic & obj)
218 return obj.tinfo()==TINFO_spinidx;
221 /** Check whether two indices form a dummy pair. */
222 bool is_dummy_pair(const idx & i1, const idx & i2);
224 /** Check whether two expressions form a dummy index pair. */
225 bool is_dummy_pair(const ex & e1, const ex & e2);
227 /** Given a vector of indices, split them into two vectors, one containing
228 * the free indices, the other containing the dummy indices (numeric
229 * indices are neither free nor dummy ones).
231 * @param it Pointer to start of index vector
232 * @param itend Pointer to end of index vector
233 * @param out_free Vector of free indices (returned, sorted)
234 * @param out_dummy Vector of dummy indices (returned, sorted) */
235 void find_free_and_dummy(exvector::const_iterator it, exvector::const_iterator itend, exvector & out_free, exvector & out_dummy);
237 /** Given a vector of indices, split them into two vectors, one containing
238 * the free indices, the other containing the dummy indices (numeric
239 * indices are neither free nor dummy ones).
241 * @param v Index vector
242 * @param out_free Vector of free indices (returned, sorted)
243 * @param out_dummy Vector of dummy indices (returned, sorted) */
244 inline void find_free_and_dummy(const exvector & v, exvector & out_free, exvector & out_dummy)
246 find_free_and_dummy(v.begin(), v.end(), out_free, out_dummy);
249 /** Given a vector of indices, find the dummy indices.
251 * @param v Index vector
252 * @param out_dummy Vector of dummy indices (returned, sorted) */
253 inline void find_dummy_indices(const exvector & v, exvector & out_dummy)
255 exvector free_indices;
256 find_free_and_dummy(v.begin(), v.end(), free_indices, out_dummy);
259 /** Count the number of dummy index pairs in an index vector. */
260 inline unsigned count_dummy_indices(const exvector & v)
262 exvector free_indices, dummy_indices;
263 find_free_and_dummy(v.begin(), v.end(), free_indices, dummy_indices);
264 return dummy_indices.size();
267 /** Count the number of dummy index pairs in an index vector. */
268 inline unsigned count_free_indices(const exvector & v)
270 exvector free_indices, dummy_indices;
271 find_free_and_dummy(v.begin(), v.end(), free_indices, dummy_indices);
272 return free_indices.size();
277 #endif // ndef __GINAC_IDX_H__