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 printraw(std::ostream & os) const;
51 void printtree(std::ostream & os, unsigned indent) const;
52 void print(std::ostream & os, unsigned upper_precedence=0) const;
53 bool info(unsigned inf) const;
55 ex subs(const lst & ls, const lst & lr) const;
57 // new virtual functions in this class
59 /** Check whether the index forms a dummy index pair with another index
60 * of the same type. */
61 virtual bool is_dummy_pair_same_type(const basic & other) const;
63 // non-virtual functions in this class
65 /** Get value of index. */
66 ex get_value(void) const {return value;}
68 /** Check whether the index is numeric. */
69 bool is_numeric(void) const {return is_ex_exactly_of_type(value, numeric);}
71 /** Check whether the index is symbolic. */
72 bool is_symbolic(void) const {return !is_ex_exactly_of_type(value, numeric);}
74 /** Get dimension of index space. */
75 ex get_dim(void) const {return dim;}
77 /** Check whether the dimension is numeric. */
78 bool is_dim_numeric(void) const {return is_ex_exactly_of_type(dim, numeric);}
80 /** Check whether the dimension is symbolic. */
81 bool is_dim_symbolic(void) const {return !is_ex_exactly_of_type(dim, numeric);}
84 ex value; /**< Expression that constitutes the index (numeric or symbolic name) */
85 ex dim; /**< Dimension of space (can be symbolic or numeric) */
89 /** This class holds an index with a variance (co- or contravariant). There
90 * is an associated metric tensor that can be used to raise/lower indices. */
91 class varidx : public idx
93 GINAC_DECLARE_REGISTERED_CLASS(varidx, idx)
97 /** Construct index with given value, dimension and variance.
99 * @param v Value of index (numeric or symbolic)
100 * @param dim Dimension of index space (numeric or symbolic)
101 * @param covariant Make covariant index (default is contravariant)
102 * @return newly constructed index */
103 varidx(const ex & v, const ex & dim, bool covariant = false);
105 // functions overriding virtual functions from bases classes
107 void print(std::ostream & os, unsigned upper_precedence=0) const;
108 bool is_dummy_pair_same_type(const basic & other) const;
110 // non-virtual functions in this class
112 /** Check whether the index is covariant. */
113 bool is_covariant(void) const {return covariant;}
115 /** Check whether the index is contravariant (not covariant). */
116 bool is_contravariant(void) const {return !covariant;}
118 /** Make a new index with the same value but the opposite variance. */
119 ex toggle_variance(void) const;
123 bool covariant; /**< x.mu, default is contravariant: x~mu */
128 inline const idx &ex_to_idx(const ex & e)
130 return static_cast<const idx &>(*e.bp);
133 inline const varidx &ex_to_varidx(const ex & e)
135 return static_cast<const varidx &>(*e.bp);
138 /** Check whether two indices form a dummy pair. */
139 bool is_dummy_pair(const idx & i1, const idx & i2);
141 /** Check whether two expressions form a dummy index pair. */
142 bool is_dummy_pair(const ex & e1, const ex & e2);
144 /** Given a vector of indices, split them into two vectors, one containing
145 * the free indices, the other containing the dummy indices (numeric
146 * indices are neither free nor dummy ones).
148 * @param it Pointer to start of index vector
149 * @param itend Pointer to end of index vector
150 * @param out_free Vector of free indices (returned, sorted)
151 * @param out_dummy Vector of dummy indices (returned, sorted) */
152 void find_free_and_dummy(exvector::const_iterator it, exvector::const_iterator itend, exvector & out_free, exvector & out_dummy);
154 /** Given a vector of indices, split them into two vectors, one containing
155 * the free indices, the other containing the dummy indices (numeric
156 * indices are neither free nor dummy ones).
158 * @param v Index vector
159 * @param out_free Vector of free indices (returned, sorted)
160 * @param out_dummy Vector of dummy indices (returned, sorted) */
161 inline void find_free_and_dummy(const exvector & v, exvector & out_free, exvector & out_dummy)
163 find_free_and_dummy(v.begin(), v.end(), out_free, out_dummy);
166 /** Given a vector of indices, find the dummy indices.
168 * @param v Index vector
169 * @param out_dummy Vector of dummy indices (returned, sorted) */
170 inline void find_dummy_indices(const exvector & v, exvector & out_dummy)
172 exvector free_indices;
173 find_free_and_dummy(v.begin(), v.end(), free_indices, out_dummy);
176 /** Count the number of dummy index pairs in an index vector. */
177 inline unsigned count_dummy_indices(const exvector & v)
179 exvector free_indices, dummy_indices;
180 find_free_and_dummy(v.begin(), v.end(), free_indices, dummy_indices);
181 return dummy_indices.size();
184 /** Count the number of dummy index pairs in an index vector. */
185 inline unsigned count_free_indices(const exvector & v)
187 exvector free_indices, dummy_indices;
188 find_free_and_dummy(v.begin(), v.end(), free_indices, dummy_indices);
189 return free_indices.size();
192 /** Given two index vectors, find those indices that appear in the first
193 * vector but not in the second one (asymmetric set difference). */
194 exvector index_set_difference(const exvector & set1, const exvector & set2);
198 #endif // ndef __GINAC_IDX_H__