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;
54 unsigned nops() const;
57 ex subs(const lst & ls, const lst & lr) const;
59 // new virtual functions in this class
61 /** Check whether the index forms a dummy index pair with another index
62 * of the same type. */
63 virtual bool is_dummy_pair_same_type(const basic & other) const;
65 // non-virtual functions in this class
67 /** Get value of index. */
68 ex get_value(void) const {return value;}
70 /** Check whether the index is numeric. */
71 bool is_numeric(void) const {return is_ex_exactly_of_type(value, numeric);}
73 /** Check whether the index is symbolic. */
74 bool is_symbolic(void) const {return !is_ex_exactly_of_type(value, numeric);}
76 /** Get dimension of index space. */
77 ex get_dim(void) const {return dim;}
79 /** Check whether the dimension is numeric. */
80 bool is_dim_numeric(void) const {return is_ex_exactly_of_type(dim, numeric);}
82 /** Check whether the dimension is symbolic. */
83 bool is_dim_symbolic(void) const {return !is_ex_exactly_of_type(dim, numeric);}
86 ex value; /**< Expression that constitutes the index (numeric or symbolic name) */
87 ex dim; /**< Dimension of space (can be symbolic or numeric) */
91 /** This class holds an index with a variance (co- or contravariant). There
92 * is an associated metric tensor that can be used to raise/lower indices. */
93 class varidx : public idx
95 GINAC_DECLARE_REGISTERED_CLASS(varidx, idx)
99 /** Construct index with given value, dimension and variance.
101 * @param v Value of index (numeric or symbolic)
102 * @param dim Dimension of index space (numeric or symbolic)
103 * @param covariant Make covariant index (default is contravariant)
104 * @return newly constructed index */
105 varidx(const ex & v, const ex & dim, bool covariant = false);
107 // functions overriding virtual functions from bases classes
109 void print(std::ostream & os, unsigned upper_precedence=0) const;
110 bool is_dummy_pair_same_type(const basic & other) const;
112 // non-virtual functions in this class
114 /** Check whether the index is covariant. */
115 bool is_covariant(void) const {return covariant;}
117 /** Check whether the index is contravariant (not covariant). */
118 bool is_contravariant(void) const {return !covariant;}
120 /** Make a new index with the same value but the opposite variance. */
121 ex toggle_variance(void) const;
125 bool covariant; /**< x.mu, default is contravariant: x~mu */
130 inline const idx &ex_to_idx(const ex & e)
132 return static_cast<const idx &>(*e.bp);
135 inline const varidx &ex_to_varidx(const ex & e)
137 return static_cast<const varidx &>(*e.bp);
140 /** Check whether two indices form a dummy pair. */
141 bool is_dummy_pair(const idx & i1, const idx & i2);
143 /** Check whether two expressions form a dummy index pair. */
144 bool is_dummy_pair(const ex & e1, const ex & e2);
146 /** Given a vector of indices, split them into two vectors, one containing
147 * the free indices, the other containing the dummy indices (numeric
148 * indices are neither free nor dummy ones).
150 * @param it Pointer to start of index vector
151 * @param itend Pointer to end of index vector
152 * @param out_free Vector of free indices (returned, sorted)
153 * @param out_dummy Vector of dummy indices (returned, sorted) */
154 void find_free_and_dummy(exvector::const_iterator it, exvector::const_iterator itend, exvector & out_free, exvector & out_dummy);
156 /** Given a vector of indices, split them into two vectors, one containing
157 * the free indices, the other containing the dummy indices (numeric
158 * indices are neither free nor dummy ones).
160 * @param v Index vector
161 * @param out_free Vector of free indices (returned, sorted)
162 * @param out_dummy Vector of dummy indices (returned, sorted) */
163 inline void find_free_and_dummy(const exvector & v, exvector & out_free, exvector & out_dummy)
165 find_free_and_dummy(v.begin(), v.end(), out_free, out_dummy);
168 /** Given a vector of indices, find the dummy indices.
170 * @param v Index vector
171 * @param out_dummy Vector of dummy indices (returned, sorted) */
172 inline void find_dummy_indices(const exvector & v, exvector & out_dummy)
174 exvector free_indices;
175 find_free_and_dummy(v.begin(), v.end(), free_indices, out_dummy);
178 /** Count the number of dummy index pairs in an index vector. */
179 inline unsigned count_dummy_indices(const exvector & v)
181 exvector free_indices, dummy_indices;
182 find_free_and_dummy(v.begin(), v.end(), free_indices, dummy_indices);
183 return dummy_indices.size();
186 /** Count the number of dummy index pairs in an index vector. */
187 inline unsigned count_free_indices(const exvector & v)
189 exvector free_indices, dummy_indices;
190 find_free_and_dummy(v.begin(), v.end(), free_indices, dummy_indices);
191 return free_indices.size();
194 /** Given two index vectors, find those indices that appear in the first
195 * vector but not in the second one (asymmetric set difference). */
196 exvector index_set_difference(const exvector & set1, const exvector & set2);
200 #endif // ndef __GINAC_IDX_H__