3 * Interface to GiNaC's indices. */
6 * GiNaC Copyright (C) 1999-2023 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
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 explicit idx(const ex & v, const ex & dim);
47 // functions overriding virtual functions from base classes
49 bool info(unsigned inf) const override;
50 size_t nops() const override;
51 ex op(size_t i) const override;
52 ex map(map_function & f) const override;
53 ex evalf() const override;
54 ex subs(const exmap & m, unsigned options = 0) const override;
55 void archive(archive_node& n) const override;
56 void read_archive(const archive_node& n, lst& syms) override;
58 ex derivative(const symbol & s) const override;
59 bool match_same_type(const basic & other) const override;
60 unsigned calchash() const override;
62 // new virtual functions in this class
64 /** Check whether the index forms a dummy index pair with another index
65 * of the same type. */
66 virtual bool is_dummy_pair_same_type(const basic & other) const;
68 // non-virtual functions in this class
70 /** Get value of index. */
71 ex get_value() const {return value;}
73 /** Check whether the index is numeric. */
74 bool is_numeric() const {return is_exactly_a<numeric>(value);}
76 /** Check whether the index is symbolic. */
77 bool is_symbolic() const {return !is_exactly_a<numeric>(value);}
79 /** Get dimension of index space. */
80 ex get_dim() const {return dim;}
82 /** Check whether the dimension is numeric. */
83 bool is_dim_numeric() const {return is_exactly_a<numeric>(dim);}
85 /** Check whether the dimension is symbolic. */
86 bool is_dim_symbolic() const {return !is_exactly_a<numeric>(dim);}
88 /** Make a new index with the same value but a different dimension. */
89 ex replace_dim(const ex & new_dim) const;
91 /** Return the minimum of the dimensions of this and another index.
92 * If this is undecidable, throw an exception. */
93 ex minimal_dim(const idx & other) const;
96 void print_index(const print_context & c, unsigned level) const;
97 void do_print(const print_context & c, unsigned level) const;
98 void do_print_csrc(const print_csrc & c, unsigned level) const;
99 void do_print_latex(const print_latex & c, unsigned level) const;
100 void do_print_tree(const print_tree & c, unsigned level) const;
103 ex value; /**< Expression that constitutes the index (numeric or symbolic name) */
104 ex dim; /**< Dimension of space (can be symbolic or numeric) */
106 GINAC_DECLARE_UNARCHIVER(idx);
109 /** This class holds an index with a variance (co- or contravariant). There
110 * is an associated metric tensor that can be used to raise/lower indices. */
111 class varidx : public idx
113 GINAC_DECLARE_REGISTERED_CLASS(varidx, idx)
115 // other constructors
117 /** Construct index with given value, dimension and variance.
119 * @param v Value of index (numeric or symbolic)
120 * @param dim Dimension of index space (numeric or symbolic)
121 * @param covariant Make covariant index (default is contravariant) */
122 varidx(const ex & v, const ex & dim, bool covariant = false);
124 // functions overriding virtual functions from base classes
126 bool is_dummy_pair_same_type(const basic & other) const override;
127 void archive(archive_node& n) const override;
128 void read_archive(const archive_node& n, lst& syms) override;
130 bool match_same_type(const basic & other) const override;
132 // non-virtual functions in this class
134 /** Check whether the index is covariant. */
135 bool is_covariant() const {return covariant;}
137 /** Check whether the index is contravariant (not covariant). */
138 bool is_contravariant() const {return !covariant;}
140 /** Make a new index with the same value but the opposite variance. */
141 ex toggle_variance() const;
144 void do_print(const print_context & c, unsigned level) const;
145 void do_print_tree(const print_tree & c, unsigned level) const;
149 bool covariant; /**< x.mu, default is contravariant: x~mu */
151 GINAC_DECLARE_UNARCHIVER(varidx);
154 /** This class holds a spinor index that can be dotted or undotted and that
155 * also has a variance. This is used in the Weyl-van-der-Waerden formalism
156 * where the dot indicates complex conjugation. There is an associated
157 * (asymmetric) metric tensor that can be used to raise/lower spinor
159 class spinidx : public varidx
161 GINAC_DECLARE_REGISTERED_CLASS(spinidx, varidx)
163 // other constructors
165 /** Construct index with given value, dimension, variance and dot.
167 * @param v Value of index (numeric or symbolic)
168 * @param dim Dimension of index space (numeric or symbolic)
169 * @param covariant Make covariant index (default is contravariant)
170 * @param dotted Make covariant dotted (default is undotted) */
171 spinidx(const ex & v, const ex & dim = 2, bool covariant = false, bool dotted = false);
173 // functions overriding virtual functions from base classes
175 bool is_dummy_pair_same_type(const basic & other) const override;
176 // complex conjugation
177 ex conjugate() const override { return toggle_dot(); }
178 void archive(archive_node& n) const override;
179 void read_archive(const archive_node& n, lst& syms) override;
181 bool match_same_type(const basic & other) const override;
183 // non-virtual functions in this class
185 /** Check whether the index is dotted. */
186 bool is_dotted() const {return dotted;}
188 /** Check whether the index is not dotted. */
189 bool is_undotted() const {return !dotted;}
191 /** Make a new index with the same value and variance but the opposite
193 ex toggle_dot() const;
195 /** Make a new index with the same value but opposite variance and
197 ex toggle_variance_dot() const;
200 void do_print(const print_context & c, unsigned level) const;
201 void do_print_latex(const print_latex & c, unsigned level) const;
202 void do_print_tree(const print_tree & c, unsigned level) const;
208 GINAC_DECLARE_UNARCHIVER(spinidx);
213 /** Check whether two indices form a dummy pair. */
214 bool is_dummy_pair(const idx & i1, const idx & i2);
216 /** Check whether two expressions form a dummy index pair. */
217 bool is_dummy_pair(const ex & e1, const ex & e2);
219 /** Given a vector of indices, split them into two vectors, one containing
220 * the free indices, the other containing the dummy indices (numeric
221 * indices are neither free nor dummy ones).
223 * @param it Pointer to start of index vector
224 * @param itend Pointer to end of index vector
225 * @param out_free Vector of free indices (returned, sorted)
226 * @param out_dummy Vector of dummy indices (returned, sorted) */
227 void find_free_and_dummy(exvector::const_iterator it, exvector::const_iterator itend, exvector & out_free, exvector & out_dummy);
229 /** Given a vector of indices, split them into two vectors, one containing
230 * the free indices, the other containing the dummy indices (numeric
231 * indices are neither free nor dummy ones).
233 * @param v Index vector
234 * @param out_free Vector of free indices (returned, sorted)
235 * @param out_dummy Vector of dummy indices (returned, sorted) */
236 inline void find_free_and_dummy(const exvector & v, exvector & out_free, exvector & out_dummy)
238 find_free_and_dummy(v.begin(), v.end(), out_free, out_dummy);
241 /** Given a vector of indices, find the dummy indices.
243 * @param v Index vector
244 * @param out_dummy Vector of dummy indices (returned, sorted) */
245 inline void find_dummy_indices(const exvector & v, exvector & out_dummy)
247 exvector free_indices;
248 find_free_and_dummy(v.begin(), v.end(), free_indices, out_dummy);
251 /** Count the number of dummy index pairs in an index vector. */
252 inline size_t count_dummy_indices(const exvector & v)
254 exvector free_indices, dummy_indices;
255 find_free_and_dummy(v.begin(), v.end(), free_indices, dummy_indices);
256 return dummy_indices.size();
259 /** Count the number of dummy index pairs in an index vector. */
260 inline size_t count_free_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 free_indices.size();
267 /** Return the minimum of two index dimensions. If this is undecidable,
268 * throw an exception. Numeric dimensions are always considered "smaller"
269 * than symbolic dimensions. */
270 ex minimal_dim(const ex & dim1, const ex & dim2);
274 #endif // ndef GINAC_IDX_H