3 * Interface to GiNaC's indexed expressions. */
6 * GiNaC Copyright (C) 1999-2005 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_INDEXED_H__
24 #define __GINAC_INDEXED_H__
34 class scalar_products;
37 /** This class holds an indexed expression. It consists of a 'base' expression
38 * (the expression being indexed) which can be accessed as op(0), and n (n >= 0)
39 * indices (all of class idx), accessible as op(1)..op(n). */
40 class indexed : public exprseq
42 GINAC_DECLARE_REGISTERED_CLASS(indexed, exprseq)
44 friend ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp);
45 friend ex simplify_indexed_product(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp);
46 friend bool reposition_dummy_indices(ex & e, exvector & variant_dummy_indices, exvector & moved_indices);
50 /** Construct indexed object with no index.
52 * @param b Base expression
53 * @return newly constructed indexed object */
54 indexed(const ex & b);
56 /** Construct indexed object with one index. The index must be of class idx.
58 * @param b Base expression
60 * @return newly constructed indexed object */
61 indexed(const ex & b, const ex & i1);
63 /** Construct indexed object with two indices. The indices must be of class idx.
65 * @param b Base expression
66 * @param i1 First index
67 * @param i2 Second index
68 * @return newly constructed indexed object */
69 indexed(const ex & b, const ex & i1, const ex & i2);
71 /** Construct indexed object with three indices. The indices must be of class idx.
73 * @param b Base expression
74 * @param i1 First index
75 * @param i2 Second index
76 * @param i3 Third index
77 * @return newly constructed indexed object */
78 indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3);
80 /** Construct indexed object with four indices. The indices must be of class idx.
82 * @param b Base expression
83 * @param i1 First index
84 * @param i2 Second index
85 * @param i3 Third index
86 * @param i4 Fourth index
87 * @return newly constructed indexed object */
88 indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3, const ex & i4);
90 /** Construct indexed object with two indices and a specified symmetry. The
91 * indices must be of class idx.
93 * @param b Base expression
94 * @param symm Symmetry of indices
95 * @param i1 First index
96 * @param i2 Second index
97 * @return newly constructed indexed object */
98 indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2);
100 /** Construct indexed object with three indices and a specified symmetry.
101 * The indices must be of class idx.
103 * @param b Base expression
104 * @param symm Symmetry of indices
105 * @param i1 First index
106 * @param i2 Second index
107 * @param i3 Third index
108 * @return newly constructed indexed object */
109 indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2, const ex & i3);
111 /** Construct indexed object with four indices and a specified symmetry. The
112 * indices must be of class idx.
114 * @param b Base expression
115 * @param symm Symmetry of indices
116 * @param i1 First index
117 * @param i2 Second index
118 * @param i3 Third index
119 * @param i4 Fourth index
120 * @return newly constructed indexed object */
121 indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2, const ex & i3, const ex & i4);
123 /** Construct indexed object with a specified vector of indices. The indices
124 * must be of class idx.
126 * @param b Base expression
127 * @param iv Vector of indices
128 * @return newly constructed indexed object */
129 indexed(const ex & b, const exvector & iv);
131 /** Construct indexed object with a specified vector of indices and
132 * symmetry. The indices must be of class idx.
134 * @param b Base expression
135 * @param symm Symmetry of indices
136 * @param iv Vector of indices
137 * @return newly constructed indexed object */
138 indexed(const ex & b, const symmetry & symm, const exvector & iv);
140 // internal constructors
141 indexed(const symmetry & symm, const exprseq & es);
142 indexed(const symmetry & symm, const exvector & v, bool discardable = false);
143 indexed(const symmetry & symm, std::auto_ptr<exvector> vp);
145 // functions overriding virtual functions from base classes
147 unsigned precedence() const {return 55;}
148 bool info(unsigned inf) const;
149 ex eval(int level = 0) const;
150 exvector get_free_indices() const;
153 ex derivative(const symbol & s) const;
154 ex thiscontainer(const exvector & v) const;
155 ex thiscontainer(std::auto_ptr<exvector> vp) const;
156 unsigned return_type() const;
157 unsigned return_type_tinfo() const { return op(0).return_type_tinfo(); }
158 ex expand(unsigned options = 0) const;
160 // new virtual functions which can be overridden by derived classes
163 // non-virtual functions in this class
165 /** Check whether all index values have a certain property.
166 * @see class info_flags */
167 bool all_index_values_are(unsigned inf) const;
169 /** Return a vector containing the object's indices. */
170 exvector get_indices() const;
172 /** Return a vector containing the dummy indices of the object, if any. */
173 exvector get_dummy_indices() const;
175 /** Return a vector containing the dummy indices in the contraction with
176 * another indexed object. This is symmetric: a.get_dummy_indices(b)
177 * == b.get_dummy_indices(a) */
178 exvector get_dummy_indices(const indexed & other) const;
180 /** Check whether the object has an index that forms a dummy index pair
181 * with a given index. */
182 bool has_dummy_index_for(const ex & i) const;
184 /** Return symmetry properties. */
185 ex get_symmetry() const {return symtree;}
188 void printindices(const print_context & c, unsigned level) const;
189 void print_indexed(const print_context & c, const char *openbrace, const char *closebrace, unsigned level) const;
190 void do_print(const print_context & c, unsigned level) const;
191 void do_print_latex(const print_latex & c, unsigned level) const;
192 void do_print_tree(const print_tree & c, unsigned level) const;
193 void validate() const;
197 ex symtree; /**< Index symmetry (tree of symmetry objects) */
203 spmapkey() : dim(wild()) {}
204 spmapkey(const ex & v1, const ex & v2, const ex & dim = wild());
206 bool operator==(const spmapkey &other) const;
207 bool operator<(const spmapkey &other) const;
209 void debugprint() const;
215 typedef std::map<spmapkey, ex> spmap;
217 /** Helper class for storing information about known scalar products which
218 * are to be automatically replaced by simplify_indexed().
220 * @see simplify_indexed */
221 class scalar_products {
223 /** Register scalar product pair and its value. */
224 void add(const ex & v1, const ex & v2, const ex & sp);
226 /** Register scalar product pair and its value for a specific space dimension. */
227 void add(const ex & v1, const ex & v2, const ex & dim, const ex & sp);
229 /** Register list of vectors. This adds all possible pairs of products
230 * a.i * b.i with the value a*b (note that this is not a scalar vector
231 * product but an ordinary product of scalars). */
232 void add_vectors(const lst & l, const ex & dim = wild());
234 /** Clear all registered scalar products. */
237 bool is_defined(const ex & v1, const ex & v2, const ex & dim) const;
238 ex evaluate(const ex & v1, const ex & v2, const ex & dim) const;
239 void debugprint() const;
242 spmap spm; /*< Map from defined scalar product pairs to their values */
248 /** Specialization of is_exactly_a<indexed>(obj) for indexed objects. */
249 template<> inline bool is_exactly_a<indexed>(const basic & obj)
251 return obj.tinfo()==TINFO_indexed;
254 /** Returns all dummy indices from the expression */
255 exvector get_all_dummy_indices(const ex & e);
257 /** More reliable version of the form. The former assumes that e is an
258 * expanded epxression. */
259 exvector get_all_dummy_indices_safely(const ex & e);
261 /** Returns b with all dummy indices, which are listed in va, renamed
262 * if modify_va is set to TRUE all dummy indices of b will be appended to va */
263 ex rename_dummy_indices_uniquely(exvector & va, const ex & b, bool modify_va = false);
265 /** Returns b with all dummy indices, which are common with a, renamed */
266 ex rename_dummy_indices_uniquely(const ex & a, const ex & b);
268 /** Same as above, where va and vb contain the indices of a and b and are sorted */
269 ex rename_dummy_indices_uniquely(const exvector & va, const exvector & vb, const ex & b);
271 /** Similar to above, where va and vb are the same and the return value is a list of two lists
272 * for substitution in b */
273 lst rename_dummy_indices_uniquely(const exvector & va, const exvector & vb);
275 /** This function returns the given expression with expanded sums
276 * for all dummy index summations, where the dimensionality of
277 * the dummy index is numeric.
278 * Optionally all indices with a variance will be substituted by
279 * indices with the corresponding numeric values without variance.
281 * @param e the given expression
282 * @param subs_idx indicates if variance of dummy indixes should be neglected
284 ex expand_dummy_sum(const ex & e, bool subs_idx = false);
288 #endif // ndef __GINAC_INDEXED_H__