3 * Interface to GiNaC's indexed expressions. */
6 * GiNaC Copyright (C) 1999-2014 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
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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.
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20 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
23 #ifndef GINAC_INDEXED_H
24 #define GINAC_INDEXED_H
33 class scalar_products;
36 /** This class holds an indexed expression. It consists of a 'base' expression
37 * (the expression being indexed) which can be accessed as op(0), and n (n >= 0)
38 * indices (all of class idx), accessible as op(1)..op(n). */
39 class indexed : public exprseq
41 GINAC_DECLARE_REGISTERED_CLASS(indexed, exprseq)
43 friend ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp);
44 friend ex simplify_indexed_product(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp);
45 friend bool reposition_dummy_indices(ex & e, exvector & variant_dummy_indices, exvector & moved_indices);
49 /** Construct indexed object with no index.
51 * @param b Base expression
52 * @return newly constructed indexed object */
53 indexed(const ex & b);
55 /** Construct indexed object with one index. The index must be of class idx.
57 * @param b Base expression
59 * @return newly constructed indexed object */
60 indexed(const ex & b, const ex & i1);
62 /** Construct indexed object with two indices. The indices must be of class idx.
64 * @param b Base expression
65 * @param i1 First index
66 * @param i2 Second index
67 * @return newly constructed indexed object */
68 indexed(const ex & b, const ex & i1, const ex & i2);
70 /** Construct indexed object with three indices. The indices must be of class idx.
72 * @param b Base expression
73 * @param i1 First index
74 * @param i2 Second index
75 * @param i3 Third index
76 * @return newly constructed indexed object */
77 indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3);
79 /** Construct indexed object with four indices. The indices must be of class idx.
81 * @param b Base expression
82 * @param i1 First index
83 * @param i2 Second index
84 * @param i3 Third index
85 * @param i4 Fourth index
86 * @return newly constructed indexed object */
87 indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3, const ex & i4);
89 /** Construct indexed object with two indices and a specified symmetry. The
90 * indices must be of class idx.
92 * @param b Base expression
93 * @param symm Symmetry of indices
94 * @param i1 First index
95 * @param i2 Second index
96 * @return newly constructed indexed object */
97 indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2);
99 /** Construct indexed object with three indices and a specified symmetry.
100 * The indices must be of class idx.
102 * @param b Base expression
103 * @param symm Symmetry of indices
104 * @param i1 First index
105 * @param i2 Second index
106 * @param i3 Third index
107 * @return newly constructed indexed object */
108 indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2, const ex & i3);
110 /** Construct indexed object with four indices and a specified symmetry. The
111 * indices must be of class idx.
113 * @param b Base expression
114 * @param symm Symmetry of indices
115 * @param i1 First index
116 * @param i2 Second index
117 * @param i3 Third index
118 * @param i4 Fourth index
119 * @return newly constructed indexed object */
120 indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2, const ex & i3, const ex & i4);
122 /** Construct indexed object with a specified vector of indices. The indices
123 * must be of class idx.
125 * @param b Base expression
126 * @param iv Vector of indices
127 * @return newly constructed indexed object */
128 indexed(const ex & b, const exvector & iv);
130 /** Construct indexed object with a specified vector of indices and
131 * symmetry. The indices must be of class idx.
133 * @param b Base expression
134 * @param symm Symmetry of indices
135 * @param iv Vector of indices
136 * @return newly constructed indexed object */
137 indexed(const ex & b, const symmetry & symm, const exvector & iv);
139 // internal constructors
140 indexed(const symmetry & symm, const exprseq & es);
141 indexed(const symmetry & symm, const exvector & v, bool discardable = false);
142 indexed(const symmetry & symm, std::auto_ptr<exvector> vp);
144 // functions overriding virtual functions from base classes
146 unsigned precedence() const {return 55;}
147 bool info(unsigned inf) const;
148 ex eval(int level = 0) const;
149 ex real_part() const;
150 ex imag_part() const;
151 exvector get_free_indices() const;
153 /** Save (a.k.a. serialize) indexed object into archive. */
154 void archive(archive_node& n) const;
155 /** Read (a.k.a. deserialize) indexed object from archive. */
156 void read_archive(const archive_node& n, lst& syms);
158 ex derivative(const symbol & s) const;
159 ex thiscontainer(const exvector & v) const;
160 ex thiscontainer(std::auto_ptr<exvector> vp) const;
161 unsigned return_type() const;
162 return_type_t return_type_tinfo() const { return op(0).return_type_tinfo(); }
163 ex expand(unsigned options = 0) const;
165 // new virtual functions which can be overridden by derived classes
168 // non-virtual functions in this class
170 /** Check whether all index values have a certain property.
171 * @see class info_flags */
172 bool all_index_values_are(unsigned inf) const;
174 /** Return a vector containing the object's indices. */
175 exvector get_indices() const;
177 /** Return a vector containing the dummy indices of the object, if any. */
178 exvector get_dummy_indices() const;
180 /** Return a vector containing the dummy indices in the contraction with
181 * another indexed object. This is symmetric: a.get_dummy_indices(b)
182 * == b.get_dummy_indices(a) */
183 exvector get_dummy_indices(const indexed & other) const;
185 /** Check whether the object has an index that forms a dummy index pair
186 * with a given index. */
187 bool has_dummy_index_for(const ex & i) const;
189 /** Return symmetry properties. */
190 ex get_symmetry() const {return symtree;}
193 void printindices(const print_context & c, unsigned level) const;
194 void print_indexed(const print_context & c, const char *openbrace, const char *closebrace, unsigned level) const;
195 void do_print(const print_context & c, unsigned level) const;
196 void do_print_latex(const print_latex & c, unsigned level) const;
197 void do_print_tree(const print_tree & c, unsigned level) const;
198 void validate() const;
202 ex symtree; /**< Index symmetry (tree of symmetry objects) */
204 GINAC_DECLARE_UNARCHIVER(indexed);
209 spmapkey() : dim(wild()) {}
210 spmapkey(const ex & v1, const ex & v2, const ex & dim = wild());
212 bool operator==(const spmapkey &other) const;
213 bool operator<(const spmapkey &other) const;
215 void debugprint() const;
221 typedef std::map<spmapkey, ex> spmap;
223 /** Helper class for storing information about known scalar products which
224 * are to be automatically replaced by simplify_indexed().
226 * @see simplify_indexed */
227 class scalar_products {
229 /** Register scalar product pair and its value. */
230 void add(const ex & v1, const ex & v2, const ex & sp);
232 /** Register scalar product pair and its value for a specific space dimension. */
233 void add(const ex & v1, const ex & v2, const ex & dim, const ex & sp);
235 /** Register list of vectors. This adds all possible pairs of products
236 * a.i * b.i with the value a*b (note that this is not a scalar vector
237 * product but an ordinary product of scalars). */
238 void add_vectors(const lst & l, const ex & dim = wild());
240 /** Clear all registered scalar products. */
243 bool is_defined(const ex & v1, const ex & v2, const ex & dim) const;
244 ex evaluate(const ex & v1, const ex & v2, const ex & dim) const;
245 void debugprint() const;
248 spmap spm; /*< Map from defined scalar product pairs to their values */
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 a nonnegative integer.
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