3 * Interface to GiNaC's symmetry definitions. */
6 * GiNaC Copyright (C) 1999-2008 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_SYMMETRY_H__
24 #define __GINAC_SYMMETRY_H__
37 /** This class describes the symmetry of a group of indices. These objects
38 * can be grouped into a tree to form complex mixed symmetries. */
39 class symmetry : public basic
41 friend class sy_is_less;
43 friend int canonicalize(exvector::iterator v, const symmetry &symm);
45 GINAC_DECLARE_REGISTERED_CLASS(symmetry, basic)
49 /** Type of symmetry */
51 none, /**< no symmetry properties */
52 symmetric, /**< totally symmetric */
53 antisymmetric, /**< totally antisymmetric */
54 cyclic /**< cyclic symmetry */
59 /** Create leaf node that represents one index. */
62 /** Create node with two children. */
63 symmetry(symmetry_type t, const symmetry &c1, const symmetry &c2);
65 // non-virtual functions in this class
67 /** Get symmetry type. */
68 symmetry_type get_type() const {return type;}
70 /** Set symmetry type. */
71 void set_type(symmetry_type t) {type = t;}
73 /** Add child node, check index sets for consistency. */
74 symmetry &add(const symmetry &c);
76 /** Verify that all indices of this node are in the range [0..n-1].
77 * This function throws an exception if the verification fails.
78 * If the top node has a type != none and no children, add all indices
79 * in the range [0..n-1] as children. */
80 void validate(unsigned n);
82 /** Check whether this node actually represents any kind of symmetry. */
83 bool has_symmetry() const {return type != none || !children.empty(); }
84 /** Check whether this node involves a cyclic symmetry. */
85 bool has_cyclic() const;
87 /** Save (a.k.a. serialize) object into archive. */
88 void archive(archive_node& n) const;
89 /** Read (a.k.a. deserialize) object from archive. */
90 void read_archive(const archive_node& n, lst& syms);
92 void do_print(const print_context & c, unsigned level) const;
93 void do_print_tree(const print_tree & c, unsigned level) const;
94 unsigned calchash() const;
98 /** Type of symmetry described by this node. */
101 /** Sorted union set of all indices handled by this node. */
102 std::set<unsigned> indices;
104 /** Vector of child nodes. */
107 GINAC_DECLARE_UNARCHIVER(symmetry);
112 inline symmetry sy_none() { return symmetry(); }
113 inline symmetry sy_none(const symmetry &c1, const symmetry &c2) { return symmetry(symmetry::none, c1, c2); }
114 inline symmetry sy_none(const symmetry &c1, const symmetry &c2, const symmetry &c3) { return symmetry(symmetry::none, c1, c2).add(c3); }
115 inline symmetry sy_none(const symmetry &c1, const symmetry &c2, const symmetry &c3, const symmetry &c4) { return symmetry(symmetry::none, c1, c2).add(c3).add(c4); }
117 inline symmetry sy_symm() { symmetry s; s.set_type(symmetry::symmetric); return s; }
118 inline symmetry sy_symm(const symmetry &c1, const symmetry &c2) { return symmetry(symmetry::symmetric, c1, c2); }
119 inline symmetry sy_symm(const symmetry &c1, const symmetry &c2, const symmetry &c3) { return symmetry(symmetry::symmetric, c1, c2).add(c3); }
120 inline symmetry sy_symm(const symmetry &c1, const symmetry &c2, const symmetry &c3, const symmetry &c4) { return symmetry(symmetry::symmetric, c1, c2).add(c3).add(c4); }
122 inline symmetry sy_anti() { symmetry s; s.set_type(symmetry::antisymmetric); return s; }
123 inline symmetry sy_anti(const symmetry &c1, const symmetry &c2) { return symmetry(symmetry::antisymmetric, c1, c2); }
124 inline symmetry sy_anti(const symmetry &c1, const symmetry &c2, const symmetry &c3) { return symmetry(symmetry::antisymmetric, c1, c2).add(c3); }
125 inline symmetry sy_anti(const symmetry &c1, const symmetry &c2, const symmetry &c3, const symmetry &c4) { return symmetry(symmetry::antisymmetric, c1, c2).add(c3).add(c4); }
127 inline symmetry sy_cycl() { symmetry s; s.set_type(symmetry::cyclic); return s; }
128 inline symmetry sy_cycl(const symmetry &c1, const symmetry &c2) { return symmetry(symmetry::cyclic, c1, c2); }
129 inline symmetry sy_cycl(const symmetry &c1, const symmetry &c2, const symmetry &c3) { return symmetry(symmetry::cyclic, c1, c2).add(c3); }
130 inline symmetry sy_cycl(const symmetry &c1, const symmetry &c2, const symmetry &c3, const symmetry &c4) { return symmetry(symmetry::cyclic, c1, c2).add(c3).add(c4); }
132 // These return references to preallocated common symmetries (similar to
133 // the numeric flyweights).
134 const symmetry & not_symmetric();
135 const symmetry & symmetric2();
136 const symmetry & symmetric3();
137 const symmetry & symmetric4();
138 const symmetry & antisymmetric2();
139 const symmetry & antisymmetric3();
140 const symmetry & antisymmetric4();
142 /** Canonicalize the order of elements of an expression vector, according to
143 * the symmetry properties defined in a symmetry tree.
145 * @param v Start of expression vector
146 * @param symm Root node of symmetry tree
147 * @return the overall sign introduced by the reordering (+1, -1 or 0)
148 * or numeric_limits<int>::max() if nothing changed */
149 extern int canonicalize(exvector::iterator v, const symmetry &symm);
151 /** Symmetrize expression over a set of objects (symbols, indices). */
152 ex symmetrize(const ex & e, exvector::const_iterator first, exvector::const_iterator last);
154 /** Symmetrize expression over a set of objects (symbols, indices). */
155 inline ex symmetrize(const ex & e, const exvector & v)
157 return symmetrize(e, v.begin(), v.end());
160 /** Antisymmetrize expression over a set of objects (symbols, indices). */
161 ex antisymmetrize(const ex & e, exvector::const_iterator first, exvector::const_iterator last);
163 /** Antisymmetrize expression over a set of objects (symbols, indices). */
164 inline ex antisymmetrize(const ex & e, const exvector & v)
166 return antisymmetrize(e, v.begin(), v.end());
169 /** Symmetrize expression by cyclic permuation over a set of objects
170 * (symbols, indices). */
171 ex symmetrize_cyclic(const ex & e, exvector::const_iterator first, exvector::const_iterator last);
173 /** Symmetrize expression by cyclic permutation over a set of objects
174 * (symbols, indices). */
175 inline ex symmetrize_cyclic(const ex & e, const exvector & v)
177 return symmetrize(e, v.begin(), v.end());
182 #endif // ndef __GINAC_SYMMETRY_H__