GiNaC/ginac/indexed.h

/** @file indexed.h
 *
 *  Interface to GiNaC's indexed expressions. */

/*
 *  GiNaC Copyright (C) 1999-2007 Johannes Gutenberg University Mainz, Germany
 *
 *  This program is free software; you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with this program; if not, write to the Free Software
 *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 */

#ifndef __GINAC_INDEXED_H__
#define __GINAC_INDEXED_H__

#include <map>

#include "exprseq.h"
#include "wildcard.h"

namespace GiNaC {


class scalar_products;
class symmetry;

/** This class holds an indexed expression. It consists of a 'base' expression
 *  (the expression being indexed) which can be accessed as op(0), and n (n >= 0)
 *  indices (all of class idx), accessible as op(1)..op(n). */
class indexed : public exprseq
{
        GINAC_DECLARE_REGISTERED_CLASS(indexed, exprseq)

        friend ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp);
        friend ex simplify_indexed_product(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp);
        friend bool reposition_dummy_indices(ex & e, exvector & variant_dummy_indices, exvector & moved_indices);

        // other constructors
public:
        /** Construct indexed object with no index.
         *
         *  @param b Base expression
         *  @return newly constructed indexed object */
        indexed(const ex & b);

        /** Construct indexed object with one index. The index must be of class idx.
         *
         *  @param b Base expression
         *  @param i1 The index
         *  @return newly constructed indexed object */
        indexed(const ex & b, const ex & i1);

        /** Construct indexed object with two indices. The indices must be of class idx.
         *
         *  @param b Base expression
         *  @param i1 First index
         *  @param i2 Second index
         *  @return newly constructed indexed object */
        indexed(const ex & b, const ex & i1, const ex & i2);

        /** Construct indexed object with three indices. The indices must be of class idx.
         *
         *  @param b Base expression
         *  @param i1 First index
         *  @param i2 Second index
         *  @param i3 Third index
         *  @return newly constructed indexed object */
        indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3);

        /** Construct indexed object with four indices. The indices must be of class idx.
         *
         *  @param b Base expression
         *  @param i1 First index
         *  @param i2 Second index
         *  @param i3 Third index
         *  @param i4 Fourth index
         *  @return newly constructed indexed object */
        indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3, const ex & i4);

        /** Construct indexed object with two indices and a specified symmetry. The
         *  indices must be of class idx.
         *
         *  @param b Base expression
         *  @param symm Symmetry of indices
         *  @param i1 First index
         *  @param i2 Second index
         *  @return newly constructed indexed object */
        indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2);

        /** Construct indexed object with three indices and a specified symmetry.
         *  The indices must be of class idx.
         *
         *  @param b Base expression
         *  @param symm Symmetry of indices
         *  @param i1 First index
         *  @param i2 Second index
         *  @param i3 Third index
         *  @return newly constructed indexed object */
        indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2, const ex & i3);

        /** Construct indexed object with four indices and a specified symmetry. The
         *  indices must be of class idx.
         *
         *  @param b Base expression
         *  @param symm Symmetry of indices
         *  @param i1 First index
         *  @param i2 Second index
         *  @param i3 Third index
         *  @param i4 Fourth index
         *  @return newly constructed indexed object */
        indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2, const ex & i3, const ex & i4);

        /** Construct indexed object with a specified vector of indices. The indices
         *  must be of class idx.
         *
         *  @param b Base expression
         *  @param iv Vector of indices
         *  @return newly constructed indexed object */
        indexed(const ex & b, const exvector & iv);

        /** Construct indexed object with a specified vector of indices and
         *  symmetry. The indices must be of class idx.
         *
         *  @param b Base expression
         *  @param symm Symmetry of indices
         *  @param iv Vector of indices
         *  @return newly constructed indexed object */
        indexed(const ex & b, const symmetry & symm, const exvector & iv);

        // internal constructors
        indexed(const symmetry & symm, const exprseq & es);
        indexed(const symmetry & symm, const exvector & v, bool discardable = false);
        indexed(const symmetry & symm, std::auto_ptr<exvector> vp);

        // functions overriding virtual functions from base classes
public:
        unsigned precedence() const {return 55;}
        bool info(unsigned inf) const;
        ex eval(int level = 0) const;
        ex real_part() const;
        ex imag_part() const;
        exvector get_free_indices() const;

protected:
        ex derivative(const symbol & s) const;
        ex thiscontainer(const exvector & v) const;
        ex thiscontainer(std::auto_ptr<exvector> vp) const;
        unsigned return_type() const;
        tinfo_t return_type_tinfo() const { return op(0).return_type_tinfo(); }
        ex expand(unsigned options = 0) const;

        // new virtual functions which can be overridden by derived classes
        // none
        
        // non-virtual functions in this class
public:
        /** Check whether all index values have a certain property.
         *  @see class info_flags */
        bool all_index_values_are(unsigned inf) const;

        /** Return a vector containing the object's indices. */
        exvector get_indices() const;

        /** Return a vector containing the dummy indices of the object, if any. */
        exvector get_dummy_indices() const;

        /** Return a vector containing the dummy indices in the contraction with
         *  another indexed object. This is symmetric: a.get_dummy_indices(b)
         *  == b.get_dummy_indices(a) */
        exvector get_dummy_indices(const indexed & other) const;

        /** Check whether the object has an index that forms a dummy index pair
         *  with a given index. */
        bool has_dummy_index_for(const ex & i) const;

        /** Return symmetry properties. */
        ex get_symmetry() const {return symtree;}

protected:
        void printindices(const print_context & c, unsigned level) const;
        void print_indexed(const print_context & c, const char *openbrace, const char *closebrace, unsigned level) const;
        void do_print(const print_context & c, unsigned level) const;
        void do_print_latex(const print_latex & c, unsigned level) const;
        void do_print_tree(const print_tree & c, unsigned level) const;
        void validate() const;

        // member variables
protected:
        ex symtree; /**< Index symmetry (tree of symmetry objects) */
};


class spmapkey {
public:
        spmapkey() : dim(wild()) {}
        spmapkey(const ex & v1, const ex & v2, const ex & dim = wild());

        bool operator==(const spmapkey &other) const;
        bool operator<(const spmapkey &other) const;

        void debugprint() const;

protected:
        ex v1, v2, dim;
};

typedef std::map<spmapkey, ex> spmap;

/** Helper class for storing information about known scalar products which
 *  are to be automatically replaced by simplify_indexed().
 *
 *  @see simplify_indexed */
class scalar_products {
public:
        /** Register scalar product pair and its value. */
        void add(const ex & v1, const ex & v2, const ex & sp);

        /** Register scalar product pair and its value for a specific space dimension. */
        void add(const ex & v1, const ex & v2, const ex & dim, const ex & sp);

        /** Register list of vectors. This adds all possible pairs of products
         *  a.i * b.i with the value a*b (note that this is not a scalar vector
         *  product but an ordinary product of scalars). */
        void add_vectors(const lst & l, const ex & dim = wild());

        /** Clear all registered scalar products. */
        void clear();

        bool is_defined(const ex & v1, const ex & v2, const ex & dim) const;
        ex evaluate(const ex & v1, const ex & v2, const ex & dim) const;
        void debugprint() const;

protected:
        spmap spm; /*< Map from defined scalar product pairs to their values */
};


// utility functions

/** Returns all dummy indices from the expression */
exvector get_all_dummy_indices(const ex & e);

/** More reliable version of the form. The former assumes that e is an
  * expanded epxression. */
exvector get_all_dummy_indices_safely(const ex & e);

/** Returns b with all dummy indices, which are listed in va, renamed 
 *  if modify_va is set to TRUE all dummy indices of b will be appended to va */
ex rename_dummy_indices_uniquely(exvector & va, const ex & b, bool modify_va = false);

/** Returns b with all dummy indices, which are common with a, renamed */
ex rename_dummy_indices_uniquely(const ex & a, const ex & b);

/** Same as above, where va and vb contain the indices of a and b and are sorted */
ex rename_dummy_indices_uniquely(const exvector & va, const exvector & vb, const ex & b);

/** Similar to above, where va and vb are the same and the return value is a list of two lists 
 *  for substitution in b */
lst rename_dummy_indices_uniquely(const exvector & va, const exvector & vb);

/** This function returns the given expression with expanded sums
 *  for all dummy index summations, where the dimensionality of 
 *  the dummy index is a nonnegative integer.
 *  Optionally all indices with a variance will be substituted by 
 *  indices with the corresponding numeric values without variance.
 *
 *  @param e the given expression
 *  @param subs_idx indicates if variance of dummy indixes should be neglected
 */
ex expand_dummy_sum(const ex & e, bool subs_idx = false);

} // namespace GiNaC

#endif // ndef __GINAC_INDEXED_H__
1	/** @file indexed.h
2	*
3	* Interface to GiNaC's indexed expressions. */
4
5	/*
6	* GiNaC Copyright (C) 1999-2007 Johannes Gutenberg University Mainz, Germany
7	*
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.
12	*
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.
17	*
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
21	*/
22
23	#ifndef __GINAC_INDEXED_H__
24	#define __GINAC_INDEXED_H__
25
26	#include <map>
27
28	#include "exprseq.h"
29	#include "wildcard.h"
30
31	namespace GiNaC {
32
33
34	class scalar_products;
35	class symmetry;
36
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
41	{
42	GINAC_DECLARE_REGISTERED_CLASS(indexed, exprseq)
43
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);
47
48	// other constructors
49	public:
50	/** Construct indexed object with no index.
51	*
52	* @param b Base expression
53	* @return newly constructed indexed object */
54	indexed(const ex & b);
55
56	/** Construct indexed object with one index. The index must be of class idx.
57	*
58	* @param b Base expression
59	* @param i1 The index
60	* @return newly constructed indexed object */
61	indexed(const ex & b, const ex & i1);
62
63	/** Construct indexed object with two indices. The indices must be of class idx.
64	*
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);
70
71	/** Construct indexed object with three indices. The indices must be of class idx.
72	*
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);
79
80	/** Construct indexed object with four indices. The indices must be of class idx.
81	*
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);
89
90	/** Construct indexed object with two indices and a specified symmetry. The
91	* indices must be of class idx.
92	*
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);
99
100	/** Construct indexed object with three indices and a specified symmetry.
101	* The indices must be of class idx.
102	*
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);
110
111	/** Construct indexed object with four indices and a specified symmetry. The
112	* indices must be of class idx.
113	*
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);
122
123	/** Construct indexed object with a specified vector of indices. The indices
124	* must be of class idx.
125	*
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);
130
131	/** Construct indexed object with a specified vector of indices and
132	* symmetry. The indices must be of class idx.
133	*
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);
139
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);
144
145	// functions overriding virtual functions from base classes
146	public:
147	unsigned precedence() const {return 55;}
148	bool info(unsigned inf) const;
149	ex eval(int level = 0) const;
150	ex real_part() const;
151	ex imag_part() const;
152	exvector get_free_indices() const;
153
154	protected:
155	ex derivative(const symbol & s) const;
156	ex thiscontainer(const exvector & v) const;
157	ex thiscontainer(std::auto_ptr<exvector> vp) const;
158	unsigned return_type() const;
159	tinfo_t return_type_tinfo() const { return op(0).return_type_tinfo(); }
160	ex expand(unsigned options = 0) const;
161
162	// new virtual functions which can be overridden by derived classes
163	// none
164
165	// non-virtual functions in this class
166	public:
167	/** Check whether all index values have a certain property.
168	* @see class info_flags */
169	bool all_index_values_are(unsigned inf) const;
170
171	/** Return a vector containing the object's indices. */
172	exvector get_indices() const;
173
174	/** Return a vector containing the dummy indices of the object, if any. */
175	exvector get_dummy_indices() const;
176
177	/** Return a vector containing the dummy indices in the contraction with
178	* another indexed object. This is symmetric: a.get_dummy_indices(b)
179	* == b.get_dummy_indices(a) */
180	exvector get_dummy_indices(const indexed & other) const;
181
182	/** Check whether the object has an index that forms a dummy index pair
183	* with a given index. */
184	bool has_dummy_index_for(const ex & i) const;
185
186	/** Return symmetry properties. */
187	ex get_symmetry() const {return symtree;}
188
189	protected:
190	void printindices(const print_context & c, unsigned level) const;
191	void print_indexed(const print_context & c, const char openbrace, const char closebrace, unsigned level) const;
192	void do_print(const print_context & c, unsigned level) const;
193	void do_print_latex(const print_latex & c, unsigned level) const;
194	void do_print_tree(const print_tree & c, unsigned level) const;
195	void validate() const;
196
197	// member variables
198	protected:
199	ex symtree; /*< Index symmetry (tree of symmetry objects) /
200	};
201
202
203	class spmapkey {
204	public:
205	spmapkey() : dim(wild()) {}
206	spmapkey(const ex & v1, const ex & v2, const ex & dim = wild());
207
208	bool operator==(const spmapkey &other) const;
209	bool operator<(const spmapkey &other) const;
210
211	void debugprint() const;
212
213	protected:
214	ex v1, v2, dim;
215	};
216
217	typedef std::map<spmapkey, ex> spmap;
218
219	/** Helper class for storing information about known scalar products which
220	* are to be automatically replaced by simplify_indexed().
221	*
222	* @see simplify_indexed */
223	class scalar_products {
224	public:
225	/** Register scalar product pair and its value. */
226	void add(const ex & v1, const ex & v2, const ex & sp);
227
228	/** Register scalar product pair and its value for a specific space dimension. */
229	void add(const ex & v1, const ex & v2, const ex & dim, const ex & sp);
230
231	/** Register list of vectors. This adds all possible pairs of products
232	* a.i * b.i with the value a*b (note that this is not a scalar vector
233	* product but an ordinary product of scalars). */
234	void add_vectors(const lst & l, const ex & dim = wild());
235
236	/** Clear all registered scalar products. */
237	void clear();
238
239	bool is_defined(const ex & v1, const ex & v2, const ex & dim) const;
240	ex evaluate(const ex & v1, const ex & v2, const ex & dim) const;
241	void debugprint() const;
242
243	protected:
244	spmap spm; /< Map from defined scalar product pairs to their values /
245	};
246
247
248	// utility functions
249
250	/** Returns all dummy indices from the expression */
251	exvector get_all_dummy_indices(const ex & e);
252
253	/** More reliable version of the form. The former assumes that e is an
254	* expanded epxression. */
255	exvector get_all_dummy_indices_safely(const ex & e);
256
257	/** Returns b with all dummy indices, which are listed in va, renamed
258	* if modify_va is set to TRUE all dummy indices of b will be appended to va */
259	ex rename_dummy_indices_uniquely(exvector & va, const ex & b, bool modify_va = false);
260
261	/** Returns b with all dummy indices, which are common with a, renamed */
262	ex rename_dummy_indices_uniquely(const ex & a, const ex & b);
263
264	/** Same as above, where va and vb contain the indices of a and b and are sorted */
265	ex rename_dummy_indices_uniquely(const exvector & va, const exvector & vb, const ex & b);
266
267	/** Similar to above, where va and vb are the same and the return value is a list of two lists
268	* for substitution in b */
269	lst rename_dummy_indices_uniquely(const exvector & va, const exvector & vb);
270
271	/** This function returns the given expression with expanded sums
272	* for all dummy index summations, where the dimensionality of
273	* the dummy index is a nonnegative integer.
274	* Optionally all indices with a variance will be substituted by
275	* indices with the corresponding numeric values without variance.
276	*
277	* @param e the given expression
278	* @param subs_idx indicates if variance of dummy indixes should be neglected
279	*/
280	ex expand_dummy_sum(const ex & e, bool subs_idx = false);
281
282	} // namespace GiNaC
283
284	#endif // ndef __GINAC_INDEXED_H__
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