GiNaC/ginac/idx.h

/** @file idx.h
 *
 *  Interface to GiNaC's indices. */

/*
 *  GiNaC Copyright (C) 1999-2001 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., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 */

#ifndef __GINAC_IDX_H__
#define __GINAC_IDX_H__

#include "ex.h"

namespace GiNaC {


/** This class holds one index of an indexed object. Indices can
 *  theoretically consist of any symbolic expression but they are usually
 *  only just a symbol (e.g. "mu", "i") or numeric (integer). Indices belong
 *  to a space with a certain numeric or symbolic dimension. */
class idx : public basic
{
        GINAC_DECLARE_REGISTERED_CLASS(idx, basic)

        // other constructors
public:
        /** Construct index with given value and dimension.
         *
         *  @param v Value of index (numeric or symbolic)
         *  @param dim Dimension of index space (numeric or symbolic)
         *  @return newly constructed index */
        explicit idx(const ex & v, const ex & dim);

        // functions overriding virtual functions from bases classes
public:
        void print(const print_context & c, unsigned level = 0) const;
        bool info(unsigned inf) const;
        unsigned nops() const;
        ex & let_op(int i);
protected:
        ex subs(const lst & ls, const lst & lr) const;

        // new virtual functions in this class
public:
        /** Check whether the index forms a dummy index pair with another index
         *  of the same type. */
        virtual bool is_dummy_pair_same_type(const basic & other) const;

        // non-virtual functions in this class
public:
        /** Get value of index. */
        ex get_value(void) const {return value;}

        /** Check whether the index is numeric. */
        bool is_numeric(void) const {return is_ex_exactly_of_type(value, numeric);}

        /** Check whether the index is symbolic. */
        bool is_symbolic(void) const {return !is_ex_exactly_of_type(value, numeric);}

        /** Get dimension of index space. */
        ex get_dim(void) const {return dim;}

        /** Check whether the dimension is numeric. */
        bool is_dim_numeric(void) const {return is_ex_exactly_of_type(dim, numeric);}

        /** Check whether the dimension is symbolic. */
        bool is_dim_symbolic(void) const {return !is_ex_exactly_of_type(dim, numeric);}

protected:
        ex value; /**< Expression that constitutes the index (numeric or symbolic name) */
        ex dim;   /**< Dimension of space (can be symbolic or numeric) */
};


/** This class holds an index with a variance (co- or contravariant). There
 *  is an associated metric tensor that can be used to raise/lower indices. */
class varidx : public idx
{
        GINAC_DECLARE_REGISTERED_CLASS(varidx, idx)

        // other constructors
public:
        /** Construct index with given value, dimension and variance.
         *
         *  @param v Value of index (numeric or symbolic)
         *  @param dim Dimension of index space (numeric or symbolic)
         *  @param covariant Make covariant index (default is contravariant)
         *  @return newly constructed index */
        varidx(const ex & v, const ex & dim, bool covariant = false);

        // functions overriding virtual functions from bases classes
public:
        void print(const print_context & c, unsigned level = 0) const;
        bool is_dummy_pair_same_type(const basic & other) const;

        // non-virtual functions in this class
public:
        /** Check whether the index is covariant. */
        bool is_covariant(void) const {return covariant;}

        /** Check whether the index is contravariant (not covariant). */
        bool is_contravariant(void) const {return !covariant;}

        /** Make a new index with the same value but the opposite variance. */
        ex toggle_variance(void) const;

        // member variables
protected:
        bool covariant; /**< x.mu, default is contravariant: x~mu */
};


// utility functions
inline const idx &ex_to_idx(const ex & e)
{
        return static_cast<const idx &>(*e.bp);
}

inline const varidx &ex_to_varidx(const ex & e)
{
        return static_cast<const varidx &>(*e.bp);
}

/** Check whether two indices form a dummy pair. */
bool is_dummy_pair(const idx & i1, const idx & i2);

/** Check whether two expressions form a dummy index pair. */
bool is_dummy_pair(const ex & e1, const ex & e2);

/** Given a vector of indices, split them into two vectors, one containing
 *  the free indices, the other containing the dummy indices (numeric
 *  indices are neither free nor dummy ones).
 *
 *  @param it Pointer to start of index vector
 *  @param itend Pointer to end of index vector
 *  @param out_free Vector of free indices (returned, sorted)
 *  @param out_dummy Vector of dummy indices (returned, sorted) */
void find_free_and_dummy(exvector::const_iterator it, exvector::const_iterator itend, exvector & out_free, exvector & out_dummy);

/** Given a vector of indices, split them into two vectors, one containing
 *  the free indices, the other containing the dummy indices (numeric
 *  indices are neither free nor dummy ones).
 *
 *  @param v Index vector
 *  @param out_free Vector of free indices (returned, sorted)
 *  @param out_dummy Vector of dummy indices (returned, sorted) */
inline void find_free_and_dummy(const exvector & v, exvector & out_free, exvector & out_dummy)
{
        find_free_and_dummy(v.begin(), v.end(), out_free, out_dummy);
}

/** Given a vector of indices, find the dummy indices.
 *
 *  @param v Index vector
 *  @param out_dummy Vector of dummy indices (returned, sorted) */
inline void find_dummy_indices(const exvector & v, exvector & out_dummy)
{
        exvector free_indices;
        find_free_and_dummy(v.begin(), v.end(), free_indices, out_dummy);
}

/** Count the number of dummy index pairs in an index vector. */
inline unsigned count_dummy_indices(const exvector & v)
{
        exvector free_indices, dummy_indices;
        find_free_and_dummy(v.begin(), v.end(), free_indices, dummy_indices);
        return dummy_indices.size();
}

/** Count the number of dummy index pairs in an index vector. */
inline unsigned count_free_indices(const exvector & v)
{
        exvector free_indices, dummy_indices;
        find_free_and_dummy(v.begin(), v.end(), free_indices, dummy_indices);
        return free_indices.size();
}

/** Given two index vectors, find those indices that appear in the first
 *  vector but not in the second one (asymmetric set difference). */
exvector index_set_difference(const exvector & set1, const exvector & set2);

} // namespace GiNaC

#endif // ndef __GINAC_IDX_H__
1	cbauer	1.1	/** @file idx.h
2			*
3	cbauer	1.5	* Interface to GiNaC's indices. */
4
5			/*
6	kreckel	1.18	* GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
7	cbauer	1.2	*
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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
21			*/
22	cbauer	1.1
23	cbauer	1.2	#ifndef __GINAC_IDX_H__
24			#define __GINAC_IDX_H__
25	cbauer	1.1
26	cbauer	1.11	#include "ex.h"
27	cbauer	1.6
28			namespace GiNaC {
29	cbauer	1.1
30	cbauer	1.19
31	cbauer	1.25	/** 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	cbauer	1.1	class idx : public basic
36			{
37	cbauer	1.14	GINAC_DECLARE_REGISTERED_CLASS(idx, basic)
38	cbauer	1.10
39	cbauer	1.14	// other constructors
40	cbauer	1.1	public:
41	cbauer	1.25	/** Construct index with given value and dimension.
42			*
43			* @param v Value of index (numeric or symbolic)
44			* @param dim Dimension of index space (numeric or symbolic)
45			* @return newly constructed index */
46			explicit idx(const ex & v, const ex & dim);
47	cbauer	1.1
48	cbauer	1.14	// functions overriding virtual functions from bases classes
49	cbauer	1.1	public:
50	cbauer	1.29	void print(const print_context & c, unsigned level = 0) const;
51	cbauer	1.14	bool info(unsigned inf) const;
52	cbauer	1.28	unsigned nops() const;
53			ex & let_op(int i);
54	cbauer	1.1	protected:
55	cbauer	1.14	ex subs(const lst & ls, const lst & lr) const;
56	cbauer	1.1
57	cbauer	1.25	// new virtual functions in this class
58	cbauer	1.1	public:
59	cbauer	1.25	/** Check whether the index forms a dummy index pair with another index
60			* of the same type. */
61			virtual bool is_dummy_pair_same_type(const basic & other) const;
62	cbauer	1.1
63	cbauer	1.14	// non-virtual functions in this class
64	cbauer	1.1	public:
65	cbauer	1.25	/** Get value of index. */
66			ex get_value(void) const {return value;}
67	cbauer	1.19
68	cbauer	1.25	/** Check whether the index is numeric. */
69			bool is_numeric(void) const {return is_ex_exactly_of_type(value, numeric);}
70	cbauer	1.19
71	cbauer	1.25	/** Check whether the index is symbolic. */
72			bool is_symbolic(void) const {return !is_ex_exactly_of_type(value, numeric);}
73
74			/** Get dimension of index space. */
75			ex get_dim(void) const {return dim;}
76
77			/** Check whether the dimension is numeric. */
78			bool is_dim_numeric(void) const {return is_ex_exactly_of_type(dim, numeric);}
79
80			/** Check whether the dimension is symbolic. */
81			bool is_dim_symbolic(void) const {return !is_ex_exactly_of_type(dim, numeric);}
82
83			protected:
84			ex value; /*< Expression that constitutes the index (numeric or symbolic name) /
85			ex dim; /*< Dimension of space (can be symbolic or numeric) /
86			};
87
88
89			/** This class holds an index with a variance (co- or contravariant). There
90			* is an associated metric tensor that can be used to raise/lower indices. */
91			class varidx : public idx
92			{
93			GINAC_DECLARE_REGISTERED_CLASS(varidx, idx)
94
95			// other constructors
96			public:
97			/** Construct index with given value, dimension and variance.
98			*
99			* @param v Value of index (numeric or symbolic)
100			* @param dim Dimension of index space (numeric or symbolic)
101			* @param covariant Make covariant index (default is contravariant)
102			* @return newly constructed index */
103			varidx(const ex & v, const ex & dim, bool covariant = false);
104
105			// functions overriding virtual functions from bases classes
106			public:
107	cbauer	1.29	void print(const print_context & c, unsigned level = 0) const;
108	cbauer	1.25	bool is_dummy_pair_same_type(const basic & other) const;
109
110			// non-virtual functions in this class
111			public:
112			/** Check whether the index is covariant. */
113	cbauer	1.19	bool is_covariant(void) const {return covariant;}
114
115	cbauer	1.25	/** Check whether the index is contravariant (not covariant). */
116			bool is_contravariant(void) const {return !covariant;}
117	cbauer	1.1
118	cbauer	1.25	/** Make a new index with the same value but the opposite variance. */
119			ex toggle_variance(void) const;
120	cbauer	1.20
121	cbauer	1.14	// member variables
122	cbauer	1.1	protected:
123	cbauer	1.25	bool covariant; /*< x.mu, default is contravariant: x~mu /
124	cbauer	1.1	};
125
126	cbauer	1.25
127	cbauer	1.6	// utility functions
128	cbauer	1.25	inline const idx &ex_to_idx(const ex & e)
129	cbauer	1.6	{
130			return static_cast<const idx &>(*e.bp);
131			}
132	cbauer	1.1
133	cbauer	1.25	inline const varidx &ex_to_varidx(const ex & e)
134			{
135			return static_cast<const varidx &>(*e.bp);
136			}
137
138			/** Check whether two indices form a dummy pair. */
139			bool is_dummy_pair(const idx & i1, const idx & i2);
140
141			/** Check whether two expressions form a dummy index pair. */
142			bool is_dummy_pair(const ex & e1, const ex & e2);
143	cbauer	1.1
144	cbauer	1.27	/** Given a vector of indices, split them into two vectors, one containing
145			* the free indices, the other containing the dummy indices (numeric
146			* indices are neither free nor dummy ones).
147			*
148			* @param it Pointer to start of index vector
149			* @param itend Pointer to end of index vector
150			* @param out_free Vector of free indices (returned, sorted)
151			* @param out_dummy Vector of dummy indices (returned, sorted) */
152			void find_free_and_dummy(exvector::const_iterator it, exvector::const_iterator itend, exvector & out_free, exvector & out_dummy);
153
154			/** Given a vector of indices, split them into two vectors, one containing
155			* the free indices, the other containing the dummy indices (numeric
156			* indices are neither free nor dummy ones).
157			*
158			* @param v Index vector
159			* @param out_free Vector of free indices (returned, sorted)
160			* @param out_dummy Vector of dummy indices (returned, sorted) */
161			inline void find_free_and_dummy(const exvector & v, exvector & out_free, exvector & out_dummy)
162			{
163			find_free_and_dummy(v.begin(), v.end(), out_free, out_dummy);
164			}
165
166			/** Given a vector of indices, find the dummy indices.
167			*
168			* @param v Index vector
169			* @param out_dummy Vector of dummy indices (returned, sorted) */
170			inline void find_dummy_indices(const exvector & v, exvector & out_dummy)
171			{
172			exvector free_indices;
173			find_free_and_dummy(v.begin(), v.end(), free_indices, out_dummy);
174			}
175
176			/** Count the number of dummy index pairs in an index vector. */
177			inline unsigned count_dummy_indices(const exvector & v)
178			{
179			exvector free_indices, dummy_indices;
180			find_free_and_dummy(v.begin(), v.end(), free_indices, dummy_indices);
181			return dummy_indices.size();
182			}
183
184			/** Count the number of dummy index pairs in an index vector. */
185			inline unsigned count_free_indices(const exvector & v)
186			{
187			exvector free_indices, dummy_indices;
188			find_free_and_dummy(v.begin(), v.end(), free_indices, dummy_indices);
189			return free_indices.size();
190			}
191
192			/** Given two index vectors, find those indices that appear in the first
193			* vector but not in the second one (asymmetric set difference). */
194			exvector index_set_difference(const exvector & set1, const exvector & set2);
195	cbauer	1.6
196			} // namespace GiNaC
197	cbauer	1.1
198	cbauer	1.2	#endif // ndef __GINAC_IDX_H__
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