/** @file indexed.h
*
- * Interface to GiNaC's index carrying objects. */
+ * Interface to GiNaC's indexed expressions. */
-#ifndef _INDEXED_H_
-#define _INDEXED_H_
+/*
+ * GiNaC Copyright (C) 1999-2004 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
+ */
-#include <string>
+#ifndef __GINAC_INDEXED_H__
+#define __GINAC_INDEXED_H__
-class indexed;
+#include <map>
#include "exprseq.h"
-#include "idx.h"
+#include "wildcard.h"
+
+namespace GiNaC {
+
-/** Base class for non-commutative indexed objects */
+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
{
-// member functions
+ GINAC_DECLARE_REGISTERED_CLASS(indexed, exprseq)
- // default constructor, destructor, copy constructor assignment operator and helpers
-public:
- indexed();
- ~indexed();
- indexed(indexed const & other);
- indexed const & operator=(indexed const & other);
-protected:
- void copy(indexed const & other);
- void destroy(bool call_parent);
+ 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
+ // 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:
- indexed(ex const & i1);
- indexed(ex const & i1, ex const & i2);
- indexed(ex const & i1, ex const & i2, ex const & i3);
- indexed(exvector const & iv);
- indexed(exvector * iv);
+ unsigned precedence() const {return 55;}
+ bool info(unsigned inf) const;
+ ex eval(int level = 0) const;
+ exvector get_free_indices() const;
- // functions overriding virtual functions from base classes
+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 { return return_types::commutative; }
+ ex expand(unsigned options = 0) const;
+
+ // new virtual functions which can be overridden by derived classes
+ // none
+
+ // non-virtual functions in this class
public:
- basic * duplicate() const;
- void printraw(ostream & os) const;
- void printtree(ostream & os, unsigned indent) const;
- void print(ostream & os, unsigned upper_precedence=0) const;
- void printcsrc(ostream & os, unsigned type, unsigned upper_precedence) const;
- bool info(unsigned inf) const;
- ex diff(symbol const & s) const;
- exvector get_indices(void) const;
+ /** 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:
- int compare_same_type(basic const & other) const;
- bool is_equal_same_type(basic const & other) const;
- unsigned return_type(void) const;
- unsigned return_type_tinfo(void) const;
- ex thisexprseq(exvector const & v) const;
- ex thisexprseq(exvector * vp) const;
-
- // new virtual functions which can be overridden by derived classes
- // none
-
- // non-virtual functions in this class
+ 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:
- void printrawindices(ostream & os) const;
- void printtreeindices(ostream & os, unsigned indent) const;
- void printindices(ostream & os) const;
- bool all_of_type_idx(void) const;
+ ex symtree; /**< Index symmetry (tree of symmetry objects) */
+};
-// member variables
- // none
+
+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;
};
-// global constants
+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();
-extern const indexed some_indexed;
-extern type_info const & typeid_indexed;
+ 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;
-// macros
+protected:
+ spmap spm; /*< Map from defined scalar product pairs to their values */
+};
-#define ex_to_indexed(X) static_cast<indexed const &>(*(X).bp)
-#endif // ndef _INDEXED_H_
+// utility functions
+
+/** Specialization of is_exactly_a<indexed>(obj) for indexed objects. */
+template<> inline bool is_exactly_a<indexed>(const basic & obj)
+{
+ return obj.tinfo()==TINFO_indexed;
+}
+} // namespace GiNaC
+#endif // ndef __GINAC_INDEXED_H__
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