/** @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) 1999-2001 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
+ */
-#include <string>
+#ifndef __GINAC_INDEXED_H__
+#define __GINAC_INDEXED_H__
-class indexed;
+#include <map>
#include "exprseq.h"
-#include "idx.h"
-/** Base class for non-commutative indexed objects */
+namespace GiNaC {
+
+
+class scalar_products;
+
+/** 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, const scalar_products & sp);
+ friend ex simplify_indexed_product(const ex & e, exvector & free_indices, const scalar_products & sp);
- // other constructors
+ // types
+public:
+ /** Type of symmetry of the object with respect to commutation of its indices. */
+ typedef enum {
+ unknown, /**< symmetry properties unknown */
+ symmetric, /**< totally symmetric */
+ antisymmetric, /**< totally antisymmetric */
+ mixed /**< mixed symmetry (unimplemented) */
+ } symmetry_type;
+
+ // other constructors
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);
+ /** 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, symmetry_type 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, symmetry_type 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, symmetry_type 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, symmetry_type symm, const exvector & iv);
+
+ // internal constructors
+ indexed(symmetry_type symm, const exprseq & es);
+ indexed(symmetry_type symm, const exvector & v, bool discardable = false);
+ indexed(symmetry_type symm, exvector * vp); // vp will be deleted
+
+ // functions overriding virtual functions from base classes
+public:
+ void printraw(std::ostream & os) const;
+ void printtree(std::ostream & os, unsigned indent) const;
+ void print(std::ostream & os, unsigned upper_precedence=0) const;
+ bool info(unsigned inf) const;
+ ex eval(int level = 0) const;
+ exvector get_free_indices(void) const;
- // functions overriding virtual functions from base classes
+protected:
+ ex thisexprseq(const exvector & v) const;
+ ex thisexprseq(exvector * vp) const;
+ unsigned return_type(void) 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;
+
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 printrawindices(std::ostream & os) const;
+ void printtreeindices(std::ostream & os, unsigned indent) const;
+ void printindices(std::ostream & os) const;
+ bool all_indices_of_type_idx(void) 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;
+ symmetry_type symmetry; /**< Index symmetry */
+};
-// member variables
- // none
+
+typedef std::pair<ex, ex> spmapkey;
+
+struct spmapkey_is_less {
+ bool operator() (const spmapkey &p, const spmapkey &q) const
+ {
+ int cmp = p.first.compare(q.first);
+ return ((cmp<0) || (!(cmp>0) && p.second.compare(q.second)<0));
+ }
+};
+
+typedef std::map<spmapkey, ex, spmapkey_is_less> 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);
+
+ /** Clear all registered scalar products. */
+ void clear(void);
+
+ bool is_defined(const ex & v1, const ex & v2) const;
+ ex evaluate(const ex & v1, const ex & v2) const;
+ void debugprint(void) const;
+
+private:
+ static spmapkey make_key(const ex & v1, const ex & v2);
+
+ spmap spm; /*< Map from defined scalar product pairs to their values */
};
-// global constants
-extern const indexed some_indexed;
-extern type_info const & typeid_indexed;
+// utility functions
+inline const indexed &ex_to_indexed(const ex &e)
+{
+ return static_cast<const indexed &>(*e.bp);
+}
-// macros
-#define ex_to_indexed(X) static_cast<indexed const &>(*(X).bp)
+/** Simplify/canonicalize expression containing indexed objects. This
+ * performs contraction of dummy indices where possible and checks whether
+ * the free indices in sums are consistent.
+ *
+ * @param e The expression to be simplified
+ * @return simplified expression */
+ex simplify_indexed(const ex & e);
+
+/** Simplify/canonicalize expression containing indexed objects. This
+ * performs contraction of dummy indices where possible, checks whether
+ * the free indices in sums are consistent, and automatically replaces
+ * scalar products by known values if desired.
+ *
+ * @param e The expression to be simplified
+ * @param sp Scalar products to be replaced automatically
+ * @return simplified expression */
+ex simplify_indexed(const ex & e, const scalar_products & sp);
-#endif // ndef _INDEXED_H_
+} // namespace GiNaC
+#endif // ndef __GINAC_INDEXED_H__
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