* Interface to GiNaC's indexed expressions. */
/*
- * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2003 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
#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)
{
GINAC_DECLARE_REGISTERED_CLASS(indexed, exprseq)
- 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);
-
- // 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;
+ 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:
* @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);
+ 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 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);
+ 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 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);
+ 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 symm Symmetry of indices
* @param iv Vector of indices
* @return newly constructed indexed object */
- indexed(const ex & b, symmetry_type symm, const exvector & iv);
+ indexed(const ex & b, const symmetry & 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
+ 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:
- void print(const print_context & c, unsigned level = 0) const;
+ unsigned precedence() const {return 55;}
bool info(unsigned inf) const;
ex eval(int level = 0) const;
- int degree(const ex & s) const;
- int ldegree(const ex & s) const;
- ex coeff(const ex & s, int n = 1) const;
- exvector get_free_indices(void) const;
+ exvector get_free_indices() const;
protected:
- ex thisexprseq(const exvector & v) const;
- ex thisexprseq(exvector * vp) const;
- unsigned return_type(void) const { return return_types::commutative; }
+ 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
bool all_index_values_are(unsigned inf) const;
/** Return a vector containing the object's indices. */
- exvector get_indices(void) const;
+ exvector get_indices() const;
/** Return a vector containing the dummy indices of the object, if any. */
- exvector get_dummy_indices(void) const;
+ exvector get_dummy_indices() const;
/** Return a vector containing the dummy indices in the contraction with
* another indexed object. */
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 assert_all_indices_of_type_idx(void) 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:
- symmetry_type symmetry; /**< Index symmetry */
+ ex symtree; /**< Index symmetry (tree of symmetry objects) */
};
-typedef std::pair<ex, ex> spmapkey;
+class spmapkey {
+public:
+ spmapkey() : dim(wild()) {}
+ spmapkey(const ex & v1, const ex & v2, const ex & dim = wild());
-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));
- }
+ 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, spmapkey_is_less> spmap;
+typedef std::map<spmapkey, ex> spmap;
/** Helper class for storing information about known scalar products which
* are to be automatically replaced by simplify_indexed().
/** 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);
+ /** 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);
- bool is_defined(const ex & v1, const ex & v2) const;
- ex evaluate(const ex & v1, const ex & v2) const;
- void debugprint(void) const;
+ /** 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());
-private:
- static spmapkey make_key(const ex & v1, const ex & v2);
+ /** 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
-inline const indexed &ex_to_indexed(const ex &e)
+
+/** Specialization of is_exactly_a<indexed>(obj) for indexed objects. */
+template<> inline bool is_exactly_a<indexed>(const basic & obj)
{
- return static_cast<const indexed &>(*e.bp);
+ return obj.tinfo()==TINFO_indexed;
}
-
-/** 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);
-
-
} // namespace GiNaC
#endif // ndef __GINAC_INDEXED_H__
git://www.ginac.de / ginac.git / blobdiff