/** @file indexed.h
*
- * Interface to GiNaC's index carrying objects. */
+ * Interface to GiNaC's indexed expressions. */
/*
- * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2006 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
*
* 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
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
#ifndef __GINAC_INDEXED_H__
#define __GINAC_INDEXED_H__
-#include <string>
-#include <ginac/exprseq.h>
+#include <map>
+
+#include "exprseq.h"
+#include "wildcard.h"
-#ifndef NO_GINAC_NAMESPACE
namespace GiNaC {
-#endif // ndef NO_GINAC_NAMESPACE
-/** 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
{
- GINAC_DECLARE_REGISTERED_CLASS(indexed, exprseq)
+ GINAC_DECLARE_REGISTERED_CLASS(indexed, exprseq)
-// member functions
+ 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);
- // default constructor, destructor, copy constructor assignment operator and helpers
+ // other constructors
public:
- indexed();
- ~indexed();
- indexed(const indexed & other);
- const indexed & operator=(const indexed & other);
-protected:
- void copy(const indexed & other);
- void destroy(bool call_parent);
+ /** 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);
- // other constructors
+ // 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(const ex & i1);
- indexed(const ex & i1, const ex & i2);
- indexed(const ex & i1, const ex & i2, const ex & i3);
- indexed(const ex & i1, const ex & i2, const ex & i3, const ex & i4);
- indexed(const exvector & iv);
- indexed(exvector * iv);
-
- // functions overriding virtual functions from base classes
+ 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:
- 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(const symbol & 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(const basic & other) const;
- bool is_equal_same_type(const basic & other) const;
- unsigned return_type(void) const;
- unsigned return_type_tinfo(void) const;
- ex thisexprseq(const exvector & 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();
+
+ 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 */
+};
-extern const indexed some_indexed;
-extern const type_info & typeid_indexed;
// utility functions
-inline const indexed &ex_to_indexed(const ex &e)
-{
- return static_cast<const indexed &>(*e.bp);
-}
-#ifndef NO_GINAC_NAMESPACE
+/** 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 NO_GINAC_NAMESPACE
#endif // ndef __GINAC_INDEXED_H__
git://www.ginac.de / ginac.git / blobdiff