* Interface to GiNaC's indices. */
/*
- * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2011 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_IDX_H__
-#define __GINAC_IDX_H__
+#ifndef GINAC_IDX_H
+#define GINAC_IDX_H
-#include <string>
-//#include <vector>
-#include <ginac/basic.h>
-#include <ginac/ex.h>
+#include "ex.h"
+#include "numeric.h"
-#ifndef NO_GINAC_NAMESPACE
namespace GiNaC {
-#endif // ndef NO_GINAC_NAMESPACE
+/** 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)
+ GINAC_DECLARE_REGISTERED_CLASS(idx, basic)
-// member functions
+ // 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);
- // default constructor, destructor, copy constructor assignment operator and helpers
+ // functions overriding virtual functions from base classes
public:
- idx();
- ~idx();
- idx (const idx & other);
- const idx & operator=(const idx & other);
+ bool info(unsigned inf) const;
+ size_t nops() const;
+ ex op(size_t i) const;
+ ex map(map_function & f) const;
+ ex evalf(int level = 0) const;
+ ex subs(const exmap & m, unsigned options = 0) const;
+ void archive(archive_node& n) const;
+ void read_archive(const archive_node& n, lst& syms);
protected:
- void copy(const idx & other);
- void destroy(bool call_parent);
+ ex derivative(const symbol & s) const;
+ bool match_same_type(const basic & other) const;
+ unsigned calchash() const;
- // other constructors
+ // new virtual functions in this class
public:
- explicit idx(bool cov);
- explicit idx(const string & n, bool cov=false);
- explicit idx(const char * n, bool cov=false);
- explicit idx(unsigned v, bool cov=false);
+ /** 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;
- // functions overriding virtual functions from bases classes
+ // 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;
- bool info(unsigned inf) const;
+ /** Get value of index. */
+ ex get_value() const {return value;}
+
+ /** Check whether the index is numeric. */
+ bool is_numeric() const {return is_exactly_a<numeric>(value);}
+
+ /** Check whether the index is symbolic. */
+ bool is_symbolic() const {return !is_exactly_a<numeric>(value);}
+
+ /** Get dimension of index space. */
+ ex get_dim() const {return dim;}
+
+ /** Check whether the dimension is numeric. */
+ bool is_dim_numeric() const {return is_exactly_a<numeric>(dim);}
+
+ /** Check whether the dimension is symbolic. */
+ bool is_dim_symbolic() const {return !is_exactly_a<numeric>(dim);}
+
+ /** Make a new index with the same value but a different dimension. */
+ ex replace_dim(const ex & new_dim) const;
+
+ /** Return the minimum of the dimensions of this and another index.
+ * If this is undecidable, throw an exception. */
+ ex minimal_dim(const idx & other) const;
+
protected:
- int compare_same_type(const basic & other) const;
- bool is_equal_same_type(const basic & other) const;
- unsigned calchash(void) const;
- ex subs(const lst & ls, const lst & lr) const;
+ void print_index(const print_context & c, unsigned level) const;
+ void do_print(const print_context & c, unsigned level) const;
+ void do_print_csrc(const print_csrc & 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;
- // new virtual functions which can be overridden by derived classes
+protected:
+ ex value; /**< Expression that constitutes the index (numeric or symbolic name) */
+ ex dim; /**< Dimension of space (can be symbolic or numeric) */
+};
+GINAC_DECLARE_UNARCHIVER(idx);
+
+
+/** 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 base classes
public:
- virtual bool is_co_contra_pair(const basic & other) const;
- virtual ex toggle_covariant(void) const;
+ bool is_dummy_pair_same_type(const basic & other) const;
+ void archive(archive_node& n) const;
+ void read_archive(const archive_node& n, lst& syms);
+protected:
+ bool match_same_type(const basic & other) const;
- // non-virtual functions in this class
+ // non-virtual functions in this class
public:
- bool is_symbolic(void) const;
- unsigned get_value(void) const;
- bool is_covariant(void) const;
- void setname(const string & n) {name=n;}
- string getname(void) const {return name;}
+ /** Check whether the index is covariant. */
+ bool is_covariant() const {return covariant;}
+
+ /** Check whether the index is contravariant (not covariant). */
+ bool is_contravariant() const {return !covariant;}
+
+ /** Make a new index with the same value but the opposite variance. */
+ ex toggle_variance() const;
- // member variables
protected:
- unsigned serial;
- bool symbolic;
- string name;
- unsigned value;
- static unsigned next_serial;
- bool covariant; // x_mu, default is contravariant: x^mu
+ void do_print(const print_context & c, unsigned level) const;
+ void do_print_tree(const print_tree & c, unsigned level) const;
+
+ // member variables
+protected:
+ bool covariant; /**< x.mu, default is contravariant: x~mu */
};
+GINAC_DECLARE_UNARCHIVER(varidx);
+
-// global constants
+/** This class holds a spinor index that can be dotted or undotted and that
+ * also has a variance. This is used in the Weyl-van-der-Waerden formalism
+ * where the dot indicates complex conjugation. There is an associated
+ * (asymmetric) metric tensor that can be used to raise/lower spinor
+ * indices. */
+class spinidx : public varidx
+{
+ GINAC_DECLARE_REGISTERED_CLASS(spinidx, varidx)
+
+ // other constructors
+public:
+ /** Construct index with given value, dimension, variance and dot.
+ *
+ * @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)
+ * @param dotted Make covariant dotted (default is undotted)
+ * @return newly constructed index */
+ spinidx(const ex & v, const ex & dim = 2, bool covariant = false, bool dotted = false);
+
+ // functions overriding virtual functions from base classes
+public:
+ bool is_dummy_pair_same_type(const basic & other) const;
+ // complex conjugation
+ ex conjugate() const { return toggle_dot(); }
+ void archive(archive_node& n) const;
+ void read_archive(const archive_node& n, lst& syms);
+protected:
+ bool match_same_type(const basic & other) const;
+
+ // non-virtual functions in this class
+public:
+ /** Check whether the index is dotted. */
+ bool is_dotted() const {return dotted;}
+
+ /** Check whether the index is not dotted. */
+ bool is_undotted() const {return !dotted;}
+
+ /** Make a new index with the same value and variance but the opposite
+ * dottedness. */
+ ex toggle_dot() const;
+
+ /** Make a new index with the same value but opposite variance and
+ * dottedness. */
+ ex toggle_variance_dot() const;
+
+protected:
+ 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;
+
+ // member variables
+protected:
+ bool dotted;
+};
+GINAC_DECLARE_UNARCHIVER(spinidx);
-extern const idx some_idx;
-extern const type_info & typeid_idx;
// utility functions
-inline const idx &ex_to_idx(const ex &e)
+
+/** 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)
{
- return static_cast<const idx &>(*e.bp);
+ find_free_and_dummy(v.begin(), v.end(), out_free, out_dummy);
}
-// global functions
+/** 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 size_t 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();
+}
-// typedef vector<ex> exvector;
+/** Count the number of dummy index pairs in an index vector. */
+inline size_t 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();
+}
-int canonicalize_indices(exvector & iv, bool antisymmetric=false);
-exvector idx_intersect(const exvector & iv1, const exvector & iv2);
-ex permute_free_index_to_front(const exvector & iv3, const exvector & iv2,
- bool antisymmetric, int * sig);
-unsigned subs_index_in_exvector(exvector & v, const ex & is, const ex & ir);
-ex subs_indices(const ex & e, const exvector & idxv_contra,
- const exvector & idxv_co);
-unsigned count_index(const ex & e, const ex & i);
+/** Return the minimum of two index dimensions. If this is undecidable,
+ * throw an exception. Numeric dimensions are always considered "smaller"
+ * than symbolic dimensions. */
+ex minimal_dim(const ex & dim1, const ex & dim2);
-#ifndef NO_GINAC_NAMESPACE
} // namespace GiNaC
-#endif // ndef NO_GINAC_NAMESPACE
-#endif // ndef __GINAC_IDX_H__
+#endif // ndef GINAC_IDX_H
git://www.ginac.de / ginac.git / blobdiff