This class holds an indexed expression. More...

#include <indexed.h>

Inheritance diagram for GiNaC::indexed:

Public Member Functions
	indexed (const ex &b)
	Construct indexed object with no index.
	indexed (const ex &b, const ex &i1)
	Construct indexed object with one index.
	indexed (const ex &b, const ex &i1, const ex &i2)
	Construct indexed object with two indices.
	indexed (const ex &b, const ex &i1, const ex &i2, const ex &i3)
	Construct indexed object with three indices.
	indexed (const ex &b, const ex &i1, const ex &i2, const ex &i3, const ex &i4)
	Construct indexed object with four indices.
	indexed (const ex &b, const symmetry &symm, const ex &i1, const ex &i2)
	Construct indexed object with two indices and a specified symmetry.
	indexed (const ex &b, const symmetry &symm, const ex &i1, const ex &i2, const ex &i3)
	Construct indexed object with three indices and a specified symmetry.
	indexed (const ex &b, const symmetry &symm, const ex &i1, const ex &i2, const ex &i3, const ex &i4)
	Construct indexed object with four indices and a specified symmetry.
	indexed (const ex &b, const exvector &iv)
	Construct indexed object with a specified vector of indices.
	indexed (const ex &b, const symmetry &symm, const exvector &iv)
	Construct indexed object with a specified vector of indices and symmetry.
	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)
unsigned	precedence () const
	Return relative operator precedence (for parenthezing output).
bool	info (unsigned inf) const
	Information about the object.
ex	eval (int level=0) const
	Perform automatic non-interruptive term rewriting rules.
ex	real_part () const
ex	imag_part () const
exvector	get_free_indices () const
	Return a vector containing the free indices of an expression.
void	archive (archive_node &n) const
	Save (a.k.a.
void	read_archive (const archive_node &n, lst &syms)
	Read (a.k.a.
bool	all_index_values_are (unsigned inf) const
	Check whether all index values have a certain property.
exvector	get_indices () const
	Return a vector containing the object's indices.
exvector	get_dummy_indices () const
	Return a vector containing the dummy indices of the object, if any.
exvector	get_dummy_indices (const indexed &other) const
	Return a vector containing the dummy indices in the contraction with another indexed object.
bool	has_dummy_index_for (const ex &i) const
	Check whether the object has an index that forms a dummy index pair with a given index.
ex	get_symmetry () const
	Return symmetry properties.
Protected Member Functions
ex	derivative (const symbol &s) const
	Implementation of ex::diff() for an indexed object always returns 0.
ex	thiscontainer (const exvector &v) const
ex	thiscontainer (std::auto_ptr< exvector > vp) const
unsigned	return_type () const
return_type_t	return_type_tinfo () const
ex	expand (unsigned options=0) const
	Expand expression, i.e.
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
	Default output to stream.
void	do_print_latex (const print_latex &c, unsigned level) const
void	do_print_tree (const print_tree &c, unsigned level) const
	Tree output to stream.
void	validate () const
	Check whether all indices are of class idx and validate the symmetry tree.
Protected Attributes
ex	symtree
	Index symmetry (tree of symmetry objects)
Friends
ex	simplify_indexed (const ex &e, exvector &free_indices, exvector &dummy_indices, const scalar_products &sp)
	Simplify indexed expression, return list of free indices.
ex	simplify_indexed_product (const ex &e, exvector &free_indices, exvector &dummy_indices, const scalar_products &sp)
	Simplify product of indexed expressions (commutative, noncommutative and simple squares), return list of free indices.
bool	reposition_dummy_indices (ex &e, exvector &variant_dummy_indices, exvector &moved_indices)
	Raise/lower dummy indices in a single indexed objects to canonicalize their variance.

Detailed Description

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).

Definition at line 39 of file indexed.h.

Constructor & Destructor Documentation

GiNaC::indexed::indexed ( const ex & b )

Construct indexed object with no index.

Parameters:

b	Base expression

Returns:: newly constructed indexed object

Definition at line 64 of file indexed.cpp.

References validate().

Referenced by eval(), GiNaC::clifford::get_metric(), and thiscontainer().

GiNaC::indexed::indexed	(	const ex &	b,
		const ex &	i1
	)

Construct indexed object with one index.

The index must be of class idx.

Parameters:

b	Base expression
i1	The index

Returns:: newly constructed indexed object

Definition at line 69 of file indexed.cpp.

References validate().

GiNaC::indexed::indexed	(	const ex &	b,
		const ex &	i1,
		const ex &	i2
	)

Construct indexed object with two indices.

The indices must be of class idx.

Parameters:

b	Base expression
i1	First index
i2	Second index

Returns:: newly constructed indexed object

Definition at line 74 of file indexed.cpp.

References validate().

GiNaC::indexed::indexed	(	const ex &	b,
		const ex &	i1,
		const ex &	i2,
		const ex &	i3
	)

Construct indexed object with three indices.

The indices must be of class idx.

Parameters:

b	Base expression
i1	First index
i2	Second index
i3	Third index

Returns:: newly constructed indexed object

Definition at line 79 of file indexed.cpp.

References validate().

GiNaC::indexed::indexed	(	const ex &	b,
		const ex &	i1,
		const ex &	i2,
		const ex &	i3,
		const ex &	i4
	)

Construct indexed object with four indices.

The indices must be of class idx.

Parameters:

b	Base expression
i1	First index
i2	Second index
i3	Third index
i4	Fourth index

Returns:: newly constructed indexed object

Definition at line 84 of file indexed.cpp.

References validate().

GiNaC::indexed::indexed	(	const ex &	b,
		const symmetry &	symm,
		const ex &	i1,
		const ex &	i2
	)

Construct indexed object with two indices and a specified symmetry.

The indices must be of class idx.

Parameters:

b	Base expression
symm	Symmetry of indices
i1	First index
i2	Second index

Returns:: newly constructed indexed object

Definition at line 89 of file indexed.cpp.

References validate().

GiNaC::indexed::indexed	(	const ex &	b,
		const symmetry &	symm,
		const ex &	i1,
		const ex &	i2,
		const ex &	i3
	)

Construct indexed object with three indices and a specified symmetry.

The indices must be of class idx.

Parameters:

b	Base expression
symm	Symmetry of indices
i1	First index
i2	Second index
i3	Third index

Returns:: newly constructed indexed object

Definition at line 94 of file indexed.cpp.

References validate().

GiNaC::indexed::indexed	(	const ex &	b,
		const symmetry &	symm,
		const ex &	i1,
		const ex &	i2,
		const ex &	i3,
		const ex &	i4
	)

Construct indexed object with four indices and a specified symmetry.

The indices must be of class idx.

Parameters:

b	Base expression
symm	Symmetry of indices
i1	First index
i2	Second index
i3	Third index
i4	Fourth index

Returns:: newly constructed indexed object

Definition at line 99 of file indexed.cpp.

References validate().

GiNaC::indexed::indexed	(	const ex &	b,
		const exvector &	iv
	)

Construct indexed object with a specified vector of indices.

The indices must be of class idx.

Parameters:

b	Base expression
iv	Vector of indices

Returns:: newly constructed indexed object

Definition at line 104 of file indexed.cpp.

References GiNaC::container_storage< C >::seq, and validate().

GiNaC::indexed::indexed	(	const ex &	b,
		const symmetry &	symm,
		const exvector &	iv
	)

Construct indexed object with a specified vector of indices and symmetry.

The indices must be of class idx.

Parameters:

b	Base expression
symm	Symmetry of indices
iv	Vector of indices

Returns:: newly constructed indexed object

Definition at line 110 of file indexed.cpp.

References GiNaC::container_storage< C >::seq, and validate().

GiNaC::indexed::indexed	(	const symmetry &	symm,
		const exprseq &	es
	)

Definition at line 116 of file indexed.cpp.

GiNaC::indexed::indexed	(	const symmetry &	symm,
		const exvector &	v,
		bool	discardable = `false`
	)

Definition at line 120 of file indexed.cpp.

GiNaC::indexed::indexed	(	const symmetry &	symm,
		std::auto_ptr< exvector >	vp
	)

Definition at line 124 of file indexed.cpp.

Member Function Documentation

unsigned GiNaC::indexed::precedence ( ) const [inline, virtual]

Return relative operator precedence (for parenthezing output).

Reimplemented from GiNaC::container< C >.

Reimplemented in GiNaC::clifford.

Definition at line 146 of file indexed.h.

Referenced by print_indexed().

bool GiNaC::indexed::info ( unsigned inf ) const [virtual]

Information about the object.

See also:: class info_flags

Reimplemented from GiNaC::container< C >.

Definition at line 239 of file indexed.cpp.

References GiNaC::info_flags::has_indices, GiNaC::info_flags::indexed, and GiNaC::container_storage< C >::seq.

Referenced by imag_part(), and real_part().

ex GiNaC::indexed::eval ( int level = 0 ) const [virtual]

Perform automatic non-interruptive term rewriting rules.

Reimplemented from GiNaC::container< C >.

Definition at line 268 of file indexed.cpp.

References GiNaC::_ex0, GiNaC::canonicalize(), GiNaC::basic::eval_indexed(), GiNaC::container< C >::evalchildren(), GiNaC::basic::ex, GINAC_ASSERT, indexed(), GiNaC::ex::is_zero(), GiNaC::ex::nops(), GiNaC::ex::op(), GiNaC::container_storage< C >::seq, symtree, and thiscontainer().

ex GiNaC::indexed::real_part ( ) const [virtual]

Reimplemented from GiNaC::container< C >.

Definition at line 308 of file indexed.cpp.

References info(), GiNaC::container< C >::op(), and GiNaC::info_flags::real.

ex GiNaC::indexed::imag_part ( ) const [virtual]

Reimplemented from GiNaC::container< C >.

Definition at line 315 of file indexed.cpp.

References info(), GiNaC::container< C >::op(), and GiNaC::info_flags::real.

exvector GiNaC::indexed::get_free_indices ( ) const [virtual]

Return a vector containing the free indices of an expression.

Reimplemented from GiNaC::basic.

Definition at line 466 of file indexed.cpp.

References GiNaC::find_free_and_dummy(), and GiNaC::container_storage< C >::seq.

Referenced by get_dummy_indices().

void GiNaC::indexed::archive ( archive_node & n ) const [virtual]

Save (a.k.a.

serialize) indexed object into archive.

Reimplemented from GiNaC::container< C >.

Reimplemented in GiNaC::clifford, and GiNaC::color.

Definition at line 155 of file indexed.cpp.

References GiNaC::archive_node::add_ex(), and symtree.

void GiNaC::indexed::read_archive	(	const archive_node &	n,
		lst &	syms
	)		`[virtual]`

Read (a.k.a.

deserialize) indexed object from archive.

Reimplemented from GiNaC::container< C >.

Reimplemented in GiNaC::clifford, and GiNaC::color.

Definition at line 132 of file indexed.cpp.

References GiNaC::archive_node::find_ex(), GiNaC::archive_node::find_unsigned(), GiNaC::not_symmetric(), GiNaC::container_storage< C >::seq, GiNaC::sy_anti(), GiNaC::sy_symm(), GiNaC::symm(), symtree, and GiNaC::symmetry::validate().

ex GiNaC::indexed::derivative ( const symbol & s ) const [protected, virtual]

Implementation of ex::diff() for an indexed object always returns 0.

See also:: ex::diff

Reimplemented from GiNaC::basic.

Definition at line 397 of file indexed.cpp.

References GiNaC::_ex0.

ex GiNaC::indexed::thiscontainer ( const exvector & v ) const [protected]

Reimplemented in GiNaC::clifford, and GiNaC::color.

Definition at line 322 of file indexed.cpp.

References indexed(), and symtree.

Referenced by eval(), and expand().

ex GiNaC::indexed::thiscontainer ( std::auto_ptr< exvector > vp ) const [protected]

Reimplemented in GiNaC::clifford, and GiNaC::color.

Definition at line 327 of file indexed.cpp.

References indexed(), and symtree.

unsigned GiNaC::indexed::return_type ( ) const [protected, virtual]

Reimplemented from GiNaC::basic.

Reimplemented in GiNaC::clifford, and GiNaC::color.

Definition at line 332 of file indexed.cpp.

References GiNaC::return_types::commutative, GiNaC::container< C >::op(), and GiNaC::ex::return_type().

return_type_t GiNaC::indexed::return_type_tinfo ( ) const [inline, protected, virtual]

Reimplemented from GiNaC::basic.

Reimplemented in GiNaC::clifford, and GiNaC::color.

Definition at line 162 of file indexed.h.

References GiNaC::container< C >::op(), and GiNaC::ex::return_type_tinfo().

ex GiNaC::indexed::expand ( unsigned options = 0 ) const [protected, virtual]

Expand expression, i.e.

multiply it out and return the result as a new expression.

Reimplemented from GiNaC::basic.

Definition at line 340 of file indexed.cpp.

References GiNaC::_ex0, GiNaC::are_ex_trivially_equal(), GiNaC::ex::expand(), GiNaC::expand(), GiNaC::expand_options::expand_indexed, GINAC_ASSERT, GiNaC::ex::nops(), GiNaC::ex::op(), GiNaC::container_storage< C >::seq, and thiscontainer().

bool GiNaC::indexed::all_index_values_are ( unsigned inf ) const

Check whether all index values have a certain property.

See also:: class info_flags

Definition at line 252 of file indexed.cpp.

References GiNaC::container_storage< C >::seq.

exvector GiNaC::indexed::get_indices ( ) const

Return a vector containing the object's indices.

Definition at line 432 of file indexed.cpp.

References GINAC_ASSERT, and GiNaC::container_storage< C >::seq.

exvector GiNaC::indexed::get_dummy_indices ( ) const

Return a vector containing the dummy indices of the object, if any.

Definition at line 438 of file indexed.cpp.

References GiNaC::find_free_and_dummy(), and GiNaC::container_storage< C >::seq.

exvector GiNaC::indexed::get_dummy_indices ( const indexed & other ) 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)

Definition at line 445 of file indexed.cpp.

References GiNaC::find_dummy_indices(), and get_free_indices().

bool GiNaC::indexed::has_dummy_index_for ( const ex & i ) const

Check whether the object has an index that forms a dummy index pair with a given index.

Definition at line 455 of file indexed.cpp.

References GiNaC::is_dummy_pair(), and GiNaC::container_storage< C >::seq.

ex GiNaC::indexed::get_symmetry ( ) const [inline]

Return symmetry properties.

Definition at line 190 of file indexed.h.

References symtree.

Referenced by GiNaC::clifford::get_metric().

void GiNaC::indexed::printindices	(	const print_context &	c,
		unsigned	level
	)		const `[protected]`

Definition at line 165 of file indexed.cpp.

References GiNaC::print_context::s, and GiNaC::container_storage< C >::seq.

Referenced by GiNaC::clifford::do_print_dflt(), do_print_tree(), and print_indexed().

void GiNaC::indexed::print_indexed	(	const print_context &	c,
		const char *	openbrace,
		const char *	closebrace,
		unsigned	level
	)		const `[protected]`

Definition at line 207 of file indexed.cpp.

References precedence(), printindices(), GiNaC::print_context::s, and GiNaC::container_storage< C >::seq.

Referenced by do_print(), and do_print_latex().

void GiNaC::indexed::do_print	(	const print_context &	c,
		unsigned	level
	)		const `[protected]`

Default output to stream.

Reimplemented from GiNaC::container< C >.

Definition at line 219 of file indexed.cpp.

References print_indexed().

void GiNaC::indexed::do_print_latex	(	const print_latex &	c,
		unsigned	level
	)		const `[protected]`

Reimplemented in GiNaC::clifford.

Definition at line 224 of file indexed.cpp.

References print_indexed().

void GiNaC::indexed::do_print_tree	(	const print_tree &	c,
		unsigned	level
	)		const `[protected]`

Tree output to stream.

Reimplemented from GiNaC::container< C >.

Definition at line 229 of file indexed.cpp.

References GiNaC::print_tree::delta_indent, GiNaC::basic::flags, GiNaC::basic::hashvalue, printindices(), GiNaC::print_context::s, GiNaC::container_storage< C >::seq, and symtree.

void GiNaC::indexed::validate ( ) const [protected]

Check whether all indices are of class idx and validate the symmetry tree.

This function is used internally to make sure that all constructed indexed objects really carry indices and not some other classes.

Definition at line 377 of file indexed.cpp.

References GINAC_ASSERT, GiNaC::ex::is_zero(), GiNaC::container_storage< C >::seq, symtree, and GiNaC::symmetry::validate().

Referenced by indexed().

Friends And Related Function Documentation

ex simplify_indexed	(	const ex &	e,
		exvector &	free_indices,
		exvector &	dummy_indices,
		const scalar_products &	sp
	)		`[friend]`

Simplify indexed expression, return list of free indices.

Referenced by GiNaC::clifford::get_metric(), and GiNaC::clifford::same_metric().

ex simplify_indexed_product	(	const ex &	e,
		exvector &	free_indices,
		exvector &	dummy_indices,
		const scalar_products &	sp
	)		`[friend]`

Simplify product of indexed expressions (commutative, noncommutative and simple squares), return list of free indices.

Definition at line 788 of file indexed.cpp.

bool reposition_dummy_indices	(	ex &	e,
		exvector &	variant_dummy_indices,
		exvector &	moved_indices
	)		`[friend]`

Raise/lower dummy indices in a single indexed objects to canonicalize their variance.

Parameters:

e	Object to work on
variant_dummy_indices	The set of indices that might need repositioning (will be changed by this function)
moved_indices	The set of indices that have been repositioned (will be changed by this function)

Returns:: true if 'e' was changed

Definition at line 625 of file indexed.cpp.

Member Data Documentation

ex GiNaC::indexed::symtree [protected]

Index symmetry (tree of symmetry objects)

Definition at line 202 of file indexed.h.

Referenced by archive(), do_print_tree(), eval(), get_symmetry(), read_archive(), thiscontainer(), and validate().

The documentation for this class was generated from the following files:

Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation