csl::Space Class Reference

Vector space that has a name, a dimension, a delta tensor and possibly a non-trivial metric. If a metric is given, the indices in this space are signed, i.e. their up- or down- position matter in expressions. More...

#include <space.h>

Public Member Functions
	Space (const std::string &t_name, int t_dim, std::vector< std::string > const &indexNames={"i", "j", "k", "l"})
	Initializes the name and the dimension of the space, no metric so only the kronecker delta is relevant, and indices are not signed. More...
	Space (const std::string &t_name, int t_dim, const std::string &name_metric, const Expr &t_metric, std::vector< std::string > const &indexNames={"i", "j", "k", "l"})
	Initializes name, dimension of the space. Here the metrix is given by the user (also its explicit tensor, like diag (-1,1,1,1) for the Minkowski Space). This constructor constructs then a Space with signed indices and a non-trivial metric. More...
virtual	~Space ()
	Destructor.
virtual void	printCode (std::ostream &out, int indentSize) const
virtual void	printDefinition (std::ostream &out, int indentSize, bool header=false) const
virtual std::string	getName () const
std::string	getNextIndexName () const
std::string	getIndexName (char spec) const
std::string_view	getIndexNameView (char spec) const
char	getSpecFromIndexName (std::string const &t_name) const
int	getDim () const
bool	getSignedIndex () const
virtual bool	hasSpecialTraceProperty (const csl::vector_expr &tensors) const
csl::vector_expr	getSignature () const
Tensor	getMetric () const
Tensor	getInverseMetric () const
Tensor	getDelta () const
Tensor	getEpsilon () const
Expr	applyMetricOnTensor (Expr const &tensor, size_t axis, bool covariant) const
Index	generateIndex (const std::string &name) const
	Generates and returns an index in the right Space (itself) of name name. More...
Index	generateIndex () const
	Generates and returns an index in the right Space (itself) of name defined by the program. For now the index is name i_{number}, but in the future one should be able to defined a set of names for a given space, for example {"mu", "nu", "rhi", "sigma"}... More...
std::vector< Index >	generateIndices (size_t N) const
std::vector< Index >	generateIndices (size_t N, const std::string &name) const
Index	generateSimilar (const Index &model) const
void	resetIndexNumber () const
void	refreshIndexName (Index &index) const
Expr	generateVector (const std::string &t_name) const
	Generates and returns a Vector in the right Space (itself) of name name, filled with Variable objects as components (X_0, X_1, ...) for a name "X". More...
std::string	generateVectorName (const std::string &t_name) const
void	addIndexNames (const std::string &name) const
void	addVectorNames (const std::string &name) const
void	addIndexNames (const std::vector< std::string > &names) const
void	addVectorNames (const std::vector< std::string > &names) const
virtual Expr	calculateTrace (csl::vector_expr tensors) const

Data Fields
bool	keepCycles = false

Static Public Attributes
static bool	applyMetric = true

Protected Attributes
std::string	name
	Name of the vector space.
int	dim
	Dimension of the space.
bool	signedIndex
	Property of indices: if true, it means that the metric is non trivial (given by the user at initialization) and that up- or down- position of indices matter in expressions.
std::map< char, std::string >	nameIndices
std::map< std::string, char >	specIndices
std::vector< std::pair< std::string, Index::ID_type > >	availableIndices
std::vector< std::pair< std::string, unsigned short > >	availableVectors
std::vector< std::string >::const_iterator	defaultName
std::vector< std::string >	defaultIndexNames
Tensor	delta
	Kronecker delta, public attribute for readability in usage. Element i,j of the tensor is then accessible by space.delta({i,j}) with i,j indices in this space. More...
Tensor	metric
	Public attribute for readability in usage. Element i,j of the tensor is then accessible by space.metric({i,j}) with i,j indices in this space. It corresponds to the metric of the space if it is non trivial, or is redirected to the kronecker delta else. More...
Tensor	inverseMetric
Tensor	epsilon

Detailed Description

Vector space that has a name, a dimension, a delta tensor and possibly a non-trivial metric. If a metric is given, the indices in this space are signed, i.e. their up- or down- position matter in expressions.

Constructor & Destructor Documentation

Space() [1/2]

csl::Space::Space	(	const std::string &	t_name,
		int	t_dim,
		std::vector< std::string > const &	indexNames = {"i", "j", "k", "l"}
	)

Initializes the name and the dimension of the space, no metric so only the kronecker delta is relevant, and indices are not signed.

Parameters

t_name	Name of the Space.
t_dim	Dimension of the Space.

Space() [2/2]

csl::Space::Space	(	const std::string &	t_name,
		int	t_dim,
		const std::string &	name_metric,
		const Expr &	t_metric,
		std::vector< std::string > const &	indexNames = {"i", "j", "k", "l"}
	)

Initializes name, dimension of the space. Here the metrix is given by the user (also its explicit tensor, like diag (-1,1,1,1) for the Minkowski Space). This constructor constructs then a Space with signed indices and a non-trivial metric.

Parameters

t_name	Name of the Space.
t_dim	Dimension of the Space.
name_metric	Name of the metric. Can be set to CSL_UNDEF. In this case the tensor metric will not be defined (but the indexed object g_ab will).
t_metric	Explicit TensorElement for the metric (should be a 2D square matrix, symmetric).

Member Function Documentation

generateIndex() [1/2]

Index csl::Space::generateIndex ( const std::string &  name ) const

inline

Generates and returns an index in the right Space (itself) of name name.

Parameters

name	Name of the Index.

Returns

An Index of name name living in the Space *this.

generateIndex() [2/2]

Index csl::Space::generateIndex ( ) const

inline

Generates and returns an index in the right Space (itself) of name defined by the program. For now the index is name i_{number}, but in the future one should be able to defined a set of names for a given space, for example {"mu", "nu", "rhi", "sigma"}...

Returns

An Index of name i_{number} living in the Space *this.

generateVector()

Expr csl::Space::generateVector

(

const std::string &

t_name

)

const

Generates and returns a Vector in the right Space (itself) of name name, filled with Variable objects as components (X_0, X_1, ...) for a name "X".

Parameters

name	Name of the Vector.

Returns

A Vector of Variables living in the Space *this.

getDim()

int csl::Space::getDim ( ) const

inline

Returns

The dimension of the Space.

getName()

std::string csl::Space::getName ( ) const

virtual

Returns

The name of the Space.

getSignedIndex()

bool csl::Space::getSignedIndex ( ) const

inline

Returns

True if the indices in this Space are signed.

False else.

Field Documentation

delta

Tensor csl::Space::delta

mutableprotected

Kronecker delta, public attribute for readability in usage. Element i,j of the tensor is then accessible by space.delta({i,j}) with i,j indices in this space.

This attribute is mutable because access functions for parents (operator() to get TensorElement) is not const, and all many Space objects are declared const. So we declare this attribute mutable so that the compiler allows it to be changed, event for Space objets declared const.

metric

Tensor csl::Space::metric

mutableprotected

Public attribute for readability in usage. Element i,j of the tensor is then accessible by space.metric({i,j}) with i,j indices in this space. It corresponds to the metric of the space if it is non trivial, or is redirected to the kronecker delta else.

This attribute is mutable because access functions for parents (operator() to get TensorElement) is not const, and all many Space objects are declared const. So we declare this attribute mutable so that the compiler allows it to be changed, event for Space objets declared const.

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

• include/space.h
• src/space.cpp