Specialization of Abstract for Indicial tensor. Building block carrying indices, and respecting Einstein's summation convention. More...

#include <indicial.h>

Inheritance diagram for csl::TensorElement:

[legend]

Public Member Functions
	TensorElement (const Index &t_index, const Parent &t_parent)
	Constructor called by an TensorParent, for a tensor with one index. More...

	TensorElement (const std::vector< Index > &indices, const Parent &t_parent)
	Constructor called by an TensorParent, for a tensor with several indices. More...

	TensorElement (const IndexStructure &indices, const Parent &t_parent)
	Constructor called by an TensorParent, for a tensor with several indices. More...

	TensorElement (const Abstract *&expression)
	Copy constructor from an Abstract*. Works only if the pointer points to another TensorElement. More...

	TensorElement (const Expr &expression)
	Copy constructor from an Expr. Works only if the pointer points to another TensorElement. More...

csl::PrimaryType	getPrimaryType () const override
	Gives the primary type of Abstract. More...

size_t	memoryOverhead () const override

bool	isIndexed () const override

int	getNIndices () const override

void	resetIndexStructure () override

IndexStructure	getIndexStructure () const override

const IndexStructure &	getIndexStructureView () const override

IndexStructure &	getIndexStructureView () override

bool	compareWithDummy (Expr_info expr, std::map< Index, Index > &constraints, bool keepAllCosntraints=false) const override
	Comparison disregarding name of dummy indices, i.e. the two expressions * are equals even if dummy indices have not the same names in this and expr. More...

csl::Type	getType () const override
	Gives the type of Abstract. More...

std::optional< Expr >	getComplexConjugate () const override
	Calculates and returns the complex conjugate of the expression. More...

std::optional< Expr >	getHermitianConjugate (const Space *space) const override

std::optional< Expr >	getHermitianConjugate (const std::vector< const Space *> &spaces) const override

std::optional< Expr >	getTransposed (const Space *space, bool applyProp=true) const override

std::optional< Expr >	getTransposed (const std::vector< const Space *> &t_spaces, bool applyProp=true) const override

Index	getIndex (int i) const override

bool	askTerm (Expr_info expr, bool exact=false) const override
	Determines if the term expr can be factorized out from the TensorElement, i.e. if expr is equal to the tensor to (may be) a renaming of index. More...

bool	dependsOn (Expr_info expr) const override
	Check recursively if the expression depends on expr. More...

bool	dependsOn (Parent_info t_parent) const override

bool	dependsExplicitlyOn (Expr_info expr) const override
	Check recursively if expr is present in the expression. More...

const std::vector< Equation * > &	getProperties () const override

void	addProperty (Equation *property) override
	Adds a property to the object. More...

void	removeProperty (Equation *property) override
	Removes a property to the object. More...

bool	checkIndexStructure (const std::vector< Index > &t_index) const override
	Checks the compatibility of the index structure of an Indicial expression with another. In a sum, two terms must have exaclty the same index structure. More...

void	selfCheckIndexStructure ()

std::optional< Expr >	replaceIndex (const Index &indexToReplace, const Index &newIndex, bool refresh=true) const override
	For indicial expressions, this function searches indexToContract and replaces it with newIndex. More...

std::optional< Expr >	replaceIndices (std::vector< Index > const &indexToReplace, std::vector< Index > const &newIndex, bool refresh=true, bool flipped=false) const override

void	replaceIndexInPlace (Index const &oldIndex, Index const &newIndex) override

csl::vector_expr	breakSpace (const Space brokenSpace, const std::vector< const Space > &newSpaces, const std::vector< std::string > &indexNames) const override

void	setIndexStructure (const IndexStructure &t_index) override
	Replaces the index structure of the object, that must be an Indicial expression. More...

bool	hasContractionProperty (Expr_info B) const override
	Tells (for an Indicial type) if there is a special contraction property with B. More...

std::vector< ContractionChain >	getContractionProperties () const override

Expr	contraction (Expr_info B) const override
	Applies a special contraction of indices. Before calling this function we must check that there is indeed a contraction by calling the function hasContractionProperty(). More...

bool	hasChainContractionProperty () const override

Expr	applyPermutation (const Permutation &permutations) const
	Applies a permutation of the indices on a copy of the TensorElement, and returns it. More...

csl::vector_expr	getPermutations (bool optimize=true) const override
	Returns a std::vector of all possible permutations of an Indicial expression. The possible permutations are determined from the posible symmetries and anti-symmetries of the object. More...

csl::vector_expr	getAlternateForms () const override
	Calculates and returns all possible alternate forms of the expression in terms of simplifications. For example 1-sin^2(x) is one of the alternate forms of cos^2(x). More...

Expr	getCanonicalPermutation () const override

void	print (int mode=0, std::ostream &out=std::cout, bool lib=false) const override
	Displays the abstract in standard output. More...

void	printCode (int mode=0, std::ostream &out=std::cout) const override

std::string	printLaTeX (int mode=0) const override
	Creates a LaTeX output for the Abstract. More...

std::vector< Parent >	getSubSymbols () const override

std::optional< Expr >	derive (Expr_info expr) const override
	Calculates the derivative of the Abstract wrt another. More...

std::optional< Expr >	evaluate (csl::eval::mode user_mode=csl::eval::base) const override
	Evaluates the Abstract. More...

unique_Expr	copy_unique () const override

Expr	refresh () const override

Expr	deepRefresh () const override

bool	operator== (Expr_info expr) const override
	Compares the Abstract with another. More...

bool	operator< (const Abstract *expr) const override

Public Member Functions inherited from csl::AbstractElement
	AbstractElement ()

	AbstractElement (const std::shared_ptr< AbstractParent > &t_parent)
	Intializes the parent and no name. More...

	~AbstractElement ()
	Destructor.

Parent	getParent () const override

Parent_info	getParent_info () const override

std::string const &	getName () const override
	Returns the Abstract's name. More...

std::string const &	getLatexName () const override

bool	getCommutable () const override
	Allows to know if the object commutes with all the others. More...

csl::ComplexProperty	getComplexProperty () const override

void	setParent (const Parent &t_parent) override
	Changes the Parent of the Element, as the name and the commutability property from those of t_parent. More...

void	setName (const std::string &t_name) override
	Change the name of the abstract. More...

void	setCommutable (bool t_commutable) override
	Allows the abstract to commute or not. More...

void	setComplexProperty (csl::ComplexProperty t_prop) override

int	isPolynomial (Expr_info variable) const override
	Determines if the expression is a mononomial term in expr, i.e. a term of the form C*expr^n with C independent of expr, n integer. More...

std::optional< Expr >	getPolynomialTerm (Expr_info variable, int order) const override
	Calculates and returns the polynomial term corresponding to this with the variable t_variable* at order order. In particular, this function assumes that the checks have already been made with the function isPolynomial(). More...

Public Member Functions inherited from csl::Complexified
bool	isReal () const override

bool	isPurelyImaginary () const override

bool	isComplexConjugate () const override

std::optional< Expr >	getRealPart () const override
	Evaluates the real part of the Abstract and returns it. More...

Expr	getImaginaryPart () const override
	Evaluates the imaginary part of the Abstract and returns it. More...

void	setConjugated (bool t_conjugated) override

void	printProp (std::ostream &fout=std::cout) const override

Public Member Functions inherited from csl::AbstractBuildingBlock
bool	isBuildingBlock () const override
	Tells if the expression is a Building Block or not. More...

virtual bool	commutesWith (Expr_info expr, int sign=-1) const override
	Tells if the object commutes with expr. More...

std::optional< Expr >	expand (bool full=false, bool inplace=false) const override
	Develops the Abstract. More...

std::optional< Expr >	factor (bool full=false) const override
	Factors the Abstract. More...

std::optional< Expr >	factor (Expr_info expr, bool full=false) const override
	Factors the Abstract wrt a particular Abstract. More...

std::optional< Expr >	getTerm () const override
	This function returns the same expression as this but amputated of its numerical factor. Example: (4cos(x) -> cos(x)). More...

std::optional< Expr >	getComplexModulus () const override
	Evaluates the modulus in the complex plane of the Abstract and returns it. More...

std::optional< Expr >	findSubExpression (Expr_info subExpression, const Expr &newExpression) const override
	Searches a sub-expression and replaces it. More...

Public Member Functions inherited from csl::Abstract
	Abstract ()
	Default Constructor. More...

virtual	~Abstract ()
	Destructor.

Expr	self ()

void	printExplicit (int mode=0) const
	Displays explicitely the expression, with types of each component. This function is only used for debug. More...

virtual LibDependency	getLibDependency () const

virtual bool	getElementary () const

virtual bool	getAllDependencies () const

virtual int	getDim () const
	Gives the dimension of the object. More...

virtual int	getOrderOf (Expr_info expr) const

virtual bool	isArbitrary () const

virtual bool	isHermitianConjugate () const

virtual bool	isInteger () const
	Tells if the expression is an integer. Either an Integer object directly, or a Float that has an integer value. More...

virtual bool	getValued () const
	Tells if the expression is valued, i.e. is a function of numbers and valued literals (a Variable or Constant is not valued by default). More...

virtual long double	getValue () const
	Returns the value of the expression, if it has one explicitely. In particular, it will work only on Numbers and valued Literals, not on functions. More...

virtual long double	getDeltaPlus () const

virtual long double	getDeltaMinus () const

virtual long long int	getNum () const

virtual long long int	getDenom () const

virtual int	getNArgs (int axis=0) const
	Returns the number of arguments of the expression. If the expression is a building block (AbstractBuildingBlock), this function returns 0. More...

virtual size_t	size () const

virtual bool	empty () const

virtual csl::vector_expr::iterator	begin ()

virtual csl::vector_expr::iterator	end ()

virtual csl::vector_expr::const_iterator	begin () const

virtual csl::vector_expr::const_iterator	end () const

virtual Expr const &	getArgument (int iArg=0) const

virtual Expr &	getArgument (int iArg=0)

virtual Expr const &	getArgument (const std::vector< int > &indices) const
	Allows to get specific arguments of expressions in multiple dimensions, by giving the indices in each dimension. More...

virtual Expr &	getArgument (const std::vector< int > &indices)

virtual const csl::vector_expr &	getVectorArgument () const
	Allows to get the entire std::vector of arguments of the expression. More...

virtual Expr	getVariable () const
	Accessor to the variable that defines certain types of expressions. More...

virtual int	getOrder () const
	Accessor to the order (integer) that defines certain types of expressions. More...

virtual int	getSign () const

virtual bool	isAnOperator () const
	Tells if the expression is an operator (like a derivetive operator). More...

virtual bool	isEmpty () const
	Tells for a Derivative or an Integral if the argument is empty i.e. if the object must apply on the next argument encountered on the right. More...

virtual bool	operatorAppliesOn (Expr_info expr) const

virtual Expr	getOperand () const
	Returns the operand of an Operator. More...

virtual std::vector< int >	getShape () const
	Accessor to the shape of the tensor in the form of a std::vector of integers. More...

virtual Expr	getInfBoundary () const

virtual Expr	getSupBoundary () const

virtual void	setSupBoundary (Expr const &t_inf)

virtual void	setInfBoundary (Expr const &t_inf)

IndexStructure	getIndexStructure (csl::Space const *space) const

virtual IndexStructure	getFreeIndexStructure () const

virtual Tensor	getPoint () const

virtual int	getNContractedPairs () const
	Returns the number of contracted pairs of indices in an Indicial expression. More...

virtual std::set< std::pair< int, int > >	getContractedPair () const

Expr	copy () const

virtual Expr	deepCopy () const

virtual void	setValue (long double t_value)
	Sets the value if there is one (for Numerical and Literal valued).

virtual void	setValue (Expr const &t_value)

virtual void	setElementary (bool t_elementary)

virtual void	setAllDependencies (bool t_allDependencies)

virtual void	addDependency (Expr const &expr)

virtual void	removeDependency (Expr const &expr)

virtual void	setArgument (const Expr &expr, int iArg=0)
	Sets the argument at position iArg (default=0). More...

virtual void	setArgument (const Expr &expr, const std::vector< int > &indices)
	Sets the argument at position {i,j,...} for multi-dimensions expressions. More...

virtual void	setEmpty (bool t_empty)

virtual void	setOperand (const Expr &operand)
	Sets the operand of an operator. More...

virtual void	setOperandPrivate (const Expr &operand, bool leaveEmpty)
	Sets the operand of an operator. More...

virtual void	setVectorArgument (const csl::vector_expr &t_argument)
	Replaced the entire std::vector of argument. More...

virtual void	setVariable (Expr const &t_variable)

virtual void	insert (const Expr &expr, bool side=1)
	Inserts an expression in a sum or a product. More...

std::optional< Expr >	contractIndex (const Index &index) const

csl::vector_expr	breakSpace (const Space brokenSpace, const std::vector< const Space > &newSpace) const

virtual void	setPoint (const Tensor &t_point)

virtual void	setFullySymmetric ()
	Sets an Indicial object fully symmetric. Allows to set quickly a frequent property of tensors. This function then erases all properties of symmetry / antisymmetry and sets fullySymmetric to True.

virtual void	setFullyAntiSymmetric ()
	Sets an Indicial object fully anti-symmetric. Allows to set quickly a frequent property of tensors. This function then erases all properties * of symmetry / antisymmetry and sets fullyAntiSymmetric to True.

virtual void	addSymmetry (int i1, int i2)
	Add a symmetry between the i1^{th} and the i2^{th} indices. If those indices are anti-symmetric, an error is thrown. More...

virtual void	addAntiSymmetry (int i1, int i2)
	Add an anti-symmetry between the i1^{th} and the i2^{th} indices. If those indices are symmetric, an error is thrown. More...

virtual int	permut (int i1, int i2)
	Tries to permut indices at place i1 and i2. If those two indices have a symmetry property, indices are swaped and the symmetry is returned. Else the fnuction does nothing and returns 0. More...

virtual Expr	getNumericalFactor () const
	Returns the numerical factor of the expression, i.e. returns C if the expression if of the form *Cx** (x having a numerical factor equal to 1), and return 1 else. More...

virtual int	getNFactor () const

virtual csl::vector_expr	getFactors () const
	Allows to get a std::vector of all terms than could factor the expression. More...

virtual void	getExponents (std::vector< Expr > const &factors, std::vector< Expr > &exponents) const
	Fills in a vector the exponents corresponding to some factors for the expression. More...

virtual bool	checkIndexStructure (const std::initializer_list< Index > &index) const
	Checks the compatibility of the index structure of an Indicial expression with another. In a sum, two terms must have exaclty the same index structure. More...

bool	compareWithDummy (Expr_info expr, bool keepAllCosntraints=false) const

virtual int	getParity (Expr_info t_variable) const
	Returns the parity property of the expression with respect to t_variable. More...

virtual bool	dependsExplicitlyOn (Parent_info parent) const

virtual bool	matchShape (Expr_info expr, bool exact=false) const
	In the case of a vectorial-type expression, this function checks if the shape of expr matches itself. More...

virtual Expr	contraction (const csl::vector_expr &chain) const

virtual long double	evaluateScalar () const
	Evaluates the value of the Abstract. More...

virtual std::optional< Expr >	collect (std::vector< Expr > const &factors, bool full=false) const
	Collects terms in sum according to some factors given by the user. More...

virtual Expr	suppressTerm (Expr_info expr) const
	Remove a factor from an expr, that must have been determined before. More...

virtual std::optional< Expr >	suppressExponent (Expr const &factor, Expr const &exponent) const
	Returns the expression where the factor factor^exponent has been suppressed. More...

virtual std::optional< Expr >	expand_if (std::function< bool(Expr const &)> const &f, bool full=false, bool inPlace=false) const
	Develops the Abstract. More...

virtual std::optional< Expr >	getComplexArgument () const
	Evaluates the argument in the complex plane of the Abstract and returns it. More...

virtual Expr	applyOperator (const Expr &operand, bool leaveEmpty=false) const
	Apply the operator on an operand, iif the expression is an operator. More...

virtual Expr	addition_own (const Expr &expr) const
	Contains implementation of special addition for Numerical- and Vectorial-types. More...

virtual Expr	multiplication_own (const Expr &expr, bool side=1) const
	Contains implementation of special multiplication for Numerical- and Vectorial-types. More...

virtual Expr	division_own (const Expr &expr) const
	Contains implementation of special division for Numerical- and Polynomial-types. For polynomial, the euclidean division of two polynomials is implemented. More...

virtual Expr	exponentiation_own (const Expr &expr) const
	Contains implementation of special exponentiation for Numerical- and Vectorial-types. More...

virtual Expr	getRegularExpression () const
	Returns a regular expression from the polynomial, that is a sum where the different powers of the variable appear explicitely. More...

virtual Expr	tensordot (const Expr &expr) const
	Returns the tensordot of two Vectorial expressions. More...

virtual Expr	dot (const Expr &expr) const
	Returns the dot product of two Vectorial expressions. More...

virtual Expr	getSum () const
	Calculates and returns the sum of all elements in the Vectorial object. More...

virtual Expr	getProduct () const
	Calculates and returns the product of all elements in the Vectorial object. More...

virtual Expr	getVectorialModulus () const
	Returns the Vectorial modulus of the Vectorial object, that is defined here as the squared root of the sum of element squared. Example: {A_{11}^2+A_{12}^2+}. More...

virtual Expr	getSubVectorial (int iExcept) const
	Allows to pick a part of a Vectorial expression, excluding the iExcept^{th} element. More...

virtual Expr	getSubVectorial (int iExcept, int jExcept) const
	Allows to pick a part of a Vectorial expression, excluding the [iExcept^{th},jExcept^{th}] element (useful for matrices). More...

virtual Expr	getSubVectorial (const std::vector< int > &exceptions) const
	Allows to pick a part of a Vectorial expression, excluding the iExcept^{th} element. More...

virtual Expr	getSubVectorial (const std::vector< std::vector< int >> &keepIndices) const

virtual Expr	getSubVectorial (std::vector< std::vector< int >>::const_iterator begin, std::vector< std::vector< int >>::const_iterator end) const

virtual Expr	determinant () const
	Returns the determinant of the object if it corresponds to a square matrix (or a scalar), 0 else. More...

virtual Expr	trace () const

virtual Expr	trace (int axis1, int axis2) const
	Calculates the trace over the axis axis1 and axis2 of a tensor. axis1 and axis2 can be the same, in which case the trace just corresponds to the sum over this particular axis. More...

virtual Expr	transpose () const
	Calculates and returns the transpose of a 2D matrix. More...

virtual Expr	hermitian () const

virtual Expr	symmetrise () const
	Calculates and returns the symmetrization of a 2D matrix. More...

virtual Expr	antisymmetrise () const
	Calculates and returns the anti-symmetrization of a 2D matrix. More...

virtual Expr	inverseMatrix () const
	Calculates and returns the inverse of a 2D square matrix. The applied method is: A^{-1} = 1/det(A)*Com(A)^T. More...

virtual Expr	applyDiracDelta (const Expr &, const Expr &) const

virtual void	operator= (double t_value)
	Equivalent to the setValue() function. More...

virtual bool	operator== (int t_value) const

virtual bool	operator== (double t_value) const

virtual bool	operator!= (int t_value) const

virtual bool	operator!= (double t_value) const

int	testDummy (Expr_info expr) const

bool	operator== (const Expr_c &expr) const

bool	operator== (const Expr &expr) const

bool	operator== (const Abstract &other) const

bool	operator!= (Expr_info expr) const

bool	operator!= (const Expr_c &expr) const
	Compares the Abstract with another. More...

bool	operator!= (const Expr &expr) const

bool	operator!= (const Abstract &other) const

virtual Expr const &	operator[] (int iArg) const
	Access operator for multi-argument expressions, equivalent to the function getArgument(). More...

virtual Expr &	operator[] (int iArg)
	Access operator for multi-argument expressions, returns a reference so this function is not const. More...

virtual bool	operator< (Expr_info expr) const =0
	Compares the simplicity of the expression to another. More...

bool	operator< (const Expr_c &expr) const
	Compares the simplicity of the expression to another. More...

bool	operator> (Expr_info expr) const
	Compares the simplicity of the expression to another. More...

bool	operator> (const Expr_c &expr) const

bool	operator<= (Expr_info expr) const

bool	operator>= (Expr_info expr) const
	Compares the simplicity of the expression to another. More...

bool	operator<= (const Expr_c &expr) const
	Compares the simplicity of the expression to another. More...

bool	operator>= (const Expr_c &expr) const

Protected Member Functions
bool	comparePermutations (Expr_info perm1, Expr_info perm2) const

void	selfCheckAutoIndices ()

Expr &	applySelfStructureOn (Expr &expr) const override

void	adjustMetricDeltaParent ()

csl::vector_expr	applyBrokenIndices (std::vector< Parent > &brokenParents, const Space broken, const std::vector< const Space > &newSpaces, const std::vector< Index > &indices) const

Protected Member Functions inherited from csl::Complexified
void	applyComplexPropertiesOn (const Expr &expr) const

void	applyComplexPropertiesOn (unique_Expr &expr) const

Protected Attributes
IndexStructure	index
	IndexStructure of the tensor.

Protected Attributes inherited from csl::AbstractElement
std::shared_ptr< AbstractParent >	parent
	Pointer to the parent that gave birth to this element.

Protected Attributes inherited from csl::Complexified
bool	conjugated = false

Friends
template<typename ... Args>
Expr	tensorelement_s (Args &&...args)

Additional Inherited Members
Static Public Member Functions inherited from csl::Abstract
static std::string	regularName (std::string const &name)

static std::string	regularName (std::string_view name)

static std::string	regularLiteral (std::string const &name)

static std::string	regularLiteral (std::string_view name)

Detailed Description

Specialization of Abstract for Indicial tensor. Building block carrying indices, and respecting Einstein's summation convention.

Constructor & Destructor Documentation

◆ TensorElement() [1/5]

csl::TensorElement::TensorElement	(	const Index &	t_index,
		const Parent &	t_parent
	)

Constructor called by an TensorParent, for a tensor with one index.

Parameters

t_index	(Only) index of the tensor.
t_parent	Pointer to the TensorParent creating the tensor.

◆ TensorElement() [2/5]

csl::TensorElement::TensorElement	(	const std::vector< Index > &	indices,
		const Parent &	t_parent
	)

Constructor called by an TensorParent, for a tensor with several indices.

Parameters

t_index	List of indices for the tensor.
t_parent	Pointer to the TensorParent creating the tensor.

◆ TensorElement() [3/5]

csl::TensorElement::TensorElement	(	const IndexStructure &	indices,
		const Parent &	t_parent
	)

Constructor called by an TensorParent, for a tensor with several indices.

Parameters

t_index	List of indices for the tensor in the form of an already created IndexStructure.
t_parent	Pointer to the TensorParent creating the tensor.

◆ TensorElement() [4/5]

csl::TensorElement::TensorElement ( const Abstract *& expression )

explicit

Copy constructor from an Abstract*. Works only if the pointer points to another TensorElement.

Parameters

expression

◆ TensorElement() [5/5]

csl::TensorElement::TensorElement ( const Expr & expression )

explicit

Copy constructor from an Expr. Works only if the pointer points to another TensorElement.

Parameters

expression

Member Function Documentation

◆ addProperty()

void csl::TensorElement::addProperty ( Equation * property )

overridevirtual

Adds a property to the object.

Parameters

property The new property to add in props.

Reimplemented from csl::Abstract.

◆ applyPermutation()

Expr csl::TensorElement::applyPermutation ( const Permutation & permutations ) const

Applies a permutation of the indices on a copy of the TensorElement, and returns it.

Parameters

permutations Permutation to apply on the new TensorElement.

Returns

◆ askTerm()

bool csl::TensorElement::askTerm	(	Expr_info	expr,
		bool	exact = `false`
	)		const

overridevirtual

Determines if the term expr can be factorized out from the TensorElement, i.e. if expr is equal to the tensor to (may be) a renaming of index.

If exact is set to true, the function returns true if the IndexStructure matches exactly. Else, the Comparator::freeIndexComparison() function is called.

Parameters

expr	Term to compare.
exact	Tells if the comparison must be exact regarding indices.

Returns: True if expr can be factorized out.; False else.

Reimplemented from csl::Abstract.

◆ checkIndexStructure()

bool csl::TensorElement::checkIndexStructure ( const std::vector< Index > & t_index ) const

overridevirtual

Checks the compatibility of the index structure of an Indicial expression with another. In a sum, two terms must have exaclty the same index structure.

Parameters

t_index A std::vector of Index to compare.

Returns: True if the two structures match.; False else.

Reimplemented from csl::Abstract.

◆ compareWithDummy()

bool csl::TensorElement::compareWithDummy	(	Expr_info	expr,
		std::map< Index, Index > &	constraints,
		bool	keepAllCosntraints = `false`
	)		const

overridevirtual

Comparison disregarding name of dummy indices, i.e. the two expressions * are equals even if dummy indices have not the same names in *this and * expr.

Parameters

expr	Expression to compare.
constraints	List of existing constraints between indices (it is modified in the function).

Returns: True if expr == *this taking constraints into account.; False else.

Reimplemented from csl::Abstract.

Reimplemented in csl::TDerivativeElement, and csl::TensorFieldElement.

◆ contraction()

Expr csl::TensorElement::contraction ( Expr_info B ) const

overridevirtual

Applies a special contraction of indices. Before calling this function we must check that there is indeed a contraction by calling the function hasContractionProperty().

Parameters

B	Expression with which *this contracts.

Returns: The result of the contraction.

Reimplemented from csl::Abstract.

◆ dependsExplicitlyOn()

bool csl::TensorElement::dependsExplicitlyOn ( Expr_info expr ) const

overridevirtual

Check recursively if expr is present in the expression.

Parameters

expr	Expression to search.

Returns: True if expr is found.; False else.

Reimplemented from csl::Abstract.

Reimplemented in csl::TDerivativeElement, and csl::TensorFieldElement.

◆ dependsOn()

bool csl::TensorElement::dependsOn ( Expr_info expr ) const

overridevirtual

Check recursively if the expression depends on expr.

Parameters

expr	Expression to search.

Returns: True if a dependency in expr is found.; False else.

Reimplemented from csl::Abstract.

Reimplemented in csl::TDerivativeElement, and csl::TensorFieldElement.

◆ derive()

optional< Expr > csl::TensorElement::derive ( Expr_info expr ) const

overridevirtual

Calculates the derivative of the Abstract wrt another.

It is possible to derive wrt any complicated expr. In this case however, the calculation is not always mathematically correct. The program just searches for equal Abstract or Abstract with the same name. In particular dx/d(exp(x))=0.

Parameters

expr	Expression wrt which we derive.

Returns: The derivative.

Reimplemented from csl::Abstract.

◆ evaluate()

optional< Expr > csl::TensorElement::evaluate ( csl::eval::mode user_mode = csl::eval::base ) const

overridevirtual

Evaluates the Abstract.

Replaces all variables by their value and evaluating. This function must be used instead of evaluateScalar() when treating not only real scalars.* In particular (x=2, y=3) x+iy evaluates to 3+ 3i whereas evaluateScalar() would return 3.

Returns: The abstract result of the evaluation.

Reimplemented from csl::AbstractElement.

Reimplemented in csl::TensorFieldElement.

◆ getAlternateForms()

csl::vector_expr csl::TensorElement::getAlternateForms ( ) const

overridevirtual

Calculates and returns all possible alternate forms of the expression in terms of simplifications. For example 1-sin^2(x) is one of the alternate forms of cos^2(x).

Those alternate forms are then compared in terms of simplicity, this allows automatic simplification. Alternates are tried to simplify, and the bests are chosed. More details and algorithms in file alternateForms.cpp.

Returns: A std::vector containing the alternate forms of the expression.

Reimplemented from csl::Abstract.

◆ getComplexConjugate()

optional< Expr > csl::TensorElement::getComplexConjugate ( ) const

overridevirtual

Calculates and returns the complex conjugate of the expression.

Returns: {*this}.

Reimplemented from csl::Complexified.

Reimplemented in csl::TDerivativeElement.

◆ getIndex()

Index csl::TensorElement::getIndex ( int i ) const

overridevirtual

Parameters

i	Spot of the index to get.

Returns: the i^{th} index of an Indicial expression.

Reimplemented from csl::Abstract.

◆ getIndexStructure()

IndexStructure csl::TensorElement::getIndexStructure ( ) const

inlineoverridevirtual

Returns: The index structure of the Indicial expression

Reimplemented from csl::Abstract.

Reimplemented in csl::TDerivativeElement.

◆ getNIndices()

int csl::TensorElement::getNIndices ( ) const

inlineoverridevirtual

Returns: The number of indices of an Indicial expression.

Reimplemented from csl::Abstract.

◆ getPermutations()

csl::vector_expr csl::TensorElement::getPermutations ( bool optimize = true ) const

overridevirtual

Returns a std::vector of all possible permutations of an Indicial expression. The possible permutations are determined from the posible symmetries and anti-symmetries of the object.

Returns: A std::vector containing all possible permutations of the tensor.

Reimplemented from csl::Abstract.

◆ getPrimaryType()

csl::PrimaryType csl::TensorElement::getPrimaryType ( ) const

inlineoverridevirtual

Gives the primary type of Abstract.

In the program this function is very often called. It allows different functions to know what type of expr they are manipulating (single number, scalar function with one argument, with multiple argumments, a Vector, etc) in order to do special treatments or simplifications.

Returns: type (a non memorized integer corresponding to the type of abstract)

Implements csl::Abstract.

Reimplemented in csl::TensorFieldElement.

◆ getProperties()

const std::vector< Equation * > & csl::TensorElement::getProperties ( ) const

overridevirtual

Returns: The properties of the object.

Reimplemented from csl::Abstract.

◆ getType()

csl::Type csl::TensorElement::getType ( ) const

inlineoverridevirtual

Gives the type of Abstract.

In the program this function is very often called. It allows different functions to know what type of expr they are manipulating (cos, product, number, etc) in order to do special treatments or simplifications.

Returns: type (a non memorized integer corresponding to the type of abstract)

Implements csl::Abstract.

Reimplemented in csl::TDerivativeElement, and csl::TensorFieldElement.

◆ hasContractionProperty()

bool csl::TensorElement::hasContractionProperty ( Expr_info B ) const

overridevirtual

Tells (for an Indicial type) if there is a special contraction property with B.

Parameters

B	Expression with which we test if there is a special contraction.

Returns: True if there is a contraction.; False else.

Reimplemented from csl::Abstract.

◆ isIndexed()

bool csl::TensorElement::isIndexed ( ) const

inlineoverridevirtual

Returns: True if the expression is indexed.; False else.

Reimplemented from csl::Abstract.

Reimplemented in csl::TensorFieldElement.

◆ operator==()

bool csl::TensorElement::operator== ( Expr_info expr ) const

overridevirtual

Compares the Abstract with another.

Here if two Abstracts have the same name, the function will return true even if they are not mathematically equal. So beware not to name different things the same way.

Parameters

expr	Abstract to compare.

Returns: True if the two Abstracts are the same (or have the same name).; False else.

Reimplemented from csl::Complexified.

Reimplemented in csl::TDerivativeElement, and csl::TensorFieldElement.

◆ print()

void csl::TensorElement::print	(	int	mode = `0`,
		std::ostream &	out = `std::cout`,
		bool	lib = `false`
	)		const

overridevirtual

Displays the abstract in standard output.

Parameters

mode	Tells if the Abstract is printed alone (default) or in another expr.

Implements csl::Abstract.

Reimplemented in csl::TDerivativeElement, and csl::TensorFieldElement.

◆ printLaTeX()

string csl::TensorElement::printLaTeX ( int mode = 0 ) const

overridevirtual

Creates a LaTeX output for the Abstract.

Parameters

mode	Tells if the Abstract is printed alone (default) or in another expr.

Returns: The string corresponding to the LaTeX output.

Reimplemented from csl::Abstract.

Reimplemented in csl::TDerivativeElement, and csl::TensorFieldElement.

◆ removeProperty()

void csl::TensorElement::removeProperty ( Equation * property )

overridevirtual

Removes a property to the object.

Parameters

property Property to remove from props.

Reimplemented from csl::Abstract.

◆ replaceIndex()

optional< Expr > csl::TensorElement::replaceIndex	(	const Index &	indexToReplace,
		const Index &	newIndex,
		bool	refresh = `true`
	)		const

overridevirtual

For indicial expressions, this function searches indexToContract and replaces it with newIndex.

Parameters

indexToContract	Index that is newly contracted.
newIndex	Dummy new index that replaces indexToContract in the expression.

Returns: True if the index has been found.; False else.

Reimplemented from csl::Abstract.

Reimplemented in csl::TDerivativeElement.

◆ setIndexStructure()

void csl::TensorElement::setIndexStructure ( const IndexStructure & t_index )

overridevirtual

Replaces the index structure of the object, that must be an Indicial expression.

Parameters

t_index A std::vector of Index which takes the place of the structure index.

Reimplemented from csl::Abstract.

Reimplemented in csl::TDerivativeElement.

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

include/indicial.h
src/alternateForms.cpp
src/indicial.cpp
src/simplification.cpp

Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ TensorElement() [1/5]

◆ TensorElement() [2/5]

◆ TensorElement() [3/5]

◆ TensorElement() [4/5]

◆ TensorElement() [5/5]

Member Function Documentation

◆ addProperty()

◆ applyPermutation()

◆ askTerm()

◆ checkIndexStructure()

◆ compareWithDummy()

◆ contraction()

◆ dependsExplicitlyOn()

◆ dependsOn()

◆ derive()

◆ evaluate()

◆ getAlternateForms()

◆ getComplexConjugate()

◆ getIndex()

◆ getIndexStructure()

◆ getNIndices()

◆ getPermutations()

◆ getPrimaryType()

◆ getProperties()

◆ getType()

◆ hasContractionProperty()

◆ isIndexed()

◆ operator==()

◆ print()

◆ printLaTeX()

◆ removeProperty()

◆ replaceIndex()

◆ setIndexStructure()