Root class of the inheritance tree of abstracts. More...

#include <abstract.h>

Inheritance diagram for csl::Abstract:

[legend]

Public Member Functions
	Abstract ()
	Default Constructor. More...

virtual	~Abstract ()
	Destructor.

Expr	self ()

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

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

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

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

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

virtual std::vector< Parent >	getSubSymbols () const =0

virtual LibDependency	getLibDependency () const

virtual size_t	memoryOverhead () const

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

virtual std::string const &	getLatexName () const

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

virtual bool	getElementary () const

virtual bool	getAllDependencies () const

virtual csl::PrimaryType	getPrimaryType () const =0
	Gives the primary type of Abstract. More...

virtual csl::Type	getType () const =0
	Gives the type of Abstract. More...

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

virtual bool	isBuildingBlock () const
	Tells if the expression is a Building Block or not. More...

virtual int	getOrderOf (Expr_info expr) const

virtual bool	isArbitrary () const

virtual bool	isIndexed () const

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

virtual bool	isReal () const

virtual bool	isPurelyImaginary () const

virtual bool	isComplexConjugate () const

virtual bool	isHermitianConjugate () const

virtual csl::ComplexProperty	getComplexProperty () const

virtual void	setComplexProperty (csl::ComplexProperty prop)

virtual void	setConjugated (bool t_conjugated)

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)

virtual int	getNIndices () const

virtual Index	getIndex (int i=0) const

virtual void	resetIndexStructure ()

virtual IndexStructure	getIndexStructure () const

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

virtual const IndexStructure &	getIndexStructureView () const

virtual IndexStructure &	getIndexStructureView ()

virtual IndexStructure	getFreeIndexStructure () const

virtual Parent	getParent () const
	For indicial expressions this function returns a pointer to the parent object of type TensorParent (not an expression). More...

virtual Parent_info	getParent_info () const

virtual Tensor	getPoint () const

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

virtual csl::vector_expr	getPermutations (bool optimize=true) const
	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...

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

Expr	copy () const

virtual unique_Expr	copy_unique () const =0

virtual Expr	deepCopy () const

virtual Expr	refresh () const

virtual Expr	deepRefresh () const

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

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

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

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

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...

virtual void	setParent (const Parent &t_parent)

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

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

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

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

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

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

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

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

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...

virtual bool	compareWithDummy (Expr_info expr, std::map< Index, Index > &constraints, bool keepAllCosntraints=false) const
	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...

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	askTerm (Expr_info expr, bool exact=false) const
	Check if expr can factor *this. More...

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

virtual bool	dependsOn (Parent_info parent) const

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

virtual bool	dependsExplicitlyOn (Parent_info parent) const

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

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

virtual int	isPolynomial (Expr_info expr) const
	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...

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

virtual bool	hasChainContractionProperty () const

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

virtual Expr	contraction (Expr_info B) const
	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...

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 >	evaluate (csl::eval::mode user_mode=csl::eval::base) const =0
	Evaluates the Abstract. More...

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

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

virtual std::optional< Expr >	factor (Expr_info factor, bool full=false) const
	Factors the Abstract wrt a particular 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 (bool full=false, bool inPlace=false) const
	Develops the Abstract. 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 >	getRealPart () const
	Evaluates the real part of the Abstract and returns it. More...

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

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

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

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

virtual Expr &	applySelfStructureOn (Expr &expr) const

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

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

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

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

virtual std::optional< Expr >	getPolynomialTerm (Expr_info t_variable, int order) const
	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...

virtual csl::vector_expr	getAlternateForms () const
	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...

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	getCanonicalPermutation () const

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

virtual bool	operator== (Expr_info expr) const =0
	Compares the Abstract with another. More...

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

Static Public Member Functions
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

Root class of the inheritance tree of abstracts.

Contains all functions that derived class needs. In particular all documented functions of the class Abstract are specialized in all the derived classes.

Note: Some functions are not documented here because not every derived class use them.

Constructor & Destructor Documentation

◆ Abstract()

csl::Abstract::Abstract ( )

inline

Default Constructor.

Initializes name empty and commutable to True.

Member Function Documentation

◆ addAntiSymmetry()

void csl::Abstract::addAntiSymmetry	(	int	i1,
		int	i2
	)

virtual

Add an anti-symmetry between the i1^{th} and the i2^{th} indices. If those indices are symmetric, an error is thrown.

Parameters

i1	Position of the first index.
i2	Position of the second index.

◆ addition_own()

Expr csl::Abstract::addition_own ( const Expr & expr ) const

virtual

Contains implementation of special addition for Numerical- and Vectorial-types.

Parameters

expr	Right operrand of the addition.

Returns: The sum of the two operands.

Reimplemented in csl::Complex, csl::IntFraction, csl::Polynomial, csl::Float, csl::AbstractVectorial, csl::Integer, and csl::NumericalEval.

◆ addProperty()

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

virtual

Adds a property to the object.

Parameters

property The new property to add in props.

Reimplemented in csl::TensorElement, and csl::AbstractLiteral.

◆ addSymmetry()

void csl::Abstract::addSymmetry	(	int	i1,
		int	i2
	)

virtual

Add a symmetry between the i1^{th} and the i2^{th} indices. If those indices are anti-symmetric, an error is thrown.

Parameters

i1	Position of the first index.
i2	Position of the second index.

◆ antisymmetrise()

Expr csl::Abstract::antisymmetrise ( ) const

virtual

Calculates and returns the anti-symmetrization of a 2D matrix.

Returns: 1/2*(A - A^T) for a matrix (2D) A.

Reimplemented in csl::Matrix, and csl::AbstractVectorial.

◆ applyOperator()

Expr csl::Abstract::applyOperator	(	const Expr &	operand,
		bool	leaveEmpty = `false`
	)		const

virtual

Apply the operator on an operand, iif the expression is an operator.

Parameters

operand Operand of the operator.

Returns: The operator filled with operand.

◆ askTerm()

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

virtual

Check if expr can factor *this.

In almost every case this corresponds just to the comparison ** *this == expr**. For Prod, Pow, Fraction types (all that are multiplicative) we must check if the factor hides in a product.

Parameters

expr	Factor to search in the expression.

Returns: True if expr is a possible factor.; False else.

Reimplemented in csl::TensorElement, csl::Pow, csl::Prod, and csl::Sum.

◆ begin() [1/2]

csl::vector_expr::iterator csl::Abstract::begin ( )

virtual

Returns: A csl::vector_expr::iterator at the beginning of argument for multi-argument expressions.

Reimplemented in csl::AbstractMultiFunc, and csl::AbstractVectorial.

◆ begin() [2/2]

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

virtual

Returns: A csl::vector_expr::iterator at the beginning of argument for multi-argument expressions.

Reimplemented in csl::AbstractMultiFunc, and csl::AbstractVectorial.

◆ checkIndexStructure() [1/2]

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

virtual

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 in csl::TensorElement.

◆ checkIndexStructure() [2/2]

virtual bool csl::Abstract::checkIndexStructure ( const std::initializer_list< Index > & index ) const

virtual

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::initializer_list of Index to compare.

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

◆ collect()

optional< Expr > csl::Abstract::collect	(	std::vector< Expr > const &	factors,
		bool	full = `false`
	)		const

virtual

Collects terms in sum according to some factors given by the user.

This function allows the factor with some specific scalar variables. For example, $ ax + ay + by $ can be factored in two ways. Either with $ (a, b) $ which gives $ a(x+y) + by $ ; or with $ (x, y) $ which gives $ ax + (a+b)y $ . With the collect function it is possible to choose precisely the set of variables that will be factored to express results in a standard way.

Parameters

factors	Factors to search in the expression.
full	Boolean (default = false) that tells if the collection must be recursive (full expression depth).

Returns: The collected expression if modifications have been done.; std::nullopt else.

Note: This function will probably replace the factor() function in the future.; For now, the collect function does not support factorization by indicial tensors, whereas factor() does.

Reimplemented in csl::AbstractMultiFunc, csl::TDerivativeElement, csl::AbstractDuoFunc, csl::Sum, and csl::AbstractFunc.

◆ commutesWith()

bool csl::Abstract::commutesWith	(	Expr_info	expr,
		int	sign = `-1`
	)		const

virtual

Tells if the object commutes with expr.

Parameters

expr

Returns: True if *this commutes with expr.; False else.

Reimplemented in csl::AbstractMultiFunc, csl::AbstractDuoFunc, csl::Variable, csl::TensorFieldElement, csl::AbstractFunc, csl::ScalarField, csl::AbstractVectorial, and csl::AbstractBuildingBlock.

◆ compareWithDummy()

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

virtual

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 in csl::IProd, csl::ISum, csl::TensorElement, csl::TDerivativeElement, csl::VectorIntegral, csl::TensorFieldElement, csl::AbstractFunc, and csl::Scalar.

◆ contraction()

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

virtual

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 in csl::TensorElement.

◆ dependsExplicitlyOn()

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

virtual

Check recursively if expr is present in the expression.

Parameters

expr	Expression to search.

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

Reimplemented in csl::TensorElement, csl::Integral, csl::AbstractMultiFunc, csl::TDerivativeElement, csl::AbstractDuoFunc, csl::TensorFieldElement, csl::AbstractFunc, csl::AbstractIntegral, csl::AbstractVectorial, csl::AbstractField, and csl::AbstractNumerical.

◆ dependsOn()

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

virtual

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 in csl::TensorElement, csl::Integral, csl::AbstractMultiFunc, csl::TDerivativeElement, csl::AbstractDuoFunc, csl::Variable, csl::TensorFieldElement, csl::AbstractFunc, csl::AbstractIntegral, csl::Constant, csl::AbstractVectorial, csl::AbstractField, and csl::AbstractNumerical.

◆ derive()

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

virtual

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 in csl::DiracDelta, csl::Factorial, csl::ATanh, csl::ASinh, csl::ACosh, csl::Tanh, csl::Sinh, csl::TensorElement, csl::Cosh, csl::Angle, csl::Integral, csl::ATan, csl::Derivative, csl::ASin, csl::ACos, csl::Pow, csl::Tan, csl::Imaginary, csl::Complex, csl::Prod, csl::Sin, csl::IntFactorial, csl::IntFraction, csl::Cos, csl::Variable, csl::Log, csl::Polynomial, csl::Float, csl::Exp, csl::Constant, csl::Integer, csl::AbstractIntegral, csl::Sum, csl::Commutator, csl::NumericalEval, and csl::Abs.

◆ determinant()

Expr csl::Abstract::determinant ( ) const

virtual

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

Returns: det(*this) if *this is a square matrix or scalar.; 0 else.

Reimplemented in csl::Matrix.

◆ division_own()

Expr csl::Abstract::division_own ( const Expr & expr ) const

virtual

Contains implementation of special division for Numerical- and Polynomial-types. For polynomial, the euclidean division of two polynomials is implemented.

Parameters

expr	Right operrand of the division.

Returns: The division of the two operands.

Reimplemented in csl::Complex, csl::IntFraction, csl::Polynomial, csl::Float, csl::Integer, and csl::NumericalEval.

◆ dot()

Expr csl::Abstract::dot ( const Expr & expr ) const

virtual

Returns the dot product of two Vectorial expressions.

Parameters

expr	The right operand of the dot product.

Returns: sum _k (*this)[i,j,...,k]*expr[k,l,m,...].

Reimplemented in csl::AbstractVectorial.

◆ end() [1/2]

csl::vector_expr::iterator csl::Abstract::end ( )

virtual

Returns: A csl::vector_expr::iterator at the end of argument for multi-argument expressions.

Reimplemented in csl::AbstractMultiFunc, and csl::AbstractVectorial.

◆ end() [2/2]

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

virtual

Returns: A csl::vector_expr::iterator at the end of argument for multi-argument expressions.

Reimplemented in csl::AbstractMultiFunc, and csl::AbstractVectorial.

◆ evaluate()

virtual std::optional<Expr> csl::Abstract::evaluate ( csl::eval::mode user_mode = csl::eval::base ) const

pure virtual

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.

Implemented in csl::Factorial, csl::ATanh, csl::ASinh, csl::IProd, csl::ACosh, csl::Tanh, csl::Sinh, csl::TensorElement, csl::Cosh, csl::Angle, csl::Integral, csl::ATan, csl::Derivative, csl::ASin, csl::ACos, csl::Pow, csl::Tan, csl::Imaginary, csl::Complex, csl::Sin, csl::Prod, csl::IntFactorial, csl::Cos, csl::IntFraction, csl::Variable, csl::Log, csl::Polynomial, csl::TensorFieldElement, csl::Float, csl::AbstractFunc, csl::Exp, csl::Constant, csl::AbstractIntegral, csl::ScalarField, csl::Integer, csl::Commutator, csl::Sum, csl::ImaginaryPart, csl::AbstractElement, csl::NumericalEval, csl::Arbitrary, csl::Abs, csl::AbstractVectorial, csl::RealPart, and csl::Scalar.

◆ evaluateScalar()

long double csl::Abstract::evaluateScalar ( ) const

virtual

Evaluates the value of the Abstract.

Tries to replace all variables by a real value. If it is not possible (for example treating a Vector or an Imaginary) the considered object is replaced by 0. A warning message is displayed in the case of i.

Returns: The value of the Abstract (double).

Reimplemented in csl::Factorial, csl::ATanh, csl::ASinh, csl::ACosh, csl::Tanh, csl::Sinh, csl::Cosh, csl::Angle, csl::ATan, csl::Derivative, csl::ASin, csl::ACos, csl::Pow, csl::Tan, csl::Imaginary, csl::Complex, csl::Sin, csl::Prod, csl::IntFactorial, csl::Cos, csl::IntFraction, csl::Variable, csl::Log, csl::Polynomial, csl::Float, csl::Exp, csl::Constant, csl::Integer, csl::Commutator, csl::Sum, csl::Abs, and csl::NumericalEval.

◆ expand()

optional< Expr > csl::Abstract::expand	(	bool	full = `false`,
		bool	inPlace = `false`
	)		const

virtual

Develops the Abstract.

This function concerns only products (and exponents) that will be flatten to give at the end a sum of independant terms.

Parameters

full	If true the expandment is recursive through all the Abstract.

Returns: The expand Abstract.

Reimplemented in csl::Pow, csl::AbstractMultiFunc, csl::Prod, csl::TDerivativeElement, csl::AbstractDuoFunc, csl::Exp, csl::AbstractVectorial, csl::AbstractFunc, and csl::AbstractBuildingBlock.

◆ expand_if()

optional< Expr > csl::Abstract::expand_if	(	std::function< bool(Expr const &)> const &	f,
		bool	full = `false`,
		bool	inPlace = `false`
	)		const

virtual

Develops the Abstract.

This function concerns only products (and exponents) that will be flatten to give at the end a sum of independant terms.

Parameters

f	Functions that returns a boolean that determines which arguments must be expanded in products.
full	If true the expandment is recursive through all the Abstract.

Returns: The expand Abstract.

Reimplemented in csl::Pow, csl::AbstractMultiFunc, csl::Prod, csl::TDerivativeElement, csl::AbstractDuoFunc, csl::Exp, csl::AbstractVectorial, and csl::AbstractFunc.

◆ exponentiation_own()

Expr csl::Abstract::exponentiation_own ( const Expr & expr ) const

virtual

Contains implementation of special exponentiation for Numerical- and Vectorial-types.

Parameters

expr exponent.

Returns: The exponentiation of the two operands.

Reimplemented in csl::Complex, csl::IntFraction, csl::Float, csl::Integer, and csl::NumericalEval.

◆ factor() [1/2]

optional< Expr > csl::Abstract::factor ( bool full = false ) const

virtual

Factors the Abstract.

This function tries to factor the Abstract wrt any factor. This will be more involved in calculation than the other factorizing function that takes the factor as a parameter. So this function must be used only if we don't know the factors we want at the end.

Parameters

full	If true the factorization is recursive through all the Abstract.

Reimplemented in csl::ISum, csl::AbstractMultiFunc, csl::TDerivativeElement, csl::AbstractDuoFunc, csl::Polynomial, csl::AbstractVectorial, csl::Sum, csl::AbstractFunc, and csl::AbstractBuildingBlock.

◆ factor() [2/2]

optional< Expr > csl::Abstract::factor	(	Expr_info	factor,
		bool	full = `false`
	)		const

virtual

Factors the Abstract wrt a particular Abstract.

Parameters

factor	Abstract wrt which we try to factor.
full	If true the factorization is recursive through all the Abstract.

Reimplemented in csl::AbstractMultiFunc, csl::TDerivativeElement, csl::AbstractDuoFunc, csl::AbstractVectorial, csl::Sum, csl::AbstractFunc, and csl::AbstractBuildingBlock.

◆ findSubExpression()

optional< Expr > csl::Abstract::findSubExpression	(	Expr_info	subExpression,
		const Expr &	newExpression
	)		const

virtual

Searches a sub-expression and replaces it.

Parameters

subExpression	Expression to search.
newExpression	Expression that replaces subExpression if it is found.

Returns: The expression with the replacement done.

Reimplemented in csl::AbstractMultiFunc, csl::Prod, csl::AbstractDuoFunc, csl::AbstractFunc, and csl::AbstractBuildingBlock.

◆ getAlternateForms()

csl::vector_expr csl::Abstract::getAlternateForms ( ) const

virtual

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 in csl::Tanh, csl::Sinh, csl::TensorElement, csl::Cosh, csl::Pow, csl::Tan, csl::Prod, csl::Sin, csl::Cos, and csl::Sum.

◆ getArgument() [1/2]

Expr const & csl::Abstract::getArgument ( int iArg = 0 ) const

virtual

Warning: This function must not be called for building blocks, one must check first that the expression has arguments.

Returns: The i^{th} argument of the expression.

Reimplemented in csl::AbstractMultiFunc, csl::TDerivativeElement, csl::AbstractDuoFunc, csl::AbstractVectorial, and csl::AbstractFunc.

◆ getArgument() [2/2]

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

virtual

Allows to get specific arguments of expressions in multiple dimensions, by giving the indices in each dimension.

Warning: This function must not be called for building blocks, one must check first that the expression has arguments.

Returns: The argument {i,j,...} of the expression.

Reimplemented in csl::AbstractVectorial.

◆ getCommutable()

bool csl::Abstract::getCommutable ( ) const

virtual

Allows to know if the object commutes with all the others.

Returns: commutable

Reimplemented in csl::AbstractMultiFunc, csl::AbstractDuoFunc, csl::Variable, csl::Constant, csl::AbstractElement, and csl::AbstractFunc.

◆ getComplexArgument()

optional< Expr > csl::Abstract::getComplexArgument ( ) const

virtual

Evaluates the argument in the complex plane of the Abstract and returns it.

Returns: The argument part of the Abstract.

Reimplemented in csl::DiracDelta, csl::Tanh, csl::Sinh, csl::Cosh, csl::ASin, csl::ACos, csl::Tan, csl::Complex, csl::Imaginary, csl::AbstractMultiFunc, csl::Sin, csl::Prod, csl::Cos, csl::AbstractDuoFunc, csl::Log, csl::Exp, csl::AbstractFunc, and csl::Sum.

◆ getComplexConjugate()

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

virtual

Calculates and returns the complex conjugate of the expression.

Returns: {*this}.

Reimplemented in csl::TensorElement, csl::Complex, csl::AbstractMultiFunc, csl::TDerivativeElement, csl::AbstractDuoFunc, csl::ImaginaryPart, csl::AbstractFunc, csl::AbstractVectorial, csl::Complexified, and csl::RealPart.

◆ getComplexModulus()

optional< Expr > csl::Abstract::getComplexModulus ( ) const

virtual

Evaluates the modulus in the complex plane of the Abstract and returns it.

Returns: The modulus part of the Abstract.

Reimplemented in csl::DiracDelta, csl::Tanh, csl::Sinh, csl::Cosh, csl::ASin, csl::ACos, csl::Tan, csl::Complex, csl::Imaginary, csl::AbstractMultiFunc, csl::Sin, csl::Prod, csl::Cos, csl::AbstractDuoFunc, csl::Log, csl::Exp, csl::AbstractVectorial, csl::AbstractFunc, csl::Sum, and csl::AbstractBuildingBlock.

◆ getContractedPair()

set< pair< int, int > > csl::Abstract::getContractedPair ( ) const

virtual

Returns: All contracted pairs of indices of an Indicial expression.

Warning: This function is not yet well implemented and may not be useful in the future.

◆ getDenom()

long long int csl::Abstract::getDenom ( ) const

virtual

Returns: The denominator for a IntFraction.

Reimplemented in csl::IntFraction.

◆ getDim()

int csl::Abstract::getDim ( ) const

virtual

Gives the dimension of the object.

Allows to know if we are manipulating a pure scalar (i.e. that can have a real value) or something else. There is the particular case of the Imaginary i that is considered as a scalar for simplicity but in reality cannot be evaluated with a real. Example: 1 + i cannot be reduced.

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

Reimplemented in csl::AbstractVectorial.

◆ getExponents()

void csl::Abstract::getExponents	(	std::vector< Expr > const &	factors,
		std::vector< Expr > &	exponents
	)		const

virtual

Fills in a vector the exponents corresponding to some factors for the expression.

For example, an expression like $2ax^2\cos y$ will have exponents $ (1, 2, 0) $ for the set of factors $ (a, x, y). $ factors and exponents must of course be of the same size. Otherwise the behaviour is undefined.

Note: This function assumes that the expression is canonical, in particular that no terms like $x\cdot x^2$ can appear.; This function does not take into account factors in sums like (this will return a factor 0 for ).

Parameters

factors	Factors.
exponents	Exponents (out variable, modified during the run).

Reimplemented in csl::Pow, and csl::Prod.

◆ getFactors()

csl::vector_expr csl::Abstract::getFactors ( ) const

virtual

Allows to get a std::vector of all terms than could factor the expression.

Returns: A std::vector containing the possible factors of *this.

Reimplemented in csl::Pow, csl::Prod, and csl::Sum.

◆ getFreeIndexStructure()

IndexStructure csl::Abstract::getFreeIndexStructure ( ) const

virtual

Returns: The free index structure of the Indicial expression

◆ getImaginaryPart()

Expr csl::Abstract::getImaginaryPart ( ) const

virtual

Evaluates the imaginary part of the Abstract and returns it.

Returns: The imaginary part of the Abstract.

Reimplemented in csl::DiracDelta, csl::Tanh, csl::Sinh, csl::Cosh, csl::ASin, csl::ACos, csl::Tan, csl::Complex, csl::Imaginary, csl::AbstractMultiFunc, csl::Sin, csl::Prod, csl::Cos, csl::AbstractDuoFunc, csl::Log, csl::Exp, csl::AbstractVectorial, csl::AbstractFunc, csl::Sum, and csl::Complexified.

◆ getIndex()

Index csl::Abstract::getIndex ( int i = 0 ) const

virtual

Parameters

i	Spot of the index to get.

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

Reimplemented in csl::TensorElement.

◆ getIndexStructure()

IndexStructure csl::Abstract::getIndexStructure ( ) const

virtual

Returns: The index structure of the Indicial expression

Reimplemented in csl::IProd, csl::ISum, csl::TensorElement, csl::TDerivativeElement, csl::VectorIntegral, csl::AbstractDuoFunc, csl::Polynomial, csl::AbstractFunc, and csl::Scalar.

◆ getName()

std::string const & csl::Abstract::getName ( ) const

virtual

Returns the Abstract's name.

Returns: name

Reimplemented in csl::Variable, csl::Constant, csl::AbstractElement, csl::Arbitrary, and csl::AbstractVectorial.

◆ getNArgs()

int csl::Abstract::getNArgs ( int axis = 0 ) const

virtual

Returns the number of arguments of the expression. If the expression is a building block (AbstractBuildingBlock), this function returns 0.

Returns: The number of arguments of the expression.

Reimplemented in csl::AbstractMultiFunc, csl::AbstractDuoFunc, csl::AbstractFunc, and csl::AbstractVectorial.

◆ getNContractedPairs()

int csl::Abstract::getNContractedPairs ( ) const

virtual

Returns the number of contracted pairs of indices in an Indicial expression.

Returns: The number of contracted pairs of indices.

◆ getNFactor()

int csl::Abstract::getNFactor ( ) const

virtual

Returns: The number of possible factors for the expression

Reimplemented in csl::Pow, and csl::Prod.

◆ getNIndices()

int csl::Abstract::getNIndices ( ) const

virtual

Returns: The number of indices of an Indicial expression.

Reimplemented in csl::TensorElement.

◆ getNum()

long long int csl::Abstract::getNum ( ) const

virtual

Returns: The numerator for a IntFraction.

Reimplemented in csl::IntFraction, and csl::Arbitrary.

◆ getNumericalFactor()

Expr csl::Abstract::getNumericalFactor ( ) const

virtual

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

Note: This function returns the factor in an Expression (then of Numerical type).

Returns: The numerical factor in front of the expression.

Reimplemented in csl::Pow, csl::Prod, csl::Sum, and csl::AbstractNumerical.

◆ getOperand()

Expr csl::Abstract::getOperand ( ) const

virtual

Returns the operand of an Operator.

Returns: operand of an Operator.

Reimplemented in csl::Integral, csl::Derivative, csl::TDerivativeElement, csl::AbstractIntegral, csl::ImaginaryPart, and csl::RealPart.

◆ getOrder()

int csl::Abstract::getOrder ( ) const

virtual

Accessor to the order (integer) that defines certain types of expressions.

Returns: order.

Reimplemented in csl::Derivative, and csl::Polynomial.

◆ getParent()

Parent csl::Abstract::getParent ( ) const

virtual

For indicial expressions this function returns a pointer to the parent object of type TensorParent (not an expression).

Returns: parent for TensorElement-type expression.

Reimplemented in csl::VectorIntegral, csl::Variable, csl::Constant, and csl::AbstractElement.

◆ getParity()

int csl::Abstract::getParity ( Expr_info t_variable ) const

virtual

Returns the parity property of the expression with respect to t_variable.

Parameters

t_variable.

Returns: 1 if the expression is even in t_variable.; -1 if the expression is odd in t_variable.; 0 else.

Reimplemented in csl::DiracDelta, csl::Factorial, csl::ATanh, csl::ASinh, csl::ACosh, csl::Tanh, csl::Sinh, csl::Cosh, csl::Angle, csl::Integral, csl::ATan, csl::Derivative, csl::ASin, csl::Pow, csl::ACos, csl::Tan, csl::Prod, csl::Sin, csl::Cos, csl::Variable, csl::Log, csl::Polynomial, csl::Exp, csl::Constant, csl::Sum, csl::Commutator, and csl::Abs.

◆ getPermutations()

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

virtual

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 in csl::TensorElement.

◆ getPolynomialTerm()

optional< Expr > csl::Abstract::getPolynomialTerm	(	Expr_info	t_variable,
		int	order
	)		const

virtual

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().

Parameters

t_variable Variable of the polynomial. Order of *this in t_variable.

Returns: The same expression as (*this) with the term t_variable^order removed.

Reimplemented in csl::Pow, csl::Prod, csl::AbstractElement, and csl::AbstractBuildingBlock.

◆ getPrimaryType()

virtual csl::PrimaryType csl::Abstract::getPrimaryType ( ) const

pure virtual

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)

Implemented in csl::TensorElement, csl::Imaginary, csl::AbstractMultiFunc, csl::IntFactorial, csl::AbstractDuoFunc, csl::Variable, csl::TensorFieldElement, csl::Constant, csl::AbstractField, csl::AbstractVectorial, csl::Arbitrary, csl::AbstractFunc, csl::AbstractLiteral, and csl::AbstractNumerical.

◆ getProduct()

Expr csl::Abstract::getProduct ( ) const

virtual

Calculates and returns the product of all elements in the Vectorial object.

Returns: The product of all elements.

Reimplemented in csl::AbstractVectorial.

◆ getProperties()

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

virtual

Returns: The properties of the object.

Reimplemented in csl::TensorElement, and csl::AbstractLiteral.

◆ getRealPart()

optional< Expr > csl::Abstract::getRealPart ( ) const

virtual

Evaluates the real part of the Abstract and returns it.

Returns: The real part of the Abstract.

Reimplemented in csl::DiracDelta, csl::Tanh, csl::Sinh, csl::Cosh, csl::ASin, csl::ACos, csl::Tan, csl::Complex, csl::Imaginary, csl::AbstractMultiFunc, csl::Sin, csl::Prod, csl::Cos, csl::AbstractDuoFunc, csl::Log, csl::Exp, csl::AbstractVectorial, csl::AbstractFunc, csl::Sum, csl::Complexified, and csl::AbstractBuildingBlock.

◆ getRegularExpression()

Expr csl::Abstract::getRegularExpression ( ) const

virtual

Returns a regular expression from the polynomial, that is a sum where the different powers of the variable appear explicitely.

Returns: a Sum expression equal to the polynomial.

Reimplemented in csl::Polynomial.

◆ getShape()

vector< int > csl::Abstract::getShape ( ) const

virtual

Accessor to the shape of the tensor in the form of a std::vector of integers.

Returns: shape.

Reimplemented in csl::AbstractVectorial.

◆ getSign()

int csl::Abstract::getSign ( ) const

virtual

Returns: The sign for a Commutator type expression.

Reimplemented in csl::Commutator.

◆ getSubVectorial() [1/3]

Expr csl::Abstract::getSubVectorial ( int iExcept ) const

virtual

Allows to pick a part of a Vectorial expression, excluding the iExcept^{th} element.

Parameters

iExcept Element to ignore.

Returns: The part of *this excluding iExcept.

Reimplemented in csl::Vector.

◆ getSubVectorial() [2/3]

Expr csl::Abstract::getSubVectorial	(	int	iExcept,
		int	jExcept
	)		const

virtual

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

Parameters

iExcept	Element of the first axis to ignore.
jExcept	Element of the second axis to ignore.

Returns: The part of *this excluding iExcept.

Reimplemented in csl::Matrix.

◆ getSubVectorial() [3/3]

virtual Expr csl::Abstract::getSubVectorial ( const std::vector< int > & exceptions ) const

virtual

Allows to pick a part of a Vectorial expression, excluding the iExcept^{th} element.

Parameters

iExcept Element to ignore.

Returns: The part of *this excluding iExcept.

Reimplemented in csl::AbstractVectorial.

◆ getSum()

Expr csl::Abstract::getSum ( ) const

virtual

Calculates and returns the sum of all elements in the Vectorial object.

Returns: The sum of all elements.

Reimplemented in csl::AbstractVectorial.

◆ getTerm()

std::optional< Expr > csl::Abstract::getTerm ( ) const

virtual

This function returns the same expression as *this but amputated of its numerical factor. Example: (4*cos(x) -> cos(x)).

Returns: The term without numerical factor corresponding to *this.

Reimplemented in csl::Pow, csl::Prod, csl::Sum, csl::AbstractNumerical, and csl::AbstractBuildingBlock.

◆ getType()

virtual csl::Type csl::Abstract::getType ( ) const

pure virtual

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)

Implemented in csl::DiracDelta, csl::Factorial, csl::ATanh, csl::ASinh, csl::ACosh, csl::Tanh, csl::Sinh, csl::Cosh, csl::TensorElement, csl::Angle, csl::Integral, csl::ATan, csl::Derivative, csl::ASin, csl::ACos, csl::Pow, csl::Tan, csl::Imaginary, csl::Complex, csl::Sin, csl::IntFactorial, csl::AbstractMultiFunc, csl::Prod, csl::HighDTensor, csl::Cos, csl::IntFraction, csl::TDerivativeElement, csl::VectorIntegral, csl::Matrix, csl::Log, csl::Polynomial, csl::AbstractDuoFunc, csl::Variable, csl::TensorFieldElement, csl::Vector, csl::Float, csl::ScalarIntegral, csl::Exp, csl::ScalarField, csl::Commutator, csl::Constant, csl::Integer, csl::ImaginaryPart, csl::Arbitrary, csl::NumericalEval, csl::Sum, csl::Abs, csl::RealPart, and csl::Scalar.

◆ getValue()

long double csl::Abstract::getValue ( ) const

virtual

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.

Returns: The value of the expression.

Reimplemented in csl::IntFactorial, csl::Variable, csl::Constant, and csl::NumericalEval.

◆ getValued()

bool csl::Abstract::getValued ( ) const

virtual

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).

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

Reimplemented in csl::Variable, and csl::Constant.

◆ getVariable()

Expr csl::Abstract::getVariable ( ) const

virtual

Accessor to the variable that defines certain types of expressions.

Returns: variable.

Reimplemented in csl::Integral, csl::Derivative, csl::VectorIntegral, csl::Polynomial, and csl::ScalarIntegral.

◆ getVectorArgument()

const csl::vector_expr & csl::Abstract::getVectorArgument ( ) const

virtual

Allows to get the entire std::vector of arguments of the expression.

Warning: This function must not be called for building blocks, one must check first that the expression has arguments.

Returns: The std::vector of argument.

Reimplemented in csl::AbstractMultiFunc, and csl::AbstractVectorial.

◆ getVectorialModulus()

Expr csl::Abstract::getVectorialModulus ( ) const

virtual

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+}.

Returns: The vectorial modulus of the expression.

Reimplemented in csl::AbstractVectorial.

◆ hasContractionProperty()

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

virtual

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 in csl::TensorElement.

◆ insert()

void csl::Abstract::insert	(	const Expr &	expr,
		bool	side = `1`
	)

virtual

Inserts an expression in a sum or a product.

Allows to insert an element in a sum or product without comparing all existing terms. This saves time when inserting element by element. The side parameter allows to insert to the left (side = 0) or to the right (side = 1) in products (useful when considering non commutating expressions.

Parameters

expr	Expression to insert.
side	Side of insertion for Prod expressions.

Reimplemented in csl::Prod, and csl::Sum.

◆ inverseMatrix()

Expr csl::Abstract::inverseMatrix ( ) const

virtual

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

Returns: A^{-1} for a matrix (2D) A if det(A) != 0.; 0 else

Reimplemented in csl::Matrix.

◆ isAnOperator()

bool csl::Abstract::isAnOperator ( ) const

virtual

Tells if the expression is an operator (like a derivetive operator).

Returns: True if the expression is an Operator.; False else.

◆ isBuildingBlock()

bool csl::Abstract::isBuildingBlock ( ) const

virtual

Tells if the expression is a Building Block or not.

Building blocks are derived classes that cannot contain further expressions, i.e. expressions that are the leafs of the recursive tree reprensent mathematical expressions: numerical or pure literal objects (variable, constant etc).

Returns: True if *this is a Building Block.; False else.

Reimplemented in csl::AbstractBuildingBlock.

◆ isEmpty()

bool csl::Abstract::isEmpty ( ) const

virtual

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.

Returns: True if the Derivative or Integral awaits an argument.; False else.

◆ isIndexed()

bool csl::Abstract::isIndexed ( ) const

virtual

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

Reimplemented in csl::IProd, csl::ISum, csl::TensorElement, csl::AbstractMultiFunc, csl::Prod, csl::VectorIntegral, csl::AbstractDuoFunc, csl::Polynomial, csl::TensorFieldElement, csl::AbstractFunc, csl::Sum, and csl::Scalar.

◆ isInteger()

bool csl::Abstract::isInteger ( ) const

virtual

Tells if the expression is an integer. Either an Integer object directly, or a Float that has an integer value.

Returns: True if *this is an Integer or a Float with integer value.; False else.

Reimplemented in csl::Float, and csl::Integer.

◆ isPolynomial()

int csl::Abstract::isPolynomial ( Expr_info expr ) const

virtual

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.

Parameters

expr	Variable of the supposed mononomial.

Returns: The order of the exponent if there is one (n in the example).; -1 else.

Reimplemented in csl::Pow, csl::AbstractMultiFunc, csl::Prod, csl::AbstractDuoFunc, csl::AbstractFunc, and csl::AbstractElement.

◆ matchShape()

bool csl::Abstract::matchShape	(	Expr_info	expr,
		bool	exact = `false`
	)		const

virtual

In the case of a vectorial-type expression, this function checks if the shape of expr matches itself.

If exact is true, the function search an exact match i.e. either the two shapes are exactly equal or one of the two objects is a scalar. If exact is false, this function only search for a possible dot product between the two expressions, and see if the last axis of *this matches the first of expr (or if one of the two objects is scalar also). Then, a product _k (*this)[i,j,...,k]*expr[k,l,m,...] is possible.

Parameters

expr	Expression of which we compare the shape.
exact	Boolean than specifies if we need an exact match or not.

Returns: True if the two shapes correspond.; False else.

Reimplemented in csl::AbstractVectorial.

◆ multiplication_own()

Expr csl::Abstract::multiplication_own	(	const Expr &	expr,
		bool	side = `1`
	)		const

virtual

Contains implementation of special multiplication for Numerical- and Vectorial-types.

Parameters

expr	Right operrand of the product.

Returns: The product of the two operands.

Reimplemented in csl::Complex, csl::IntFraction, csl::Polynomial, csl::Float, csl::AbstractVectorial, csl::Integer, and csl::NumericalEval.

◆ operator!=() [1/3]

bool csl::Abstract::operator!= ( int t_value ) const

virtual

Returns: False if the expression is valued and is equal to t_value.; True else.

◆ operator!=() [2/3]

bool csl::Abstract::operator!= ( double t_value ) const

virtual

Returns: False if the expression is valued and is equal to t_value.; True else.

◆ operator!=() [3/3]

bool csl::Abstract::operator!= ( const Expr_c & expr ) const

inline

Compares the Abstract with another.

Parameters

expr	Abstract to compare.

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

◆ operator<() [1/2]

virtual bool csl::Abstract::operator< ( Expr_info expr ) const

pure virtual

Compares the simplicity of the expression to another.

Parameters

expr	Expression to compare.

Returns: False if expr is simpler or equivalent.; True else.

Implemented in csl::AbstractMultiFunc, csl::AbstractDuoFunc, and csl::Scalar.

◆ operator<() [2/2]

bool csl::Abstract::operator< ( const Expr_c & expr ) const

inline

Compares the simplicity of the expression to another.

Parameters

expr	Expression to compare.

Returns: False if expr is simpler or equivalent.; True else.

◆ operator<=()

bool csl::Abstract::operator<= ( const Expr_c & expr ) const

inline

Compares the simplicity of the expression to another.

Parameters

expr	Expression to compare.

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

◆ operator=()

void csl::Abstract::operator= ( double t_value )

virtual

Equivalent to the setValue() function.

Parameters

t_value The new value of the expression.

Reimplemented in csl::IntFraction, csl::Variable, csl::Float, and csl::Constant.

◆ operator==() [1/3]

bool csl::Abstract::operator== ( int t_value ) const

virtual

Returns: True if the expression is valued and is equal to t_value.; False else.

◆ operator==() [2/3]

bool csl::Abstract::operator== ( double t_value ) const

virtual

Returns: True if the expression is valued and is equal to t_value.; False else.

◆ operator==() [3/3]

virtual bool csl::Abstract::operator== ( Expr_info expr ) const

pure virtual

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.

Implemented in csl::DiracDelta, csl::IProd, csl::ISum, csl::TensorElement, csl::Angle, csl::Integral, csl::Derivative, csl::Pow, csl::Imaginary, csl::Complex, csl::Prod, csl::IntFactorial, csl::TDerivativeElement, csl::IntFraction, csl::Variable, csl::VectorIntegral, csl::Polynomial, csl::Float, csl::TensorFieldElement, csl::ScalarIntegral, csl::AbstractVectorial, csl::AbstractFunc, csl::Constant, csl::Sum, csl::Integer, csl::ScalarField, csl::Commutator, csl::ImaginaryPart, csl::NumericalEval, csl::Complexified, csl::Arbitrary, csl::RealPart, and csl::Scalar.

◆ operator>()

bool csl::Abstract::operator> ( Expr_info expr ) const

inline

Compares the simplicity of the expression to another.

Parameters

expr	Expression to compare.

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

◆ operator>=()

bool csl::Abstract::operator>= ( Expr_info expr ) const

inline

Compares the simplicity of the expression to another.

Parameters

expr	Expression to compare.

Returns: True if expr is simpler or equivalent.; False else.

◆ operator[]() [1/2]

Expr const & csl::Abstract::operator[] ( int iArg ) const

virtual

Access operator for multi-argument expressions, equivalent to the function getArgument().

Parameters

iArg	Index of the argument to get.

Returns: argument[iArg].

Reimplemented in csl::AbstractMultiFunc, csl::TDerivativeElement, csl::AbstractDuoFunc, csl::AbstractVectorial, and csl::AbstractFunc.

◆ operator[]() [2/2]

Expr & csl::Abstract::operator[] ( int iArg )

virtual

Access operator for multi-argument expressions, returns a reference so this function is not const.

Parameters

iArg	Index of the argument to get.

Returns: A reference to argument[iArg].

Reimplemented in csl::AbstractMultiFunc, csl::TDerivativeElement, csl::AbstractDuoFunc, csl::AbstractVectorial, and csl::AbstractFunc.

◆ permut()

int csl::Abstract::permut	(	int	i1,
		int	i2
	)

virtual

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.

Parameters

i1	Position of the first index.
i2	Position of the second index.

Returns: 1 if the permutation **(i1,i2) is symmetric**.; -1 if the permutation **(i1,i2) is anti-symmetric**.; 0 else (and do not permut the two indices).

◆ print()

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

pure virtual

Displays the abstract in standard output.

Parameters

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

Implemented in csl::DiracDelta, csl::Factorial, csl::ATanh, csl::ASinh, csl::ACosh, csl::Tanh, csl::Sinh, csl::TensorElement, csl::Cosh, csl::Angle, csl::Integral, csl::ATan, csl::Derivative, csl::ASin, csl::ACos, csl::Pow, csl::Tan, csl::Imaginary, csl::Complex, csl::Sin, csl::Prod, csl::IntFactorial, csl::Cos, csl::IntFraction, csl::TDerivativeElement, csl::VectorIntegral, csl::Variable, csl::Log, csl::Polynomial, csl::TensorFieldElement, csl::Float, csl::ScalarIntegral, csl::Exp, csl::Constant, csl::ScalarField, csl::Integer, csl::Commutator, csl::ImaginaryPart, csl::Sum, csl::Arbitrary, csl::NumericalEval, csl::Abs, csl::AbstractVectorial, csl::RealPart, and csl::Scalar.

◆ printExplicit()

void csl::Abstract::printExplicit ( int mode = 0 ) const

Displays explicitely the expression, with types of each component. This function is only used for debug.

Parameters

mode	Mode of printing.

◆ printLaTeX()

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

virtual

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 in csl::DiracDelta, csl::Factorial, csl::ATanh, csl::ASinh, csl::ACosh, csl::Tanh, csl::Sinh, csl::TensorElement, csl::Cosh, csl::Angle, csl::Integral, csl::ATan, csl::Derivative, csl::ASin, csl::ACos, csl::Pow, csl::Tan, csl::Imaginary, csl::Complex, csl::Sin, csl::Prod, csl::IntFactorial, csl::Cos, csl::IntFraction, csl::TDerivativeElement, csl::VectorIntegral, csl::Variable, csl::Log, csl::Polynomial, csl::TensorFieldElement, csl::Float, csl::ScalarIntegral, csl::Exp, csl::Constant, csl::ScalarField, csl::Integer, csl::Commutator, csl::Sum, csl::ImaginaryPart, csl::Arbitrary, csl::NumericalEval, csl::Abs, csl::AbstractVectorial, csl::RealPart, and csl::Scalar.

◆ removeProperty()

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

virtual

Removes a property to the object.

Parameters

property Property to remove from props.

Reimplemented in csl::TensorElement, and csl::AbstractLiteral.

◆ replaceIndex()

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

virtual

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 in csl::IProd, csl::ISum, csl::TensorElement, csl::AbstractMultiFunc, csl::TDerivativeElement, csl::AbstractDuoFunc, and csl::AbstractFunc.

◆ setArgument() [1/2]

void csl::Abstract::setArgument	(	const Expr &	expr,
		int	iArg = `0`
	)

virtual

Sets the argument at position iArg (default=0).

Parameters

expr	Expression that replaces the argument.
iArg	the position of the argument to change.

Reimplemented in csl::IProd, csl::AbstractMultiFunc, csl::TDerivativeElement, csl::AbstractDuoFunc, csl::AbstractVectorial, and csl::AbstractFunc.

◆ setArgument() [2/2]

virtual void csl::Abstract::setArgument	(	const Expr &	expr,
		const std::vector< int > &	indices
	)

virtual

Sets the argument at position {i,j,...} for multi-dimensions expressions.

Parameters

expr	Expression that replaces the argument.
indices	An std::vector containing the series of indices corresponding to the argument to replace.

Reimplemented in csl::AbstractVectorial.

◆ setCommutable()

void csl::Abstract::setCommutable ( bool t_commutable )

virtual

Allows the abstract to commute or not.

Parameters

t_commutable Must be true if the abstract can commute.

Reimplemented in csl::Variable, csl::Constant, and csl::AbstractElement.

◆ setIndexStructure()

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

virtual

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 in csl::TensorElement, and csl::TDerivativeElement.

◆ setName()

void csl::Abstract::setName ( const std::string & t_name )

virtual

Change the name of the abstract.

Parameters

t_name Replaces name.

Reimplemented in csl::Variable, csl::Constant, and csl::AbstractElement.

◆ setOperand()

void csl::Abstract::setOperand ( const Expr & operand )

virtual

Sets the operand of an operator.

Parameters

operand New operand.

Reimplemented in csl::Integral, csl::Derivative, csl::TDerivativeElement, csl::AbstractIntegral, csl::ImaginaryPart, and csl::RealPart.

◆ setOperandPrivate()

void csl::Abstract::setOperandPrivate	(	const Expr &	operand,
		bool	leaveEmpty
	)

virtual

Sets the operand of an operator.

Parameters

operand	New operand.
leaveEmpty	Boolean that tells if the operator must stay empty (if true, then it will again apply later) or not (if false).

◆ setVectorArgument()

void csl::Abstract::setVectorArgument ( const csl::vector_expr & t_argument )

virtual

Replaced the entire std::vector of argument.

Parameters

t_argument std::vector of expressions to copy.

Reimplemented in csl::AbstractMultiFunc, and csl::AbstractVectorial.

◆ suppressExponent()

std::optional< Expr > csl::Abstract::suppressExponent	(	Expr const &	factor,
		Expr const &	exponent
	)		const

virtual

Returns the expression where the factor factor^exponent has been suppressed.

This function works the same manner as getExponents().

Parameters

factor	Factor to suppress.
exponent	Exponent of the factor to suppress.

Returns: The modified expression if the factor has been found.; std::nullopt else.

Note: This function may replace in the future the functions askTerm() and suppressTerm().

Reimplemented in csl::Pow, and csl::Prod.

◆ suppressTerm()

Expr csl::Abstract::suppressTerm ( Expr_info expr ) const

virtual

Remove a factor from an expr, that must have been determined before.

Parameters

factor Expression to remove

Returns: The expr in which factor has been removed

Reimplemented in csl::IProd, csl::Integral, csl::Pow, csl::Prod, csl::Sum, and csl::AbstractIntegral.

◆ symmetrise()

Expr csl::Abstract::symmetrise ( ) const

virtual

Calculates and returns the symmetrization of a 2D matrix.

Returns: 1/2*(A + A^T) for a matrix (2D) A.

Reimplemented in csl::Matrix, and csl::AbstractVectorial.

◆ tensordot()

Expr csl::Abstract::tensordot ( const Expr & expr ) const

virtual

Returns the tensordot of two Vectorial expressions.

Parameters

expr	The right operand of the tensordot

Returns: The tensor dot of *this and expr.

Reimplemented in csl::AbstractVectorial.

◆ trace() [1/2]

Expr csl::Abstract::trace ( ) const

virtual

Returns: i A{ii} for a square matrix A.; A for a scalar A.; 0 else.

Reimplemented in csl::Matrix.

◆ trace() [2/2]

Expr csl::Abstract::trace	(	int	axis1,
		int	axis2
	)		const

virtual

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.

Parameters

axis1	First axis to contract.
axis2	Second axis to contract.

Returns: the trace over axis axis1 and axis2.

Reimplemented in csl::AbstractVectorial.

◆ transpose()

Expr csl::Abstract::transpose ( ) const

virtual

Calculates and returns the transpose of a 2D matrix.

Returns: A^T for a matrix (2D) A.

Reimplemented in csl::Matrix.

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

include/abstract.h
src/abstract.cpp

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ Abstract()

Member Function Documentation

◆ addAntiSymmetry()

◆ addition_own()

◆ addProperty()

◆ addSymmetry()

◆ antisymmetrise()

◆ applyOperator()

◆ askTerm()

◆ begin() [1/2]

◆ begin() [2/2]

◆ checkIndexStructure() [1/2]

◆ checkIndexStructure() [2/2]

◆ collect()

◆ commutesWith()

◆ compareWithDummy()

◆ contraction()

◆ dependsExplicitlyOn()

◆ dependsOn()

◆ derive()

◆ determinant()

◆ division_own()

◆ dot()

◆ end() [1/2]

◆ end() [2/2]

◆ evaluate()

◆ evaluateScalar()

◆ expand()

◆ expand_if()

◆ exponentiation_own()

◆ factor() [1/2]

◆ factor() [2/2]

◆ findSubExpression()

◆ getAlternateForms()

◆ getArgument() [1/2]

◆ getArgument() [2/2]

◆ getCommutable()

◆ getComplexArgument()

◆ getComplexConjugate()

◆ getComplexModulus()

◆ getContractedPair()

◆ getDenom()

◆ getDim()

◆ getExponents()

◆ getFactors()

◆ getFreeIndexStructure()

◆ getImaginaryPart()

◆ getIndex()

◆ getIndexStructure()

◆ getName()

◆ getNArgs()

◆ getNContractedPairs()

◆ getNFactor()

◆ getNIndices()

◆ getNum()

◆ getNumericalFactor()

◆ getOperand()

◆ getOrder()

◆ getParent()

◆ getParity()

◆ getPermutations()

◆ getPolynomialTerm()

◆ getPrimaryType()

◆ getProduct()

◆ getProperties()

◆ getRealPart()

◆ getRegularExpression()

◆ getShape()

◆ getSign()

◆ getSubVectorial() [1/3]

◆ getSubVectorial() [2/3]

◆ getSubVectorial() [3/3]

◆ getSum()

◆ getTerm()

◆ getType()

◆ getValue()