Inheritance diagram for csl::VectorIntegral:

[legend]

Public Member Functions
	VectorIntegral (const Tensor &t_variables)

	VectorIntegral (const Expr &operand, const Tensor &t_variables)

	VectorIntegral (const Expr &operand, const Tensor &t_variable, bool t_empty)

	VectorIntegral (const Expr &operand, const Tensor &t_variable, const Expr &t_inf, const Expr &t_sup)

	VectorIntegral (const Tensor &t_variable, const Expr &t_inf, const Expr &t_sup)

	VectorIntegral (const Expr &operand, const Tensor &t_variable, bool t_empty, const Expr &t_inf, const Expr &t_sup)

	~VectorIntegral ()
	Destructor.

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

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

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

Parent_info	getParent_info () const override

void	setParent (const Parent &t_variable) 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...

unique_Expr	copy_unique () const override

Expr	deepCopy () const override

Expr	refresh () const override

Expr	deepRefresh () const override

bool	isIndexed () const override

bool	operatorAppliesOn (Expr_info expr) const override

IndexStructure	getIndexStructure () const override

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

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...

bool	operator< (const Abstract *expr) const override

Public Member Functions inherited from csl::AbstractIntegral
	AbstractIntegral (const Expr &operand)

	AbstractIntegral (const Expr &operand, bool t_empty)

	AbstractIntegral (const Expr &operand, const Expr &t_inf, const Expr &t_sup)

	AbstractIntegral (const Expr &operand, bool t_empty, const Expr &t_inf, const Expr &t_sup)

	~AbstractIntegral ()
	Destructor.

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

Expr	getSupBoundary () const override

Expr	getInfBoundary () const override

void	setSupBoundary (Expr const &t_inf) override

void	setInfBoundary (Expr const &t_sup) override

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

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

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

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

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

bool	dependsOn (const AbstractParent *parent) const override

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

Public Member Functions inherited from csl::Operator< AbstractFunc >
	Operator (Args &&...args)

bool	getCommutable () const override

bool	commutesWith (Expr_info other, int sign=-1) const override

bool	isAnOperator () const override

bool	isEmpty () const override

void	setEmpty (bool t_empty) override

void	setOperandPrivate (const Expr &operand, bool leaveEmpty) override

Expr	applyOperator (const Expr &expr, bool leaveEmpty=false) const override

std::optional< Expr >	expand (bool full=false, bool inplace=false) const override

std::optional< Expr >	expand_if (std::function< bool(Expr const &)> const &f, bool full=false, bool inplace=false) const override

Public Member Functions inherited from csl::AbstractFunc
	AbstractFunc ()
	Default constructor. More...

	AbstractFunc (const Expr &t_argument)

csl::PrimaryType	getPrimaryType () const override

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

bool	isIndexed () const override

size_t	size () const 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...

IndexStructure	getIndexStructure () const override

Tensor	getPoint () const override

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

Expr const &	getArgument (int iArg=0) const override
	Returns the argument of the function. More...

Expr &	getArgument (int iArg=0) override

bool	isReal () const override

bool	isPurelyImaginary () 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...

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

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

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

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

void	setArgument (const Expr &t_argument, int iArg=0) override
	Replaced the argument of the AbstractFunc. More...

virtual 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...

virtual std::optional< Expr >	replaceIndices (std::vector< csl::Index > const &oldIndices, std::vector< csl::Index > const &newIndices, bool refresh=true, bool flipped=false) const override

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

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

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

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

bool	dependsOn (const AbstractParent *parent) const override

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

bool	dependsExplicitlyOn (Parent_info expr) const override

int	isPolynomial (Expr_info expr) 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 >	evaluate (csl::eval::mode user_mode=csl::eval::base) const override
	Evaluates the function after evaluating the argument. More...

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

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

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::Abstract
	Abstract ()
	Default Constructor. More...

virtual	~Abstract ()
	Destructor.

Expr	self ()

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 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	getElementary () const

virtual bool	getAllDependencies () const

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 const std::vector< Equation * > &	getProperties () 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 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 (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 int	getOrder () const
	Accessor to the order (integer) that defines certain types of expressions. More...

virtual int	getSign () const

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

virtual int	getNIndices () const

virtual Index	getIndex (int i=0) const

virtual void	resetIndexStructure ()

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

virtual const IndexStructure &	getIndexStructureView () const

virtual IndexStructure &	getIndexStructureView ()

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

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 (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 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 >	suppressExponent (Expr const &factor, Expr const &exponent) const
	Returns the expression where the factor factor^exponent has been suppressed. 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	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

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 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 Attributes
Tensor	variables

Protected Attributes inherited from csl::AbstractIntegral
Expr	inf

Expr	sup

Protected Attributes inherited from csl::Operator< AbstractFunc >
bool	empty

Protected Attributes inherited from csl::AbstractFunc
Expr	argument
	Argument of the considered function.

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)

Protected Member Functions inherited from csl::AbstractFunc
Expr	evalNumerical (Expr const &argument) const

Member Function Documentation

◆ compareWithDummy()

bool csl::VectorIntegral::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.

◆ getIndexStructure()

IndexStructure csl::VectorIntegral::getIndexStructure ( ) const

overridevirtual

Returns: The index structure of the Indicial expression

Reimplemented from csl::Abstract.

◆ getParent()

Parent csl::VectorIntegral::getParent ( ) const

overridevirtual

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 from csl::Abstract.

◆ getType()

csl::Type csl::VectorIntegral::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.

◆ getVariable()

Expr csl::VectorIntegral::getVariable ( ) const

overridevirtual

Accessor to the variable that defines certain types of expressions.

Returns: variable.

Reimplemented from csl::Abstract.

◆ isIndexed()

bool csl::VectorIntegral::isIndexed ( ) const

overridevirtual

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

Reimplemented from csl::Abstract.

◆ operator==()

bool csl::VectorIntegral::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.

Implements csl::Abstract.

◆ print()

void csl::VectorIntegral::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.

◆ printLaTeX()

string csl::VectorIntegral::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.

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

include/pseudoIntegral.h
src/pseudoIntegral.cpp
src/simplification.cpp

Public Member Functions

Protected Attributes

Additional Inherited Members

Member Function Documentation

◆ compareWithDummy()

◆ getIndexStructure()

◆ getParent()

◆ getType()

◆ getVariable()

◆ isIndexed()

◆ operator==()

◆ print()

◆ printLaTeX()