Handle numbers in expr. More...

#include <numerical.h>

Inheritance diagram for csl::Float:

Public Member Functions
	Float ()
	Default constructor. expanded = CSL_0;. More...

	Float (long double t_value)

csl::Type	getType () const override
	Returns the type corresponding to an object Float. More...

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

void	setValue (long double t_value) override
	Sets the value of the Float. More...

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

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

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

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

unique_Expr	copy_unique () const override

Expr	refresh () const override

Expr	multiplication_own (const Expr &expr, bool side=1) const override
	Multiplicates two numbers. More...

Expr	addition_own (const Expr &expr) const override
	Adds two pure Numbers. More...

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

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

std::optional< Expr >	derive (Expr_info expr) const override
	Derives the Float. More...

void	operator= (int t_value)
	Sets value to t_value. More...

void	operator= (double t_value) override
	Sets value to t_value. 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::AbstractNumerical
csl::PrimaryType	getPrimaryType () const override
	Gives the primary type of Abstract. More...

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

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

Expr	getNumericalFactor () const override
	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...

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

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

bool	dependsOn (Parent_info) const override

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

bool	dependsExplicitlyOn (Parent_info) const override

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

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

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

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

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

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

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

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

virtual	~Abstract ()
	Destructor.

Expr	self ()

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

virtual bool	getElementary () const

virtual bool	getAllDependencies () const

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

virtual int	getOrderOf (Expr_info expr) const

virtual bool	isArbitrary () const

virtual bool	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	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 Expr	deepCopy () 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 (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 int	getNFactor () const

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

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

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

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

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

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

virtual Expr	getImaginaryPart () const
	Evaluates the imaginary part 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 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	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 bool	operator== (int t_value) const

virtual bool	operator== (double t_value) const

virtual bool	operator!= (int t_value) const

virtual bool	operator!= (double t_value) const

int	testDummy (Expr_info expr) const

bool	operator== (const Expr_c &expr) const

bool	operator== (const Expr &expr) const

bool	operator== (const Abstract &other) const

bool	operator!= (Expr_info expr) const

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

bool	operator!= (const Expr &expr) const

bool	operator!= (const Abstract &other) const

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

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

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

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

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

bool	operator> (const Expr_c &expr) const

bool	operator<= (Expr_info expr) const

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

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

bool	operator>= (const Expr_c &expr) const

Protected Attributes
long double	value
	Value of the number.

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

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

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

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

Detailed Description

Handle numbers in expr.

Handle the same manner for now double or int values (in a double).

Constructor & Destructor Documentation

◆ Float() [1/2]

csl::Float::Float ( )

inline

Default constructor. expanded = CSL_0;.

Initialize value to 0.

◆ Float() [2/2]

csl::Float::Float ( long double t_value )

inlineexplicit

Initialize a Float with the value t_value.

Parameters

t_value double.

Member Function Documentation

◆ addition_own()

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

overridevirtual

Adds two pure Numbers.

If expr is not a Number, returns 0. Else returns a Number which value is equal to the sum of value and expr.value.

Parameters

expr	Other Number for the sum.

Returns: value+expr.evaluateScalar().

Reimplemented from csl::Abstract.

◆ derive()

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

overridevirtual

Derives the Float.

The derivative of a Float is always 0.

Parameters

expr	Argument of the derivation.

Returns: 0

Reimplemented from csl::Abstract.

◆ division_own()

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

overridevirtual

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 from csl::Abstract.

◆ evaluate()

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

overridevirtual

Evaluates the Abstract.

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

Returns: The abstract result of the evaluation.

Implements csl::Abstract.

◆ evaluateScalar()

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

overridevirtual

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 from csl::Abstract.

◆ exponentiation_own()

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

overridevirtual

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

Parameters

expr exponent.

Returns: The exponentiation of the two operands.

Reimplemented from csl::Abstract.

◆ getType()

csl::Type csl::Float::getType ( ) const

overridevirtual

Returns the type corresponding to an object Float.

Returns: 0

Implements csl::Abstract.

◆ isInteger()

bool csl::Float::isInteger ( ) const

overridevirtual

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 from csl::Abstract.

◆ multiplication_own()

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

overridevirtual

Multiplicates two numbers.

If expr is not a Number, returns 0. Else returns a Number which value is equal to the product of value and expr.value.

Parameters

expr	Other Number for the multiplication.

Returns: value*expr.evaluateScalar().

Reimplemented from csl::Abstract.

◆ operator=() [1/2]

void csl::Float::operator= ( int t_value )

Sets value to t_value.

Parameters

t_value

◆ operator=() [2/2]

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

overridevirtual

Sets value to t_value.

Parameters

t_value

Reimplemented from csl::Abstract.

◆ operator==()

bool csl::Float::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::Float::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::Float::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.

◆ setValue()

void csl::Float::setValue ( long double t_value )

overridevirtual

Sets the value of the Float.

Parameters

t_value New value for the Float.

Reimplemented from csl::Abstract.

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

include/numerical.h
src/numerical.cpp
src/simplification.cpp

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Float() [1/2]

◆ Float() [2/2]

Member Function Documentation

◆ addition_own()

◆ derive()

◆ division_own()

◆ evaluate()

◆ evaluateScalar()

◆ exponentiation_own()

◆ getType()

◆ isInteger()

◆ multiplication_own()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ print()

◆ printLaTeX()

◆ setValue()