This class represents a univariate polynomial with coefficients of an arbitrary type. More...

#include <UnivariatePolynomial.h>

Inheritance diagram for carl::UnivariatePolynomial< Coefficient >:

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Collaboration diagram for carl::UnivariatePolynomial< Coefficient >:

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Public Types
using	NumberType = typename UnderlyingNumberType< Coefficient >::type
	The number type that is ultimately used for the coefficients. More...

using	IntNumberType = typename IntegralType< NumberType >::type
	The integral type that belongs to the number type. More...

using	CACHE = void

using	CoeffType = Coefficient

using	PolyType = UnivariatePolynomial< Coefficient >

using	RootType = IntRepRealAlgebraicNumber< NumberType >

Public Member Functions
	UnivariatePolynomial ()=delete
	Default constructor shall not exist. More...

	UnivariatePolynomial (const UnivariatePolynomial &p)
	Copy constructor. More...

	UnivariatePolynomial (UnivariatePolynomial &&p) noexcept
	Move constructor. More...

UnivariatePolynomial &	operator= (const UnivariatePolynomial &p)
	Copy assignment operator. More...

UnivariatePolynomial &	operator= (UnivariatePolynomial &&p) noexcept
	Move assignment operator. More...

	UnivariatePolynomial (Variable mainVar)
	Construct a zero polynomial with the given main variable. More...

	UnivariatePolynomial (Variable mainVar, const Coefficient &coeff, std::size_t degree=0)
	Construct $coeff \cdot mainVar^{degree}$ . More...

	UnivariatePolynomial (Variable mainVar, std::initializer_list< Coefficient > coefficients)
	Construct polynomial with the given coefficients. More...

template<typename C = Coefficient, DisableIf< std::is_same< C, typename UnderlyingNumberType< C >::type >> = dummy>
	UnivariatePolynomial (Variable mainVar, std::initializer_list< typename UnderlyingNumberType< C >::type > coefficients)
	Construct polynomial with the given coefficients from the underlying number type of the coefficient type. More...

	UnivariatePolynomial (Variable mainVar, const std::vector< Coefficient > &coefficients)
	Construct polynomial with the given coefficients. More...

	UnivariatePolynomial (Variable mainVar, std::vector< Coefficient > &&coefficients)
	Construct polynomial with the given coefficients, moving the coefficients. More...

	UnivariatePolynomial (Variable mainVar, const std::map< uint, Coefficient > &coefficients)
	Construct polynomial with the given coefficients. More...

	~UnivariatePolynomial ()=default
	Destructor. More...

bool	is_zero () const
	Checks if the polynomial is equal to zero. More...

bool	is_one () const
	Checks if the polynomial is equal to one. More...

UnivariatePolynomial	one () const
	Creates a polynomial of value one with the same main variable. More...

const Coefficient &	lcoeff () const
	Returns the leading coefficient. More...

const Coefficient &	tcoeff () const
	Returns the trailing coefficient. More...

bool	is_constant () const
	Checks whether the polynomial is constant with respect to the main variable. More...

bool	is_linear_in_main_var () const

bool	is_number () const
	Checks whether the polynomial is only a number. More...

NumberType	constant_part () const
	Returns the constant part of this polynomial. More...

bool	is_univariate () const
	Checks if the polynomial is univariate, that means if only one variable occurs. More...

uint	degree () const
	Get the maximal exponent of the main variable. More...

uint	total_degree () const
	Returns the total degree of the polynomial, that is the maximum degree of any monomial. More...

void	truncate ()
	Removes the leading term from the polynomial. More...

const std::vector< Coefficient > &	coefficients () const &
	Retrieves the coefficients defining this polynomial. More...

std::vector< Coefficient > &	coefficients () &
	Returns the coefficients as non-const reference. More...

std::vector< Coefficient > &&	coefficients () &&
	Returns the coefficients as rvalue. The polynomial may be in an undefined state afterwards! More...

Variable	main_var () const
	Retrieves the main variable of this polynomial. More...

bool	has (Variable v) const
	Checks if the given variable occurs in the polynomial. More...

template<typename C = Coefficient, EnableIf< is_subset_of_rationals_type< C >> = dummy>
Coefficient	coprime_factor () const
	Calculates a factor that would make the coefficients of this polynomial coprime integers. More...

template<typename C = Coefficient, DisableIf< is_subset_of_rationals_type< C >> = dummy>
UnderlyingNumberType< Coefficient >::type	coprime_factor () const

template<typename C = Coefficient, EnableIf< is_subset_of_rationals_type< C >> = dummy>
UnivariatePolynomial< typename IntegralType< Coefficient >::type >	coprime_coefficients () const
	Constructs a new polynomial that is scaled such that the coefficients are coprime. More...

template<typename C = Coefficient, DisableIf< is_subset_of_rationals_type< C >> = dummy>
UnivariatePolynomial< Coefficient >	coprime_coefficients () const

template<typename C = Coefficient, EnableIf< is_subset_of_rationals_type< C >> = dummy>
UnivariatePolynomial< typename IntegralType< Coefficient >::type >	coprime_coefficients_sign_preserving () const

template<typename C = Coefficient, DisableIf< is_subset_of_rationals_type< C >> = dummy>
UnivariatePolynomial< Coefficient >	coprime_coefficients_sign_preserving () const

bool	is_normal () const
	Checks whether the polynomial is unit normal. More...

UnivariatePolynomial	normalized () const
	The normal part of a polynomial is the polynomial divided by the unit part. More...

Coefficient	unit_part () const
	The unit part of a polynomial over a field is its leading coefficient for nonzero polynomials, and one for zero polynomials. More...

UnivariatePolynomial	negate_variable () const
	Constructs a new polynomial `q` such that where `p` is this polynomial. More...

UnivariatePolynomial	reverse_coefficients () const
	Reverse coefficients safely. More...

bool	divides (const UnivariatePolynomial &divisor) const
	Checks if this polynomial is divisible by the given divisor, that is if the remainder is zero. More...

UnivariatePolynomial &	mod (const Coefficient &modulus)
	Replaces every coefficient `c` by `c mod modulus`. More...

UnivariatePolynomial	mod (const Coefficient &modulus) const
	Constructs a new polynomial where every coefficient `c` is replaced by `c mod modulus`. More...

UnivariatePolynomial	pow (std::size_t exp) const
	Returns this polynomial to the given power. More...

Coefficient	evaluate (const Coefficient &value) const

carl::Sign	sgn (const Coefficient &value) const
	Calculates the sign of the polynomial at some point. More...

template<typename SubstitutionType , typename C = Coefficient, EnableIf< is_instantiation_of< MultivariatePolynomial, C >> = dummy>
UnivariatePolynomial< Coefficient >	evaluateCoefficient (const std::map< Variable, SubstitutionType > &) const

template<typename SubstitutionType , typename C = Coefficient, DisableIf< is_instantiation_of< MultivariatePolynomial, C >> = dummy>
UnivariatePolynomial< Coefficient >	evaluateCoefficient (const std::map< Variable, SubstitutionType > &) const

template<typename T = Coefficient, EnableIf< has_normalize< T >> = dummy>
UnivariatePolynomial &	normalizeCoefficients ()

template<typename T = Coefficient, DisableIf< has_normalize< T >> = dummy>
UnivariatePolynomial &	normalizeCoefficients ()

template<typename C = Coefficient, EnableIf< is_instantiation_of< GFNumber, C >> = dummy>
UnivariatePolynomial< typename IntegralType< Coefficient >::type >	to_integer_domain () const
	Works only from rationals, if the numbers are already integers. More...

template<typename C = Coefficient, DisableIf< is_instantiation_of< GFNumber, C >> = dummy>
UnivariatePolynomial< typename IntegralType< Coefficient >::type >	to_integer_domain () const

UnivariatePolynomial< GFNumber< typename IntegralType< Coefficient >::type > >	toFiniteDomain (const GaloisField< typename IntegralType< Coefficient >::type > *galoisField) const

template<typename C = Coefficient, DisableIf< is_number_type< C >> = dummy>
UnivariatePolynomial< NumberType >	toNumberCoefficients () const
	Asserts that is_univariate() is true. More...

template<typename NewCoeff >
UnivariatePolynomial< NewCoeff >	convert () const

template<typename NewCoeff >
UnivariatePolynomial< NewCoeff >	convert (const std::function< NewCoeff(const Coefficient &)> &f) const

NumberType	numeric_content (std::size_t i) const
	Returns the numeric content part of the i'th coefficient. More...

NumberType	numeric_unit () const
	Returns the numeric unit part of the polynomial. More...

template<typename N = NumberType, EnableIf< is_subset_of_rationals_type< N >> = dummy>
UnderlyingNumberType< Coefficient >::type	numeric_content () const
	Obtains the numeric content part of this polynomial. More...

template<typename C = Coefficient, EnableIf< is_number_type< C >> = dummy>
IntNumberType	main_denom () const
	Compute the main denominator of all numeric coefficients of this polynomial. More...

template<typename C = Coefficient, DisableIf< is_number_type< C >> = dummy>
IntNumberType	main_denom () const

Coefficient	synthetic_division (const Coefficient &zeroOfDivisor)

bool	zero_is_root () const
	Checks if zero is a real root of this polynomial. More...

bool	less (const UnivariatePolynomial< Coefficient > &rhs, const PolynomialComparisonOrder &order=PolynomialComparisonOrder::Default) const

UnivariatePolynomial	operator- () const

template<typename C = Coefficient, EnableIf< is_number_type< C >> = dummy>
bool	is_consistent () const
	Asserts that this polynomial over numeric coefficients complies with the requirements and assumptions for UnivariatePolynomial objects. More...

template<typename C = Coefficient, DisableIf< is_number_type< C >> = dummy>
bool	is_consistent () const
	Asserts that this polynomial over polynomial coefficients complies with the requirements and assumptions for UnivariatePolynomial objects. More...

void	strip_leading_zeroes ()

In-place addition operators
UnivariatePolynomial &	operator+= (const Coefficient &rhs)
	Add something to this polynomial and return the changed polynomial. More...

UnivariatePolynomial &	operator+= (const UnivariatePolynomial &rhs)
	Add something to this polynomial and return the changed polynomial. More...

In-place subtraction operators
UnivariatePolynomial &	operator-= (const Coefficient &rhs)
	Subtract something from this polynomial and return the changed polynomial. More...

UnivariatePolynomial &	operator-= (const UnivariatePolynomial &rhs)
	Subtract something from this polynomial and return the changed polynomial. More...

In-place multiplication operators
template<typename C = Coefficient, EnableIf< is_number_type< C >> = dummy>
UnivariatePolynomial &	operator*= (Variable rhs)
	Multiply this polynomial with something and return the changed polynomial. More...

template<typename C = Coefficient, DisableIf< is_number_type< C >> = dummy>
UnivariatePolynomial &	operator*= (Variable rhs)
	Multiply this polynomial with something and return the changed polynomial. More...

UnivariatePolynomial &	operator*= (const Coefficient &rhs)
	Multiply this polynomial with something and return the changed polynomial. More...

template<typename I = Coefficient, DisableIf< std::is_same< Coefficient, I >> ...>
UnivariatePolynomial &	operator*= (const typename IntegralType< Coefficient >::type &rhs)
	Multiply this polynomial with something and return the changed polynomial. More...

UnivariatePolynomial &	operator*= (const UnivariatePolynomial &rhs)
	Multiply this polynomial with something and return the changed polynomial. More...

In-place division operators
template<typename C = Coefficient, EnableIf< is_field_type< C >> = dummy>
UnivariatePolynomial &	operator/= (const Coefficient &rhs)
	Divide this polynomial by something and return the changed polynomial. More...

template<typename C = Coefficient, DisableIf< is_field_type< C >> = dummy>
UnivariatePolynomial &	operator/= (const Coefficient &rhs)
	Divide this polynomial by something and return the changed polynomial. More...

Private Attributes
Variable	mMainVar
	The main variable. More...

std::vector< Coefficient >	mCoefficients
	The coefficients. More...

Friends
template<class T >
class	UnivariatePolynomial
	Declare all instantiations of univariate polynomials as friends. More...

template<typename C >
bool	operator< (const UnivariatePolynomial< C > &lhs, const UnivariatePolynomial< C > &rhs)

template<typename C >
std::ostream &	operator<< (std::ostream &os, const UnivariatePolynomial< C > &rhs)
	Streaming operator for univariate polynomials. More...

Equality comparison operators
template<typename C >
bool	operator== (const C &lhs, const UnivariatePolynomial< C > &rhs)
	Checks if the two arguments are equal. More...

template<typename C >
bool	operator== (const UnivariatePolynomial< C > &lhs, const C &rhs)
	Checks if the two arguments are equal. More...

template<typename C >
bool	operator== (const UnivariatePolynomial< C > &lhs, const UnivariatePolynomial< C > &rhs)
	Checks if the two arguments are equal. More...

template<typename C >
bool	operator== (const UnivariatePolynomialPtr< C > &lhs, const UnivariatePolynomialPtr< C > &rhs)
	Checks if the two arguments are equal. More...

Inequality comparison operators
template<typename C >
bool	operator!= (const UnivariatePolynomial< C > &lhs, const UnivariatePolynomial< C > &rhs)
	Checks if the two arguments are not equal. More...

template<typename C >
bool	operator!= (const UnivariatePolynomialPtr< C > &lhs, const UnivariatePolynomialPtr< C > &rhs)
	Checks if the two arguments are not equal. More...

Addition operators
template<typename C >
UnivariatePolynomial< C >	operator+ (const UnivariatePolynomial< C > &lhs, const UnivariatePolynomial< C > &rhs)
	Performs an addition involving a polynomial. More...

template<typename C >
UnivariatePolynomial< C >	operator+ (const C &lhs, const UnivariatePolynomial< C > &rhs)
	Performs an addition involving a polynomial. More...

template<typename C >
UnivariatePolynomial< C >	operator+ (const UnivariatePolynomial< C > &lhs, const C &rhs)
	Performs an addition involving a polynomial. More...

Subtraction operators
template<typename C >
UnivariatePolynomial< C >	operator- (const UnivariatePolynomial< C > &lhs, const UnivariatePolynomial< C > &rhs)
	Performs a subtraction involving a polynomial. More...

template<typename C >
UnivariatePolynomial< C >	operator- (const C &lhs, const UnivariatePolynomial< C > &rhs)
	Performs a subtraction involving a polynomial. More...

template<typename C >
UnivariatePolynomial< C >	operator- (const UnivariatePolynomial< C > &lhs, const C &rhs)
	Performs a subtraction involving a polynomial. More...

Multiplication operators
template<typename C >
UnivariatePolynomial< C >	operator* (const UnivariatePolynomial< C > &lhs, const UnivariatePolynomial< C > &rhs)
	Perform a multiplication involving a polynomial. More...

template<typename C >
UnivariatePolynomial< C >	operator* (const UnivariatePolynomial< C > &lhs, Variable rhs)
	Perform a multiplication involving a polynomial. More...

template<typename C >
UnivariatePolynomial< C >	operator* (Variable lhs, const UnivariatePolynomial< C > &rhs)
	Perform a multiplication involving a polynomial. More...

template<typename C >
UnivariatePolynomial< C >	operator* (const C &lhs, const UnivariatePolynomial< C > &rhs)
	Perform a multiplication involving a polynomial. More...

template<typename C >
UnivariatePolynomial< C >	operator* (const UnivariatePolynomial< C > &lhs, const C &rhs)
	Perform a multiplication involving a polynomial. More...

template<typename C >
UnivariatePolynomial< C >	operator* (const IntegralTypeIfDifferent< C > &lhs, const UnivariatePolynomial< C > &rhs)
	Perform a multiplication involving a polynomial. More...

template<typename C >
UnivariatePolynomial< C >	operator* (const UnivariatePolynomial< C > &lhs, const IntegralTypeIfDifferent< C > &rhs)
	Perform a multiplication involving a polynomial. More...

template<typename C , typename O , typename P >
UnivariatePolynomial< MultivariatePolynomial< C, O, P > >	operator* (const UnivariatePolynomial< MultivariatePolynomial< C, O, P >> &lhs, const C &rhs)
	Perform a multiplication involving a polynomial. More...

template<typename C , typename O , typename P >
UnivariatePolynomial< MultivariatePolynomial< C, O, P > >	operator* (const C &lhs, const UnivariatePolynomial< MultivariatePolynomial< C, O, P >> &rhs)
	Perform a multiplication involving a polynomial. More...

Division operators
template<typename C >
UnivariatePolynomial< C >	operator/ (const UnivariatePolynomial< C > &lhs, const C &rhs)
	Perform a division involving a polynomial. More...

Detailed Description

template<typename Coefficient>
class carl::UnivariatePolynomial< Coefficient >

This class represents a univariate polynomial with coefficients of an arbitrary type.

A univariate polynomial is defined by a variable (the main variable) and the coefficients. The coefficients may be of any type. The intention is to use a numbers or polynomials as coefficients. If polynomials are used as coefficients, this can be seen as a multivariate polynomial with a distinguished main variable.

Most methods are specifically adapted for polynomial coefficients, if necessary.

Definition at line 61 of file UnivariatePolynomial.h.

Member Typedef Documentation

◆ CACHE

template<typename Coefficient >

using carl::UnivariatePolynomial< Coefficient >::CACHE = void

Definition at line 83 of file UnivariatePolynomial.h.

◆ CoeffType

template<typename Coefficient >

using carl::UnivariatePolynomial< Coefficient >::CoeffType = Coefficient

Definition at line 84 of file UnivariatePolynomial.h.

◆ IntNumberType

template<typename Coefficient >

using carl::UnivariatePolynomial< Coefficient >::IntNumberType = typename IntegralType<NumberType>::type

The integral type that belongs to the number type.

Definition at line 81 of file UnivariatePolynomial.h.

◆ NumberType

template<typename Coefficient >

using carl::UnivariatePolynomial< Coefficient >::NumberType = typename UnderlyingNumberType<Coefficient>::type

The number type that is ultimately used for the coefficients.

Definition at line 77 of file UnivariatePolynomial.h.

◆ PolyType

template<typename Coefficient >

using carl::UnivariatePolynomial< Coefficient >::PolyType = UnivariatePolynomial<Coefficient>

Definition at line 85 of file UnivariatePolynomial.h.

◆ RootType

template<typename Coefficient >

using carl::UnivariatePolynomial< Coefficient >::RootType = IntRepRealAlgebraicNumber<NumberType>

Definition at line 86 of file UnivariatePolynomial.h.

Constructor & Destructor Documentation

◆ UnivariatePolynomial() [1/10]

template<typename Coefficient >

carl::UnivariatePolynomial< Coefficient >::UnivariatePolynomial ( )

delete

Default constructor shall not exist.

Use UnivariatePolynomial(Variable) instead.

◆ UnivariatePolynomial() [2/10]

template<typename Coefficient >

carl::UnivariatePolynomial< Coefficient >::UnivariatePolynomial ( const UnivariatePolynomial< Coefficient > & p )

Copy constructor.

◆ UnivariatePolynomial() [3/10]

template<typename Coefficient >

carl::UnivariatePolynomial< Coefficient >::UnivariatePolynomial ( UnivariatePolynomial< Coefficient > && p )

noexcept

Move constructor.

◆ UnivariatePolynomial() [4/10]

template<typename Coefficient >

carl::UnivariatePolynomial< Coefficient >::UnivariatePolynomial ( Variable mainVar )

explicit

Construct a zero polynomial with the given main variable.

Parameters

mainVar New main variable.

◆ UnivariatePolynomial() [5/10]

template<typename Coefficient >

carl::UnivariatePolynomial< Coefficient >::UnivariatePolynomial	(	Variable	mainVar,
		const Coefficient &	coeff,
		std::size_t	degree = `0`
	)

Construct $coeff \cdot mainVar^{degree}$ .

Parameters

mainVar	New main variable.
coeff	Leading coefficient.
degree	Degree.

◆ UnivariatePolynomial() [6/10]

template<typename Coefficient >

carl::UnivariatePolynomial< Coefficient >::UnivariatePolynomial	(	Variable	mainVar,
		std::initializer_list< Coefficient >	coefficients
	)

Construct polynomial with the given coefficients.

Parameters

mainVar	New main variable.
coefficients	List of coefficients.

◆ UnivariatePolynomial() [7/10]

template<typename Coefficient >

template<typename C = Coefficient, DisableIf< std::is_same< C, typename UnderlyingNumberType< C >::type >> = dummy>

carl::UnivariatePolynomial< Coefficient >::UnivariatePolynomial	(	Variable	mainVar,
		std::initializer_list< typename UnderlyingNumberType< C >::type >	coefficients
	)

Construct polynomial with the given coefficients from the underlying number type of the coefficient type.

Parameters

mainVar	New main variable.
coefficients	List of coefficients.

◆ UnivariatePolynomial() [8/10]

template<typename Coefficient >

carl::UnivariatePolynomial< Coefficient >::UnivariatePolynomial	(	Variable	mainVar,
		const std::vector< Coefficient > &	coefficients
	)

Construct polynomial with the given coefficients.

Parameters

mainVar	New main variable.
coefficients	Vector of coefficients.

◆ UnivariatePolynomial() [9/10]

template<typename Coefficient >

carl::UnivariatePolynomial< Coefficient >::UnivariatePolynomial	(	Variable	mainVar,
		std::vector< Coefficient > &&	coefficients
	)

Construct polynomial with the given coefficients, moving the coefficients.

Parameters

mainVar	New main variable.
coefficients	Vector of coefficients.

◆ UnivariatePolynomial() [10/10]

template<typename Coefficient >

carl::UnivariatePolynomial< Coefficient >::UnivariatePolynomial	(	Variable	mainVar,
		const std::map< uint, Coefficient > &	coefficients
	)

Construct polynomial with the given coefficients.

Parameters

mainVar	New main variable.
coefficients	Assignment of degree to coefficients.

◆ ~UnivariatePolynomial()

template<typename Coefficient >

carl::UnivariatePolynomial< Coefficient >::~UnivariatePolynomial ( )

default

Destructor.

Member Function Documentation

◆ coefficients() [1/3]

template<typename Coefficient >

std::vector<Coefficient>& carl::UnivariatePolynomial< Coefficient >::coefficients ( ) &

inline

Returns the coefficients as non-const reference.

Definition at line 329 of file UnivariatePolynomial.h.

◆ coefficients() [2/3]

template<typename Coefficient >

std::vector<Coefficient>&& carl::UnivariatePolynomial< Coefficient >::coefficients ( ) &&

inline

Returns the coefficients as rvalue. The polynomial may be in an undefined state afterwards!

Definition at line 333 of file UnivariatePolynomial.h.

◆ coefficients() [3/3]

template<typename Coefficient >

const std::vector<Coefficient>& carl::UnivariatePolynomial< Coefficient >::coefficients ( ) const &

inline

Retrieves the coefficients defining this polynomial.

Returns: Coefficients.

Definition at line 325 of file UnivariatePolynomial.h.

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◆ constant_part()

template<typename Coefficient >

NumberType carl::UnivariatePolynomial< Coefficient >::constant_part ( ) const

inline

Returns the constant part of this polynomial.

Returns: Constant part.

Definition at line 253 of file UnivariatePolynomial.h.

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◆ convert() [1/2]

template<typename Coefficient >

template<typename NewCoeff >

UnivariatePolynomial<NewCoeff> carl::UnivariatePolynomial< Coefficient >::convert ( ) const

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◆ convert() [2/2]

template<typename Coefficient >

template<typename NewCoeff >

UnivariatePolynomial<NewCoeff> carl::UnivariatePolynomial< Coefficient >::convert ( const std::function< NewCoeff(const Coefficient &)> & f ) const

◆ coprime_coefficients() [1/2]

template<typename Coefficient >

template<typename C = Coefficient, EnableIf< is_subset_of_rationals_type< C >> = dummy>

UnivariatePolynomial<typename IntegralType<Coefficient>::type> carl::UnivariatePolynomial< Coefficient >::coprime_coefficients ( ) const

Constructs a new polynomial that is scaled such that the coefficients are coprime.

It is calculated by multiplying it with the coprime factor. By definition, this results in a polynomial with integral coefficients.

Returns: This polynomial multiplied with the coprime factor.

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◆ coprime_coefficients() [2/2]

template<typename Coefficient >

template<typename C = Coefficient, DisableIf< is_subset_of_rationals_type< C >> = dummy>

UnivariatePolynomial<Coefficient> carl::UnivariatePolynomial< Coefficient >::coprime_coefficients ( ) const

◆ coprime_coefficients_sign_preserving() [1/2]

template<typename Coefficient >

template<typename C = Coefficient, EnableIf< is_subset_of_rationals_type< C >> = dummy>

UnivariatePolynomial<typename IntegralType<Coefficient>::type> carl::UnivariatePolynomial< Coefficient >::coprime_coefficients_sign_preserving ( ) const

◆ coprime_coefficients_sign_preserving() [2/2]

template<typename Coefficient >

template<typename C = Coefficient, DisableIf< is_subset_of_rationals_type< C >> = dummy>

UnivariatePolynomial<Coefficient> carl::UnivariatePolynomial< Coefficient >::coprime_coefficients_sign_preserving ( ) const

◆ coprime_factor() [1/2]

template<typename Coefficient >

template<typename C = Coefficient, EnableIf< is_subset_of_rationals_type< C >> = dummy>

Coefficient carl::UnivariatePolynomial< Coefficient >::coprime_factor ( ) const

Calculates a factor that would make the coefficients of this polynomial coprime integers.

We consider a set of integers coprime, if they share no common factor. Technically, the coprime factor is where N is the set of the numerators and D is the set of the denominators of all coefficients.

Returns: Coprime factor of this polynomial.

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◆ coprime_factor() [2/2]

template<typename Coefficient >

template<typename C = Coefficient, DisableIf< is_subset_of_rationals_type< C >> = dummy>

UnderlyingNumberType<Coefficient>::type carl::UnivariatePolynomial< Coefficient >::coprime_factor ( ) const

◆ degree()

template<typename Coefficient >

uint carl::UnivariatePolynomial< Coefficient >::degree ( ) const

inline

Get the maximal exponent of the main variable.

As the degree of the zero polynomial is $-\infty$ , we assert that this polynomial is not zero. This must be checked by the caller before calling this method.

See also: [3], page 38

Returns: Degree.

Definition at line 284 of file UnivariatePolynomial.h.

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◆ divides()

template<typename Coefficient >

bool carl::UnivariatePolynomial< Coefficient >::divides ( const UnivariatePolynomial< Coefficient > & divisor ) const

Checks if this polynomial is divisible by the given divisor, that is if the remainder is zero.

Parameters

divisor Polynomial.

Returns: If divisor divides this polynomial.

◆ evaluate()

template<typename Coefficient >

Coefficient carl::UnivariatePolynomial< Coefficient >::evaluate ( const Coefficient & value ) const

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◆ evaluateCoefficient() [1/2]

template<typename Coefficient >

template<typename SubstitutionType , typename C = Coefficient, EnableIf< is_instantiation_of< MultivariatePolynomial, C >> = dummy>

UnivariatePolynomial<Coefficient> carl::UnivariatePolynomial< Coefficient >::evaluateCoefficient ( const std::map< Variable, SubstitutionType > & ) const

inline

Definition at line 482 of file UnivariatePolynomial.h.

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◆ evaluateCoefficient() [2/2]

template<typename Coefficient >

template<typename SubstitutionType , typename C = Coefficient, DisableIf< is_instantiation_of< MultivariatePolynomial, C >> = dummy>

UnivariatePolynomial<Coefficient> carl::UnivariatePolynomial< Coefficient >::evaluateCoefficient ( const std::map< Variable, SubstitutionType > & ) const

inline

Definition at line 487 of file UnivariatePolynomial.h.

◆ has()

template<typename Coefficient >

bool carl::UnivariatePolynomial< Coefficient >::has ( Variable v ) const

inline

Checks if the given variable occurs in the polynomial.

Parameters

v Variable.

Returns: If v occurs in the polynomial.

Definition at line 350 of file UnivariatePolynomial.h.

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◆ is_consistent() [1/2]

template<typename Coefficient >

template<typename C = Coefficient, EnableIf< is_number_type< C >> = dummy>

bool carl::UnivariatePolynomial< Coefficient >::is_consistent ( ) const

Asserts that this polynomial over numeric coefficients complies with the requirements and assumptions for UnivariatePolynomial objects.

The leading term is not zero.

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◆ is_consistent() [2/2]

template<typename Coefficient >

template<typename C = Coefficient, DisableIf< is_number_type< C >> = dummy>

bool carl::UnivariatePolynomial< Coefficient >::is_consistent ( ) const

Asserts that this polynomial over polynomial coefficients complies with the requirements and assumptions for UnivariatePolynomial objects.

The leading term is not zero.
The main variable does not occur in any coefficient.

◆ is_constant()

template<typename Coefficient >

bool carl::UnivariatePolynomial< Coefficient >::is_constant ( ) const

inline

Checks whether the polynomial is constant with respect to the main variable.

Returns: If polynomial is constant.

Definition at line 223 of file UnivariatePolynomial.h.

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◆ is_linear_in_main_var()

template<typename Coefficient >

bool carl::UnivariatePolynomial< Coefficient >::is_linear_in_main_var ( ) const

inline

Definition at line 229 of file UnivariatePolynomial.h.

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◆ is_normal()

template<typename Coefficient >

bool carl::UnivariatePolynomial< Coefficient >::is_normal ( ) const

Checks whether the polynomial is unit normal.

A polynomial is unit normal, if the leading coefficient is unit normal, that is if it is either one or minus one.

See also: [3], page 39

Returns: If polynomial is normal.

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◆ is_number()

template<typename Coefficient >

bool carl::UnivariatePolynomial< Coefficient >::is_number ( ) const

inline

Checks whether the polynomial is only a number.

Returns: If polynomial is a number.

Definition at line 239 of file UnivariatePolynomial.h.

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◆ is_one()

template<typename Coefficient >

bool carl::UnivariatePolynomial< Coefficient >::is_one ( ) const

inline

Checks if the polynomial is equal to one.

Returns: If polynomial is one.

Definition at line 177 of file UnivariatePolynomial.h.

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◆ is_univariate()

template<typename Coefficient >

bool carl::UnivariatePolynomial< Coefficient >::is_univariate ( ) const

inline

Checks if the polynomial is univariate, that means if only one variable occurs.

Returns: true.

Definition at line 267 of file UnivariatePolynomial.h.

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◆ is_zero()

template<typename Coefficient >

bool carl::UnivariatePolynomial< Coefficient >::is_zero ( ) const

inline

Checks if the polynomial is equal to zero.

Returns: If polynomial is zero.

Definition at line 167 of file UnivariatePolynomial.h.

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◆ lcoeff()

template<typename Coefficient >

const Coefficient& carl::UnivariatePolynomial< Coefficient >::lcoeff ( ) const

inline

Returns the leading coefficient.

Asserts, that the polynomial is not empty.

Returns: The leading coefficient.

Definition at line 203 of file UnivariatePolynomial.h.

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◆ less()

template<typename Coefficient >

bool carl::UnivariatePolynomial< Coefficient >::less	(	const UnivariatePolynomial< Coefficient > &	rhs,
		const PolynomialComparisonOrder &	order = `PolynomialComparisonOrder::Default`
	)		const

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◆ main_denom() [1/2]

template<typename Coefficient >

template<typename C = Coefficient, EnableIf< is_number_type< C >> = dummy>

IntNumberType carl::UnivariatePolynomial< Coefficient >::main_denom ( ) const

Compute the main denominator of all numeric coefficients of this polynomial.

This method only applies if the Coefficient type is a number.

Returns: the main denominator of all coefficients of this polynomial.

◆ main_denom() [2/2]

template<typename Coefficient >

template<typename C = Coefficient, DisableIf< is_number_type< C >> = dummy>

IntNumberType carl::UnivariatePolynomial< Coefficient >::main_denom ( ) const

◆ main_var()

template<typename Coefficient >

Variable carl::UnivariatePolynomial< Coefficient >::main_var ( ) const

inline

Retrieves the main variable of this polynomial.

Returns: Main variable.

Definition at line 341 of file UnivariatePolynomial.h.

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◆ mod() [1/2]

template<typename Coefficient >

UnivariatePolynomial& carl::UnivariatePolynomial< Coefficient >::mod ( const Coefficient & modulus )

Replaces every coefficient c by c mod modulus.

Parameters

modulus Modulus.

Returns: This.

◆ mod() [2/2]

template<typename Coefficient >

UnivariatePolynomial carl::UnivariatePolynomial< Coefficient >::mod ( const Coefficient & modulus ) const

Constructs a new polynomial where every coefficient c is replaced by c mod modulus.

Parameters

modulus Modulus.

Returns: New polynomial.

◆ negate_variable()

template<typename Coefficient >

UnivariatePolynomial carl::UnivariatePolynomial< Coefficient >::negate_variable ( ) const

inline

Constructs a new polynomial q such that where p is this polynomial.

Returns: New polynomial with negated variable.

Definition at line 419 of file UnivariatePolynomial.h.

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◆ normalizeCoefficients() [1/2]

template<typename Coefficient >

template<typename T = Coefficient, EnableIf< has_normalize< T >> = dummy>

UnivariatePolynomial& carl::UnivariatePolynomial< Coefficient >::normalizeCoefficients ( )

inline

Definition at line 494 of file UnivariatePolynomial.h.

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◆ normalizeCoefficients() [2/2]

template<typename Coefficient >

template<typename T = Coefficient, DisableIf< has_normalize< T >> = dummy>

UnivariatePolynomial& carl::UnivariatePolynomial< Coefficient >::normalizeCoefficients ( )

inline

Definition at line 504 of file UnivariatePolynomial.h.

◆ normalized()

template<typename Coefficient >

UnivariatePolynomial carl::UnivariatePolynomial< Coefficient >::normalized ( ) const

The normal part of a polynomial is the polynomial divided by the unit part.

See also: [3], page 42.

Returns: This polynomial divided by the unit part.

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◆ numeric_content() [1/2]

template<typename Coefficient >

template<typename N = NumberType, EnableIf< is_subset_of_rationals_type< N >> = dummy>

UnderlyingNumberType<Coefficient>::type carl::UnivariatePolynomial< Coefficient >::numeric_content ( ) const

Obtains the numeric content part of this polynomial.

The numeric content part of a polynomial is defined as the gcd() of the numeric content parts of all coefficients. This is only possible if the underlying number type is either integral or fractional.

As for fractional numbers, we consider the following definition: gcd( a/b, c/d ) = gcd( a/b*l, c/d*l ) / l where l = lcm(b,d).

Returns: numeric content part of the polynomial.

See also: UnivariatePolynomials::numeric_content(std::size_t)

◆ numeric_content() [2/2]

template<typename Coefficient >

NumberType carl::UnivariatePolynomial< Coefficient >::numeric_content ( std::size_t i ) const

inline

Returns the numeric content part of the i'th coefficient.

If the coefficients are numbers, this is simply the i'th coefficient. If the coefficients are polynomials, this is the numeric content part of the i'th coefficient.

Parameters

i	number of the coefficient

Returns: numeric content part of i'th coefficient.

Definition at line 540 of file UnivariatePolynomial.h.

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◆ numeric_unit()

template<typename Coefficient >

NumberType carl::UnivariatePolynomial< Coefficient >::numeric_unit ( ) const

inline

Returns the numeric unit part of the polynomial.

If the coefficients are numbers, this is the sign of the leading coefficient. If the coefficients are polynomials, this is the unit part of the leading coefficient.s

Returns: unit part of the polynomial.

Definition at line 556 of file UnivariatePolynomial.h.

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◆ one()

template<typename Coefficient >

UnivariatePolynomial carl::UnivariatePolynomial< Coefficient >::one ( ) const

inline

Creates a polynomial of value one with the same main variable.

Returns: One.

Definition at line 186 of file UnivariatePolynomial.h.

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◆ operator*=() [1/5]

template<typename Coefficient >

UnivariatePolynomial& carl::UnivariatePolynomial< Coefficient >::operator*= ( const Coefficient & rhs )

Multiply this polynomial with something and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator*=() [2/5]

template<typename Coefficient >

template<typename I = Coefficient, DisableIf< std::is_same< Coefficient, I >> ...>

UnivariatePolynomial& carl::UnivariatePolynomial< Coefficient >::operator*= ( const typename IntegralType< Coefficient >::type & rhs )

Multiply this polynomial with something and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator*=() [3/5]

template<typename Coefficient >

UnivariatePolynomial& carl::UnivariatePolynomial< Coefficient >::operator*= ( const UnivariatePolynomial< Coefficient > & rhs )

Multiply this polynomial with something and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator*=() [4/5]

template<typename Coefficient >

template<typename C = Coefficient, EnableIf< is_number_type< C >> = dummy>

UnivariatePolynomial& carl::UnivariatePolynomial< Coefficient >::operator*= ( Variable rhs )

Multiply this polynomial with something and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator*=() [5/5]

template<typename Coefficient >

template<typename C = Coefficient, DisableIf< is_number_type< C >> = dummy>

UnivariatePolynomial& carl::UnivariatePolynomial< Coefficient >::operator*= ( Variable rhs )

Multiply this polynomial with something and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator+=() [1/2]

template<typename Coefficient >

UnivariatePolynomial& carl::UnivariatePolynomial< Coefficient >::operator+= ( const Coefficient & rhs )

Add something to this polynomial and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator+=() [2/2]

template<typename Coefficient >

UnivariatePolynomial& carl::UnivariatePolynomial< Coefficient >::operator+= ( const UnivariatePolynomial< Coefficient > & rhs )

Add something to this polynomial and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator-()

template<typename Coefficient >

UnivariatePolynomial carl::UnivariatePolynomial< Coefficient >::operator- ( ) const

◆ operator-=() [1/2]

template<typename Coefficient >

UnivariatePolynomial& carl::UnivariatePolynomial< Coefficient >::operator-= ( const Coefficient & rhs )

Subtract something from this polynomial and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator-=() [2/2]

template<typename Coefficient >

UnivariatePolynomial& carl::UnivariatePolynomial< Coefficient >::operator-= ( const UnivariatePolynomial< Coefficient > & rhs )

Subtract something from this polynomial and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator/=() [1/2]

template<typename Coefficient >

template<typename C = Coefficient, EnableIf< is_field_type< C >> = dummy>

UnivariatePolynomial& carl::UnivariatePolynomial< Coefficient >::operator/= ( const Coefficient & rhs )

Divide this polynomial by something and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator/=() [2/2]

template<typename Coefficient >

template<typename C = Coefficient, DisableIf< is_field_type< C >> = dummy>

UnivariatePolynomial& carl::UnivariatePolynomial< Coefficient >::operator/= ( const Coefficient & rhs )

Divide this polynomial by something and return the changed polynomial.

Parameters

rhs	Right hand side.

Returns: Changed polynomial.

◆ operator=() [1/2]

template<typename Coefficient >

UnivariatePolynomial& carl::UnivariatePolynomial< Coefficient >::operator= ( const UnivariatePolynomial< Coefficient > & p )

Copy assignment operator.

◆ operator=() [2/2]

template<typename Coefficient >

UnivariatePolynomial& carl::UnivariatePolynomial< Coefficient >::operator= ( UnivariatePolynomial< Coefficient > && p )

noexcept

Move assignment operator.

◆ pow()

template<typename Coefficient >

UnivariatePolynomial carl::UnivariatePolynomial< Coefficient >::pow ( std::size_t exp ) const

Returns this polynomial to the given power.

Parameters

exp Exponent.

Returns: This to the power of exp.

◆ reverse_coefficients()

template<typename Coefficient >

UnivariatePolynomial carl::UnivariatePolynomial< Coefficient >::reverse_coefficients ( ) const

inline

Reverse coefficients safely.

Definition at line 430 of file UnivariatePolynomial.h.

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◆ sgn()

template<typename Coefficient >

carl::Sign carl::UnivariatePolynomial< Coefficient >::sgn ( const Coefficient & value ) const

inline

Calculates the sign of the polynomial at some point.

Parameters

value Point to evaluate.

Returns: Sign at value.

Definition at line 477 of file UnivariatePolynomial.h.

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◆ strip_leading_zeroes()

template<typename Coefficient >

void carl::UnivariatePolynomial< Coefficient >::strip_leading_zeroes ( )

inline

Definition at line 794 of file UnivariatePolynomial.h.

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◆ synthetic_division()

template<typename Coefficient >

Coefficient carl::UnivariatePolynomial< Coefficient >::synthetic_division ( const Coefficient & zeroOfDivisor )

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◆ tcoeff()

template<typename Coefficient >

const Coefficient& carl::UnivariatePolynomial< Coefficient >::tcoeff ( ) const

inline

Returns the trailing coefficient.

Asserts, that the polynomial is not empty.

Returns: The trailing coefficient.

Definition at line 213 of file UnivariatePolynomial.h.

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◆ to_integer_domain() [1/2]

template<typename Coefficient >

template<typename C = Coefficient, EnableIf< is_instantiation_of< GFNumber, C >> = dummy>

UnivariatePolynomial<typename IntegralType<Coefficient>::type> carl::UnivariatePolynomial< Coefficient >::to_integer_domain ( ) const

Works only from rationals, if the numbers are already integers.

Returns

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◆ to_integer_domain() [2/2]

template<typename Coefficient >

template<typename C = Coefficient, DisableIf< is_instantiation_of< GFNumber, C >> = dummy>

UnivariatePolynomial<typename IntegralType<Coefficient>::type> carl::UnivariatePolynomial< Coefficient >::to_integer_domain ( ) const

◆ toFiniteDomain()

template<typename Coefficient >

UnivariatePolynomial<GFNumber<typename IntegralType<Coefficient>::type> > carl::UnivariatePolynomial< Coefficient >::toFiniteDomain ( const GaloisField< typename IntegralType< Coefficient >::type > * galoisField ) const

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◆ toNumberCoefficients()

template<typename Coefficient >

template<typename C = Coefficient, DisableIf< is_number_type< C >> = dummy>

UnivariatePolynomial<NumberType> carl::UnivariatePolynomial< Coefficient >::toNumberCoefficients ( ) const

Asserts that is_univariate() is true.

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◆ total_degree()

template<typename Coefficient >

uint carl::UnivariatePolynomial< Coefficient >::total_degree ( ) const

inline

Returns the total degree of the polynomial, that is the maximum degree of any monomial.

As the degree of the zero polynomial is $-\infty$ , we assert that this polynomial is not zero. This must be checked by the caller before calling this method.

See also: [3], page 38

Returns: Total degree.

Definition at line 296 of file UnivariatePolynomial.h.

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◆ truncate()

template<typename Coefficient >

void carl::UnivariatePolynomial< Coefficient >::truncate ( )

inline

Removes the leading term from the polynomial.

Definition at line 315 of file UnivariatePolynomial.h.

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◆ unit_part()

template<typename Coefficient >

Coefficient carl::UnivariatePolynomial< Coefficient >::unit_part ( ) const

The unit part of a polynomial over a field is its leading coefficient for nonzero polynomials, and one for zero polynomials.

The unit part of a polynomial over a ring is the sign of the polynomial for nonzero polynomials, and one for zero polynomials.

See also: [3], page 42.

Returns: The unit part of the polynomial.

◆ zero_is_root()

template<typename Coefficient >

bool carl::UnivariatePolynomial< Coefficient >::zero_is_root ( ) const

inline

Checks if zero is a real root of this polynomial.

Returns: True if zero is a root.

Definition at line 596 of file UnivariatePolynomial.h.

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Friends And Related Function Documentation

◆ operator!= [1/2]

template<typename Coefficient >

template<typename C >

bool operator!=	(	const UnivariatePolynomial< C > &	lhs,
		const UnivariatePolynomial< C > &	rhs
	)

friend

Checks if the two arguments are not equal.

Parameters

lhs	First argument.
rhs	Second argument.

Returns: lhs != rhs

◆ operator!= [2/2]

template<typename Coefficient >

template<typename C >

bool operator!=	(	const UnivariatePolynomialPtr< C > &	lhs,
		const UnivariatePolynomialPtr< C > &	rhs
	)

friend

Checks if the two arguments are not equal.

Parameters

lhs	First argument.
rhs	Second argument.

Returns: lhs != rhs

◆ operator* [1/9]

template<typename Coefficient >

template<typename C >

UnivariatePolynomial<C> operator*	(	const C &	lhs,
		const UnivariatePolynomial< C > &	rhs
	)

friend

Perform a multiplication involving a polynomial.

Parameters

lhs	Left hand side.
rhs	Right hand side.

Returns: lhs * rhs

◆ operator* [2/9]

template<typename Coefficient >

template<typename C , typename O , typename P >

UnivariatePolynomial<MultivariatePolynomial<C,O,P> > operator*	(	const C &	lhs,
		const UnivariatePolynomial< MultivariatePolynomial< C, O, P >> &	rhs
	)

friend

Perform a multiplication involving a polynomial.

Parameters

lhs	Left hand side.
rhs	Right hand side.

Returns: lhs * rhs

◆ operator* [3/9]

template<typename Coefficient >

template<typename C >

UnivariatePolynomial<C> operator*	(	const IntegralTypeIfDifferent< C > &	lhs,
		const UnivariatePolynomial< C > &	rhs
	)

friend

Perform a multiplication involving a polynomial.

Parameters

lhs	Left hand side.
rhs	Right hand side.

Returns: lhs * rhs

◆ operator* [4/9]

template<typename Coefficient >

template<typename C >

UnivariatePolynomial<C> operator*	(	const UnivariatePolynomial< C > &	lhs,
		const C &	rhs
	)

friend

Perform a multiplication involving a polynomial.

Parameters

lhs	Left hand side.
rhs	Right hand side.

Returns: lhs * rhs

◆ operator* [5/9]

template<typename Coefficient >

template<typename C >

UnivariatePolynomial<C> operator*	(	const UnivariatePolynomial< C > &	lhs,
		const IntegralTypeIfDifferent< C > &	rhs
	)

friend

Perform a multiplication involving a polynomial.

Parameters

lhs	Left hand side.
rhs	Right hand side.

Returns: lhs * rhs

◆ operator* [6/9]

template<typename Coefficient >

template<typename C >

UnivariatePolynomial<C> operator*	(	const UnivariatePolynomial< C > &	lhs,
		const UnivariatePolynomial< C > &	rhs
	)

friend

Perform a multiplication involving a polynomial.

Parameters

lhs	Left hand side.
rhs	Right hand side.

Returns: lhs * rhs

◆ operator* [7/9]

template<typename Coefficient >

template<typename C >

UnivariatePolynomial<C> operator*	(	const UnivariatePolynomial< C > &	lhs,
		Variable	rhs
	)

friend

Perform a multiplication involving a polynomial.

Parameters

lhs	Left hand side.
rhs	Right hand side.

Returns: lhs * rhs

◆ operator* [8/9]

template<typename Coefficient >

template<typename C , typename O , typename P >

UnivariatePolynomial<MultivariatePolynomial<C,O,P> > operator*	(	const UnivariatePolynomial< MultivariatePolynomial< C, O, P >> &	lhs,
		const C &	rhs
	)

friend

Perform a multiplication involving a polynomial.

Parameters

lhs	Left hand side.
rhs	Right hand side.

Returns: lhs * rhs

◆ operator* [9/9]

template<typename Coefficient >

template<typename C >

UnivariatePolynomial<C> operator*	(	Variable	lhs,
		const UnivariatePolynomial< C > &	rhs
	)

friend

Perform a multiplication involving a polynomial.

Parameters

lhs	Left hand side.
rhs	Right hand side.

Returns: lhs * rhs

◆ operator+ [1/3]

template<typename Coefficient >

template<typename C >

UnivariatePolynomial<C> operator+	(	const C &	lhs,
		const UnivariatePolynomial< C > &	rhs
	)

friend

Performs an addition involving a polynomial.

Parameters

lhs	First argument.
rhs	Second argument.

Returns: lhs + rhs

◆ operator+ [2/3]

template<typename Coefficient >

template<typename C >

UnivariatePolynomial<C> operator+	(	const UnivariatePolynomial< C > &	lhs,
		const C &	rhs
	)

friend

Performs an addition involving a polynomial.

Parameters

lhs	First argument.
rhs	Second argument.

Returns: lhs + rhs

◆ operator+ [3/3]

template<typename Coefficient >

template<typename C >

UnivariatePolynomial<C> operator+	(	const UnivariatePolynomial< C > &	lhs,
		const UnivariatePolynomial< C > &	rhs
	)

friend

Performs an addition involving a polynomial.

Parameters

lhs	First argument.
rhs	Second argument.

Returns: lhs + rhs

◆ operator- [1/3]

template<typename Coefficient >

template<typename C >

UnivariatePolynomial<C> operator-	(	const C &	lhs,
		const UnivariatePolynomial< C > &	rhs
	)

friend

Performs a subtraction involving a polynomial.

Parameters

lhs	First argument.
rhs	Second argument.

Returns: lhs - rhs

◆ operator- [2/3]

template<typename Coefficient >

template<typename C >

UnivariatePolynomial<C> operator-	(	const UnivariatePolynomial< C > &	lhs,
		const C &	rhs
	)

friend

Performs a subtraction involving a polynomial.

Parameters

lhs	First argument.
rhs	Second argument.

Returns: lhs - rhs

◆ operator- [3/3]

template<typename Coefficient >

template<typename C >

UnivariatePolynomial<C> operator-	(	const UnivariatePolynomial< C > &	lhs,
		const UnivariatePolynomial< C > &	rhs
	)

friend

Performs a subtraction involving a polynomial.

Parameters

lhs	First argument.
rhs	Second argument.

Returns: lhs - rhs

◆ operator/

template<typename Coefficient >

template<typename C >

UnivariatePolynomial<C> operator/	(	const UnivariatePolynomial< C > &	lhs,
		const C &	rhs
	)

friend

Perform a division involving a polynomial.

Parameters

lhs	Left hand side.
rhs	Right hand side.

Returns: lhs / rhs

◆ operator<

template<typename Coefficient >

template<typename C >

bool operator<	(	const UnivariatePolynomial< C > &	lhs,
		const UnivariatePolynomial< C > &	rhs
	)

friend

◆ operator<<

template<typename Coefficient >

template<typename C >

std::ostream& operator<<	(	std::ostream &	os,
		const UnivariatePolynomial< C > &	rhs
	)

friend

Streaming operator for univariate polynomials.

Parameters

os	Output stream.
rhs	Polynomial.

Returns: os

◆ operator== [1/4]

template<typename Coefficient >

template<typename C >

bool operator==	(	const C &	lhs,
		const UnivariatePolynomial< C > &	rhs
	)

friend

Checks if the two arguments are equal.

Parameters

lhs	First argument.
rhs	Second argument.

Returns: lhs == rhs

◆ operator== [2/4]

template<typename Coefficient >

template<typename C >

bool operator==	(	const UnivariatePolynomial< C > &	lhs,
		const C &	rhs
	)

friend

Checks if the two arguments are equal.

Parameters

lhs	First argument.
rhs	Second argument.

Returns: lhs == rhs

◆ operator== [3/4]

template<typename Coefficient >

template<typename C >

bool operator==	(	const UnivariatePolynomial< C > &	lhs,
		const UnivariatePolynomial< C > &	rhs
	)

friend

Checks if the two arguments are equal.

Parameters

lhs	First argument.
rhs	Second argument.

Returns: lhs == rhs

◆ operator== [4/4]

template<typename Coefficient >

template<typename C >

bool operator==	(	const UnivariatePolynomialPtr< C > &	lhs,
		const UnivariatePolynomialPtr< C > &	rhs
	)

friend

Checks if the two arguments are equal.

Parameters

lhs	First argument.
rhs	Second argument.

Returns: lhs == rhs

◆ UnivariatePolynomial

template<typename Coefficient >

template<class T >

friend class UnivariatePolynomial

friend

Declare all instantiations of univariate polynomials as friends.

Definition at line 66 of file UnivariatePolynomial.h.

Field Documentation

◆ mCoefficients

template<typename Coefficient >

std::vector<Coefficient> carl::UnivariatePolynomial< Coefficient >::mCoefficients

private

The coefficients.

Definition at line 71 of file UnivariatePolynomial.h.

◆ mMainVar

template<typename Coefficient >

Variable carl::UnivariatePolynomial< Coefficient >::mMainVar

private

The main variable.

Definition at line 69 of file UnivariatePolynomial.h.

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

carl-arith/numbers/typetraits.h
carl-arith/poly/umvpoly/UnivariatePolynomial.h

Public Types

Public Member Functions

Private Attributes

Friends

Detailed Description

template<typename Coefficient> class carl::UnivariatePolynomial< Coefficient >

Member Typedef Documentation

◆ CACHE

◆ CoeffType

◆ IntNumberType

◆ NumberType

◆ PolyType

◆ RootType

Constructor & Destructor Documentation

◆ UnivariatePolynomial() [1/10]

◆ UnivariatePolynomial() [2/10]

◆ UnivariatePolynomial() [3/10]

◆ UnivariatePolynomial() [4/10]

◆ UnivariatePolynomial() [5/10]

◆ UnivariatePolynomial() [6/10]

◆ UnivariatePolynomial() [7/10]

◆ UnivariatePolynomial() [8/10]

◆ UnivariatePolynomial() [9/10]

◆ UnivariatePolynomial() [10/10]

◆ ~UnivariatePolynomial()

Member Function Documentation

◆ coefficients() [1/3]

◆ coefficients() [2/3]

◆ coefficients() [3/3]

◆ constant_part()

◆ convert() [1/2]

◆ convert() [2/2]

◆ coprime_coefficients() [1/2]

◆ coprime_coefficients() [2/2]

◆ coprime_coefficients_sign_preserving() [1/2]

◆ coprime_coefficients_sign_preserving() [2/2]

◆ coprime_factor() [1/2]

◆ coprime_factor() [2/2]

◆ degree()

◆ divides()

◆ evaluate()

◆ evaluateCoefficient() [1/2]

◆ evaluateCoefficient() [2/2]

◆ has()

◆ is_consistent() [1/2]

◆ is_consistent() [2/2]

◆ is_constant()

◆ is_linear_in_main_var()

◆ is_normal()

◆ is_number()

◆ is_one()

◆ is_univariate()

◆ is_zero()

◆ lcoeff()

◆ less()

◆ main_denom() [1/2]

◆ main_denom() [2/2]

◆ main_var()

◆ mod() [1/2]

◆ mod() [2/2]

◆ negate_variable()

◆ normalizeCoefficients() [1/2]

◆ normalizeCoefficients() [2/2]

◆ normalized()

◆ numeric_content() [1/2]

◆ numeric_content() [2/2]

◆ numeric_unit()

◆ one()

◆ operator*=() [1/5]

◆ operator*=() [2/5]

◆ operator*=() [3/5]

◆ operator*=() [4/5]

◆ operator*=() [5/5]

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-()

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator/=() [1/2]

◆ operator/=() [2/2]

template<typename Coefficient>
class carl::UnivariatePolynomial< Coefficient >