Ring (in fact, a unique factorization domain) of polynomial with coefficients in class NTL_ZZ_p (integers mod a wordsize prime). More...

#include <ntl-zz_px.h>

Inherits NTL_ZZ_pX_Initialiser, and UnparametricOperations< NTL::ZZ_pX >.

Public Member Functions
	NTL_ZZ_pX (const integer &p, size_t e=1)
	Standard LinBox field constructor. More...

	NTL_ZZ_pX (CoeffField cf)
	Constructor from a coefficient field.

template<class ANY >
Element &	init (Element &p, const ANY &y) const
	Initialize p to the constant y (p = y*x^0)

Element &	init (Element &p, const Coeff &y) const
	Initialize p to the constant y (p = y*x^0)

template<class ANY >
Element &	init (Element &p, const std::vector< ANY > &v) const
	Initialize p from a vector of coefficients. More...

Element &	init (Element &p, const std::vector< Coeff > &v) const
	Initialize p from a vector of coefficients. More...

template<class ANY >
std::vector< ANY > &	convert (std::vector< ANY > &v, const Element &p) const
	Convert p to a vector of coefficients. More...

std::vector< Coeff > &	convert (std::vector< Coeff > &v, const Element &p) const
	Convert p to a vector of coefficients. More...

bool	isZero (const Element &x) const
	Test if an element equals zero.

bool	isOne (const Element &x) const
	Test if an element equals one.

const CoeffField &	getCoeffField () const
	The LinBox field for coefficients.

size_t	deg (const Element &p) const
	Get the degree of a polynomial Unlike NTL, deg(0)=0.

Element &	rev (Element &r, const Element &p)
	r will be set to the reverse of p. More...

Element &	revin (Element &r)
	r is itself reversed. More...

Coeff &	leadCoeff (Coeff &c, const Element &p) const
	Get the leading coefficient of this polynomial. More...

Coeff &	getCoeff (Coeff &c, const Element &p, size_t i) const
	Get the coefficient of x^i in a given polynomial.

Element &	setCoeff (Element &p, size_t i, const Coeff &c) const
	Set the coefficient of x^i in a given polynomial.

Element &	quo (Element &res, const Element &a, const Element &b) const
	Get the quotient of two polynomials.

Element &	quoin (Element &a, const Element &b) const
	a = quotient of a, b

Element &	rem (Element &res, const Element &a, const Element &b) const
	Get the remainder under polynomial division.

Element &	remin (Element &a, const Element &b) const
	a = remainder of a,b

void	quorem (Element &q, Element &r, const Element &a, const Element &b) const
	Get the quotient and remainder under polynomial division.

integer &	characteristic (integer &c) const
	Get characteristic of the field - same as characteristic of coefficient field. More...

integer &	cardinality (integer &c) const
	Get the cardinality of the field. More...

std::ostream &	write (std::ostream &os) const
	Write a description of the field.

Detailed Description

Ring (in fact, a unique factorization domain) of polynomial with coefficients in class NTL_ZZ_p (integers mod a wordsize prime).

All the same functions as any other ring, with the addition of: Coeff (type), CoeffField (type), getCoeffField, setCoeff, getCoeff, leadCoeff, deg

Constructor & Destructor Documentation

◆ NTL_ZZ_pX()

NTL_ZZ_pX	(	const integer &	p,
		size_t	e = `1`
	)

inline

Standard LinBox field constructor.

The paramters here (prime, exponent) are only used to initialize the coefficient field.

Member Function Documentation

◆ init() [1/2]

Element& init	(	Element &	p,
		const std::vector< ANY > &	v
	)		const

inline

Initialize p from a vector of coefficients.

The vector should be ordered the same way NTL does it: the front of the vector corresponds to the trailing coefficients, and the back of the vector corresponds to the leading coefficients. That is, v[i] = coefficient of x^i.

◆ init() [2/2]

Element& init	(	Element &	p,
		const std::vector< Coeff > &	v
	)		const

inline

Initialize p from a vector of coefficients.

The vector should be ordered the same way NTL does it: the front of the vector corresponds to the trailing coefficients, and the back of the vector corresponds to the leading coefficients. That is, v[i] = coefficient of x^i.

◆ convert() [1/2]

std::vector<ANY>& convert	(	std::vector< ANY > &	v,
		const Element &	p
	)		const

inline

Convert p to a vector of coefficients.

The vector will be ordered the same way NTL does it: the front of the vector corresponds to the trailing coefficients, and the back of the vector corresponds to the leading coefficients. That is, v[i] = coefficient of x^i.

◆ convert() [2/2]

std::vector<Coeff>& convert	(	std::vector< Coeff > &	v,
		const Element &	p
	)		const

inline

Convert p to a vector of coefficients.

The vector will be ordered the same way NTL does it: the front of the vector corresponds to the trailing coefficients, and the back of the vector corresponds to the leading coefficients. That is, v[i] = coefficient of x^i.

◆ rev()

Element& rev	(	Element &	r,
		const Element &	p
	)

inline

r will be set to the reverse of p.

◆ revin()

Element& revin ( Element & r )

inline

r is itself reversed.

◆ leadCoeff()

Coeff& leadCoeff	(	Coeff &	c,
		const Element &	p
	)		const

inline

Get the leading coefficient of this polynomial.

◆ characteristic()

integer& characteristic ( integer & c ) const

inline

Get characteristic of the field - same as characteristic of coefficient field.

◆ cardinality()

integer& cardinality ( integer & c ) const

inline

Get the cardinality of the field.

Since the cardinality is infinite, by convention we return -1.

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

ntl-zz_px.h

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ NTL_ZZ_pX()

Member Function Documentation

◆ init() [1/2]

◆ init() [2/2]

◆ convert() [1/2]

◆ convert() [2/2]

◆ rev()

◆ revin()

◆ leadCoeff()

◆ characteristic()

◆ cardinality()