#include <ntl-ZZ_pX.h>

Inherits UnparametricField< K >.

Public Member Functions
	NTL_ZZ_pX (const integer &p, size_t e=1)
	NTL_ZZ_pX (CoeffField cf)
template<class ANY >
Element &	init (Element &p, const ANY &y) const
Element &	init (Element &p, const Coeff &y) const
template<class ANY >
Element &	init (Element &p, const std::vector< ANY > &v) const
Element &	init (Element &p, const std::vector< Coeff > &v) const
template<class ANY >
std::vector< ANY > &	convert (std::vector< ANY > &v, const Element &p) const
std::vector< Coeff > &	convert (std::vector< Coeff > &v, const Element &p) const
bool	isZero (const Element &x) const
bool	isOne (const Element &x) const
const CoeffField &	getCoeffField () const
size_t	deg (const Element &p) const
Element &	rev (Element &r, const Element &p)
Element &	revin (Element &r)
Coeff &	leadCoeff (Coeff &c, const Element &p) const
Coeff &	getCoeff (Coeff &c, const Element &p, size_t i) const
Element &	setCoeff (Element &p, size_t i, const Coeff &c) const
Element &	quo (Element &res, const Element &a, const Element &b) const
Element &	quoin (Element &a, const Element &b) const
Element &	rem (Element &res, const Element &a, const Element &b) const
Element &	remin (Element &a, const Element &b) const
void	quorem (Element &q, Element &r, const Element &a, const Element &b) const
integer &	characteristic (integer &c) const
integer &	cardinality (integer &c) const
Public Member Functions inherited from UnparametricField< K >
template<>
NTL::zz_p &	init (NTL::zz_p &x, const integer &y) const
template<>
integer &	convert (integer &x, const NTL::zz_p &y) const
template<>
integer &	cardinality (integer &c) const
template<>
integer &	characteristic (integer &c) const
template<>
NTL::zz_p &	inv (NTL::zz_p &x, const NTL::zz_p &y) const
template<>
bool	isZero (const NTL::zz_p &x) const
template<>
bool	isOne (const NTL::zz_p &x) const
template<>
NTL::zz_p &	invin (NTL::zz_p &x) const
template<>
std::ostream &	write (std::ostream &os) const
template<>
std::ostream &	write (std::ostream &os) const
template<>
std::ostream &	write (std::ostream &os) const
	UnparametricField (integer q=0, size_t e=1)
	UnparametricField (const UnparametricField &F)
	construct this field as copy of F.
	~UnparametricField ()
const UnparametricField &	operator= (const UnparametricField &F) const
Element &	init (Element &x, const integer &y=0) const
	x := y. Caution: it is via cast to long. Good candidate for specialization.
integer &	convert (integer &x, const Element &y) const
	x := y. Caution: it is via cast to long. Good candidate for specialization.
double &	convert (double &x, const Element &y) const
	x := y. Caution: it is via cast to long. Good candidate for specialization. –dpritcha
Element &	assign (Element &x, const Element &y) const
integer &	cardinality (integer &c) const
	c := cardinality of this field (-1 if infinite).
integer &	characteristic (integer &c) const
	c := characteristic of this field (zero or prime).
bool	areEqual (const Element &x, const Element &y) const
	x == y
bool	isZero (const Element &x) const
	x == 0
bool	isOne (const Element &x) const
	x == 1
Element &	add (Element &x, const Element &y, const Element &z) const
	x := y + z
Element &	sub (Element &x, const Element &y, const Element &z) const
	x := y - z
Element &	mul (Element &x, const Element &y, const Element &z) const
	x := y*z
Element &	div (Element &x, const Element &y, const Element &z) const
	x := y/z
Element &	neg (Element &x, const Element &y) const
	x := -y
Element &	inv (Element &x, const Element &y) const
	x := 1/y
Element &	axpy (Element &z, const Element &a, const Element &x, const Element &y) const
	z := a*x + y
Element &	addin (Element &x, const Element &y) const
	x := x + y
Element &	subin (Element &x, const Element &y) const
	x := x - y
Element &	mulin (Element &x, const Element &y) const
	x := x*y
Element &	divin (Element &x, const Element &y) const
	x := x/y
Element &	negin (Element &x) const
	x := -x
Element &	invin (Element &x) const
	x := 1/x
Element &	axpyin (Element &y, const Element &a, const Element &x) const
	y := a*x + y
std::ostream &	write (std::ostream &os) const
std::istream &	read (std::istream &is) const
std::ostream &	write (std::ostream &os, const Element &x) const
std::istream &	read (std::istream &is, Element &x) const
	UnparametricField (const K &A)
	Default constructor.
const K &	operator() (void) const
K &	operator() (void)
template<>
NTL::RR &	init (NTL::RR &x, const integer &y) const
template<>
integer &	convert (integer &x, const NTL::RR &y) const
template<>
NTL::RR &	inv (NTL::RR &x, const NTL::RR &y) const
template<>
bool	isZero (const NTL::RR &x) const
template<>
bool	isOne (const NTL::RR &x) const
template<>
NTL::RR &	invin (NTL::RR &x) const
template<>
std::ostream &	write (std::ostream &os) const
template<>
	UnparametricField (integer q, size_t e)
template<>
NTL::ZZ_p &	init (NTL::ZZ_p &x, const integer &y) const
template<>
integer &	convert (integer &x, const NTL::ZZ_p &y) const
template<>
integer &	cardinality (integer &c) const
template<>
integer &	characteristic (integer &c) const
template<>
NTL::ZZ_p &	inv (NTL::ZZ_p &x, const NTL::ZZ_p &y) const
template<>
bool	isZero (const NTL::ZZ_p &x) const
template<>
bool	isOne (const NTL::ZZ_p &x) const
template<>
NTL::ZZ_p &	invin (NTL::ZZ_p &x) const
template<>
std::ostream &	write (std::ostream &os) const

Additional Inherited Members
Public Types inherited from UnparametricField< K >
typedef K	Element
typedef UnparametricRandIter< K >	RandIter
	Type of random field element generators.

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	(	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.

NTL_ZZ_pX ( CoeffField cf )

inline

Constructor from a coefficient field

Member Function Documentation

Element& init	(	Element &	p,
		const ANY &	y
	)		const

inline

Initialize p to the constant y (p = y*x^0)

Element& init	(	Element &	p,
		const Coeff &	y
	)		const

inline

Initialize p to the constant y (p = y*x^0)

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.

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.

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.

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.

bool isZero ( const Element & x ) const

inline

Test if an element equals zero

bool isOne ( const Element & x ) const

inline

Test if an element equals one

const CoeffField& getCoeffField ( ) const

inline

The LinBox field for coefficients

size_t deg ( const Element & p ) const

inline

Get the degree of a polynomial Unlike NTL, deg(0)=0.

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

inline

r will be set to the reverse of p.

Element& revin ( Element & r )

inline

r is itself reversed.

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

inline

Get the leading coefficient of this polynomial.

Coeff& getCoeff	(	Coeff &	c,
		const Element &	p,
		size_t	i
	)		const

inline

Get the coefficient of x^i in a given polynomial

Element& setCoeff	(	Element &	p,
		size_t	i,
		const Coeff &	c
	)		const

inline

Set the coefficient of x^i in a given polynomial

Element& quo	(	Element &	res,
		const Element &	a,
		const Element &	b
	)		const

inline

Get the quotient of two polynomials

Element& quoin	(	Element &	a,
		const Element &	b
	)		const

inline

a = quotient of a, b

Element& rem	(	Element &	res,
		const Element &	a,
		const Element &	b
	)		const

inline

Get the remainder under polynomial division

Element& remin	(	Element &	a,
		const Element &	b
	)		const

inline

a = remainder of a,b

void quorem	(	Element &	q,
		Element &	r,
		const Element &	a,
		const Element &	b
	)		const

inline

Get the quotient and remainder under polynomial division

integer& characteristic ( integer & c ) const

inline

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

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:

/build/linbox-TzW5I9/linbox-1.1.6~rc0/linbox/field/ntl-ZZ_pX.h

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation