Wrapper of zz_p from NTL. More...

#include <ntl-zz_p.h>

Inheritance diagram for NTL_ZZ_p:

Public Member Functions
Element &	init (Element &x, const NTL::ZZ &y) const
	Specialization for NTL::ZZ. More...

NTL::ZZ &	convert (NTL::ZZ &x, const Element &y) const
	Specialization for NTL::ZZ. More...

integer &	convert (integer &x, const Element &y) const
	Conversion of field element to an integer. More...

integer &	cardinality (integer &c) const
	Cardinality. More...

integer &	characteristic (integer &c) const
	Characteristic. More...

Element &	inv (Element &x, const Element &y) const
	Multiplicative Inverse. More...

bool	isZero (const Element &x) const
	Zero equality. More...

bool	isOne (const Element &x) const
	One equality. More...

bool	isMOne (const Element &x) const
	MOne equality. More...

bool	isUnit (const Element &x) const
	Unit test. More...

Element &	invin (Element &x) const
	Inplace Multiplicative Inverse. More...

std::ostream &	write (std::ostream &os) const
	Print field. More...

std::ostream &	write (std::ostream &os, const Element &x) const
	Print field. More...

NTL_ZZ_p
Arbitrary precision integers modulus a positive integer. While NTL allows any integer to serve as the modulus, only prime moduli yield fields. Therefore, while arthmetic operations may be valid for any modulus, only prime moduli are supported in this implementation. The primality of the modulus will not be checked, so it is the programmer's responsibility to supply a prime modulus. These specializations allow the Givaro::ZRing template class to be used to wrap NTL's `ZZ_p` class as a LinBox field.
	NTL_ZZ_p (integer q, size_t e=1)

	NTL_ZZ_p (NTL::ZZ d, size_t e=1)

	NTL_ZZ_p ()
	NULL constructor.

Detailed Description

Wrapper of zz_p from NTL.

Uses nice mod p via floating pt trick.

Constructor & Destructor Documentation

◆ NTL_ZZ_p() [1/2]

NTL_ZZ_p	(	integer	q,
		size_t	e = `1`
	)

inline

Parameters

q,e

◆ NTL_ZZ_p() [2/2]

NTL_ZZ_p	(	NTL::ZZ	d,
		size_t	e = `1`
	)

inline

Parameters

d,e

Member Function Documentation

◆ init()

Element& init	(	Element &	x,
		const NTL::ZZ &	y
	)		const

inline

Specialization for NTL::ZZ.

Returns: reference to field element.

Parameters

x	field element to contain output (reference returned)
y	NTL::ZZ.

◆ convert() [1/2]

NTL::ZZ& convert	(	NTL::ZZ &	x,
		const Element &	y
	)		const

inline

Specialization for NTL::ZZ.

Returns: reference to NTL::ZZ

Parameters

x	NTL::ZZ to contain output (reference returned).
y	constant reference to field element.

◆ convert() [2/2]

integer& convert	(	integer &	x,
		const Element &	y
	)		const

inline

Conversion of field element to an integer.

This function assumes the output field element x has already been constructed, but that it is not already initialized. This done by converting to a std::string : inefficient but correct.

Returns: reference to integer.

Parameters

x	reference to integer to contain output (reference returned).
y	constant reference to field element.

◆ cardinality()

integer& cardinality ( integer & c ) const

inline

Cardinality.

Return integer representing cardinality of the field. Returns the modulus of the field, which should be prime.

Returns: integer representing cardinality of the field

◆ characteristic()

integer& characteristic ( integer & c ) const

inline

Characteristic.

Return integer representing characteristic of the field. Returns the modulus of the field, which should be prime.

Returns: integer representing characteristic of the field.

◆ inv()

Element& inv	(	Element &	x,
		const Element &	y
	)		const

inline

Multiplicative Inverse.

x = 1 / y This function assumes both field elements have already been constructed and initialized.

Returns: reference to x.

Parameters

x	field element (reference returned).
y	field element.

◆ isZero()

bool isZero ( const Element & x ) const

inline

Zero equality.

Test if field element is equal to zero. This function assumes the field element has already been constructed and initialized. In this specialization, NTL's IsZero function is called.

Returns: boolean true if equals zero, false if not.

Parameters

x	field element.

◆ isOne()

bool isOne ( const Element & x ) const

inline

One equality.

Test if field element is equal to one. This function assumes the field element has already been constructed and initialized. In this specialization, NTL's IsOne function is called.

Returns: boolean true if equals one, false if not.

Parameters

x	field element.

◆ isMOne()

bool isMOne ( const Element & x ) const

inline

MOne equality.

Test if field element is equal to one. This function assumes the field element has already been constructed and initialized. In this specialization, NTL's IsMOne function is called.

Returns: boolean true if equals one, false if not.

Parameters

x	field element.

◆ isUnit()

bool isUnit ( const Element & x ) const

inline

Unit test.

Test if field element is invertible. This function assumes the field element has already been constructed and initialized. In this specialization, NTL's InvModStatus function is called. inline long InvModStatus(ZZ& x, const ZZ& a, const ZZ& n) // if gcd(a,n) = 1, then ReturnValue = 0, x = a^{-1} mod n // otherwise, ReturnValue = 1, x = gcd(a, n)

Returns: boolean true if invertible, false if not.

Parameters

x	field element.

◆ invin()

Element& invin ( Element & x ) const

inline

Inplace Multiplicative Inverse.

x = 1 / x This function assumes both field elements have already been constructed and initialized.

Returns: reference to x.

Parameters

x	field element (reference returned).

◆ write() [1/2]

std::ostream& write ( std::ostream & os ) const

inline

Print field.

Returns: output stream to which field is written.

Parameters

os	output stream to which field is written.

◆ write() [2/2]

std::ostream& write	(	std::ostream &	os,
		const Element &	x
	)		const

inline

Print field.

Returns: output stream to which field is written.

Parameters

os	output stream to which field is written.
x

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

ntl-zz_p.h

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ NTL_ZZ_p() [1/2]

◆ NTL_ZZ_p() [2/2]

Member Function Documentation

◆ init()

◆ convert() [1/2]

◆ convert() [2/2]

◆ cardinality()

◆ characteristic()

◆ inv()

◆ isZero()

◆ isOne()

◆ isMOne()

◆ isUnit()

◆ invin()

◆ write() [1/2]

◆ write() [2/2]