NTL_zz_p Struct Reference

long ints modulo a positive integer. More...

#include <ntl-lzz_p.h>

Inheritance diagram for NTL_zz_p:

Public Types
typedef NTL::zz_p	Element
typedef Givaro::UnparametricOperations< Element >	Father_t
typedef UnparametricRandIter< NTL::zz_p >	RandIter

Public Member Functions
	NTL_zz_p (integer p, size_t e=1)
	NTL_zz_p ()
Element &	init (Element &x) const
Element &	init (Element &x, const double &y) const
Element &	init (Element &x, const integer &y) const
Element &	init (Element &x, const NTL::zz_p &y) const
template<class ANY>
ANY &	convert (ANY &x, const Element &y) const
Element &	pow (Element &res, const Element &x, long exp) const
Element &	powin (Element &x, long exp) const
template<typename Residu_t>
Residu_t &	cardinality (Residu_t &c) const
	Cardinality.
integer	cardinality () const
template<typename Residu_t>
Residu_t &	characteristic (Residu_t &c) const
	Characteristic.
integer	characteristic () const
Element &	inv (Element &x, const Element &y) const
	Multiplicative Inverse.
bool	isZero (const Element &x) const
	Zero equality.
bool	isOne (const Element &x) const
	One equality.
bool	isUnit (const Element &x) const
	Unit test.
bool	isMOne (const Element &x) const
	MOne equality.
Element &	invin (Element &x) const
	Inplace Multiplicative Inverse.
std::ostream &	write (std::ostream &os) const
	Print field.
std::ostream &	write (std::ostream &os, const std::string &) const
std::ostream &	write (std::ostream &os, const Element &x) const

Static Public Member Functions
static integer	maxCardinality ()

Data Fields
const Element	zero
const Element	one
const Element	mOne

Detailed Description

long ints modulo a positive integer.

While NTL allows any int to serve as the modulus, only prime moduli yield fields. The primality of the modulus will not be checked, so it is the programmer's responsibility to supply a prime modulus if a field is wanted. These specializations allow the Givaro::ZRing template class to be used to wrap NTL's zz_p class as a LinBox field. Uses nice trick for mod p via floating point.

Member Typedef Documentation

Element

typedef NTL::zz_p Element

Father_t

typedef Givaro::UnparametricOperations<Element> Father_t

RandIter

typedef UnparametricRandIter<NTL::zz_p> RandIter

Constructor & Destructor Documentation

NTL_zz_p() [1/2]

NTL_zz_p ( integer p, size_t e = 1 )

inline

NTL_zz_p() [2/2]

NTL_zz_p ( )

inline

Member Function Documentation

init() [1/4]

Element & init ( Element & x ) const

inline

init() [2/4]

Element & init ( Element & x, const double & y ) const

inline

init() [3/4]

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

inline

init() [4/4]

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

inline

convert()

template<class ANY>

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

inline

maxCardinality()

static integer maxCardinality ( )

inlinestatic

pow()

Element & pow ( Element & res, const Element & x, long exp ) const

inline

powin()

Element & powin ( Element & x, long exp ) const

inline

cardinality() [1/2]

template<typename Residu_t>

Residu_t & cardinality ( Residu_t & 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

cardinality() [2/2]

integer cardinality ( ) const

inline

characteristic() [1/2]

template<typename Residu_t>

Residu_t & characteristic ( Residu_t & 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.

characteristic() [2/2]

integer characteristic ( ) const

inline

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.

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.

Returns

boolean true if invertible, 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.

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() [1/3]

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() [2/3]

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

inline

write() [3/3]

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

inline

Field Documentation

zero

const Element zero

one

const Element one

mOne

const Element mOne

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

• ntl-lzz_p.h