extend Wrapper of ZZ_p from NTL. More...

#include <PIR-ntl-ZZ_p.h>

Inherits UnparametricField< K >.

Public Types
Common Object Interface for a LinBox Field.
These methods and member types are required of all LinBox fields. See FieldArchetype for detailed specifications.
typedef UnparametricRandIter< K >	RandIter
	Type of random field element generators.
Public Member Functions
template<>
NTL::zz_p &	inv (NTL::zz_p &x, const NTL::zz_p &y) const
template<>
NTL::zz_p &	invin (NTL::zz_p &x) const
template<>
bool	isZero (const NTL::zz_p &x) const
template<>
bool	isOne (const NTL::zz_p &x) const
Field Object Basics.
Element &	inv (Element &x, const Element &y) const
	c := characteristic of this field (zero or prime).
Element &	invin (Element &x) const
	c := characteristic of this field (zero or prime).
std::ostream &	write (std::ostream &os) const
	c := characteristic of this field (zero or prime).
std::ostream &	write (std::ostream &os, const Element &p) const
	c := characteristic of this field (zero or prime).
bool	isZero (const Element &x) const
	c := characteristic of this field (zero or prime).
bool	isOne (const Element &x) const
	c := characteristic of this field (zero or prime).
long unsigned int	characteristic (long unsigned int &p) const
	c := characteristic of this field (zero or prime).
long unsigned int	characteristic () const
	c := characteristic of this field (zero or prime).
integer &	characteristic (integer &c) const
	c := characteristic of this field (zero or prime).
long unsigned int	cardinality () const
	c := characteristic of this field (zero or prime).
integer &	cardinality (integer &c) const
	c := cardinality of this field (-1 if infinite).
template<typename Src >
Element &	init (Element &x, const Src &s) const
	c := characteristic of this field (zero or prime).
std::istream &	read (std::istream &is, Element &x) const
	c := characteristic of this field (zero or prime).
std::istream &	read (std::istream &is) const
	c := characteristic of this field (zero or prime).
template<typename T >
T &	convert (T &x, const Element &y) const
	c := characteristic of this field (zero or prime).
class RR.
Rational number field. This field is provided as a convenience in a few places. Use with caution because expression swell. This specialization allows the UnparametricField template class to be used to wrap NTL's RR class as a LinBox field.
template<>
NTL::RR &	inv (NTL::RR &x, const NTL::RR &y) const
template<>
NTL::RR &	invin (NTL::RR &x) const
template<>
bool	isZero (const NTL::RR &x) const
template<>
bool	isOne (const NTL::RR &x) const

template<>
NTL::ZZ_p &	inv (NTL::ZZ_p &x, const NTL::ZZ_p &y) const
template<>
NTL::ZZ_p &	invin (NTL::ZZ_p &x) const
template<>
bool	isZero (const NTL::ZZ_p &x) const
template<>
bool	isOne (const NTL::ZZ_p &x) const
Implementation-Specific Methods.
These methods are not required of all LinBox fields and are included only for the implementation of this field template.
const K &	operator() (void) const
	Constant access operator.
K &	operator() (void)
	Access operator.
Static Public Member Functions
template<class Element2 >
static Element &	init (Element &x, const Element2 &y)
	Init x from y.
static Element &	init (Element &x, const Element &y)
	Init from a NTL::ZZ_p.
static Element &	init (Element &x, const integer &y)
	I don't know how to init from integer.
static integer &	convert (integer &x, const Element &y)
	Convert y to an Element.
static Element &	assign (Element &x, const Element &y)
	x = y.
static bool	areEqual (const Element &x, const Element &y)
	Test if x == y.
static bool	isZero (const Element &x)
	Test if x == 0.
static bool	isOne (const Element &x)
	Test if x == 1.
static Element &	add (Element &x, const Element &y, const Element &z)
	return x = y + z
static Element &	sub (Element &x, const Element &y, const Element &z)
	return x = y - z
template<class Int >
static Element &	mul (Element &x, const Element &y, const Int &z)
	return x = y * z
static Element &	div (Element &x, const Element &y, const Element &z)
	If exists a, such that a * z =y, return x = one of them.
static Element &	inv (Element &x, const Element &y)
	If y is a unit, return x = 1 / y, otherwsie, throw an exception.
static Element &	neg (Element &x, const Element &y)
	return x = -y;
template<class Int >
static Element &	axpy (Element &r, const Element &a, const Int &x, const Element &y)
	return r = a x + y
static Element &	addin (Element &x, const Element &y)
	return x += y;
static Element &	subin (Element &x, const Element &y)
	return x -= y;
template<class Int >
static Element &	mulin (Element &x, const Int &y)
	return x *= y;
static Element &	divin (Element &x, const Element &y)
	If y divides x, return x /= y, otherwise throw an exception.
static Element &	invin (Element &x)
	If x is a unit, x = 1 / x, otherwise, throw an exception.
static Element &	negin (Element &x)
	return x = -x;
template<class Int >
static Element &	axpyin (Element &r, const Element &a, const Int &x)
	return r += a x
static std::ostream &	write (std::ostream &out, const Element &y)
	out << y;
static std::istream &	read (std::istream &in, Element &x)
	read x from istream in
static bool	isUnit (const Element &x)
	some PIR function
static Element &	gcd (Element &g, const Element &a, const Element &b)
	return g = gcd (a, b)
static Element &	gcdin (Element &g, const Element &b)
	return g = gcd (g, b)
static Element &	xgcd (Element &g, Element &s, Element &t, const Element &a, const Element &b)
	g = gcd(a, b) = as + bt.
static Element &	dxgcd (Element &g, Element &s, Element &t, Element &a1, Element &b1, const Element &a, const Element &b)
	g = gcd(a, b) = as + bt.
static bool	isDivisor (const Element &a, const Element &b)
	Test if a \| b.
static Element &	normal (Element &a, const Element &b)
	a = normalization of b.

Detailed Description

extend Wrapper of ZZ_p from NTL.

Add PIR functions

Member Function Documentation

static Element& div	(	Element &	x,
		const Element &	y,
		const Element &	z
	)		`[inline, static]`

If exists a, such that a * z =y, return x = one of them.

Otherwise, throw an exception

static bool isUnit ( const Element & x ) [inline, static]

some PIR function

Test if x is a unit.

static Element& xgcd	(	Element &	g,
		Element &	s,
		Element &	t,
		const Element &	a,
		const Element &	b
	)		`[inline, static]`

g = gcd(a, b) = a*s + b*t.

and gcd (s, t) is a unit.

static Element& dxgcd	(	Element &	g,
		Element &	s,
		Element &	t,
		Element &	a1,
		Element &	b1,
		const Element &	a,
		const Element &	b
	)		`[inline, static]`

g = gcd(a, b) = a*s + b*t.

and gcd (s, t) is a unit. s * a1 + t * b1 = a unit.

NTL::zz_p & inv	(	NTL::zz_p &	x,
		const NTL::zz_p &	y
	)		const `[inherited]`

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.

NTL::RR & inv	(	NTL::RR &	x,
		const NTL::RR &	y
	)		const `[inherited]`

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.

NTL::ZZ_p & inv	(	NTL::ZZ_p &	x,
		const NTL::ZZ_p &	y
	)		const `[inherited]`

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.

NTL::zz_p & invin ( NTL::zz_p & x ) const [inherited]

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).

NTL::RR & invin ( NTL::RR & x ) const [inherited]

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).

NTL::ZZ_p & invin ( NTL::ZZ_p & x ) const [inherited]

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).

bool isZero ( const NTL::zz_p & x ) const [inherited]

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.

bool isZero ( const NTL::RR & x ) const [inherited]

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.

bool isZero ( const NTL::ZZ_p & x ) const [inherited]

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.

bool isOne ( const NTL::zz_p & x ) const [inherited]

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.

bool isOne ( const NTL::RR & x ) const [inherited]

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.

bool isOne ( const NTL::ZZ_p & x ) const [inherited]

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.

const K& operator() ( void ) const [inline, inherited]

Constant access operator.

Returns:: constant reference to field object

K& operator() ( void ) [inline, inherited]

Access operator.

Returns:: reference to field object

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

PIR-ntl-ZZ_p.h

Public Types

Public Member Functions

Static Public Member Functions

Detailed Description

Member Function Documentation