NTL_ZZ Class Reference

the integer ring. More...

#include <ntl-zz.h>

Public Types
typedef NTL_ZZRandIter	RandIter
typedef NTL_ZZ	Father_t
typedef NTL::ZZ	Element
typedef NTL::ZZ	Residu_t

Public Member Functions
	NTL_ZZ (int p=0, int exp=1)
integer &	cardinality (integer &c) const
integer &	characteristic (integer &c) const
template<class IntType>
IntType &	characteristic (IntType &c) const
std::ostream &	write (std::ostream &out) const
std::istream &	read (std::istream &in) const
template<class Element2>
Element &	init (Element &x, const Element2 &y) const
	Init x from y.
Element &	init (Element &x, const Element &y) const
	Init from a NTL::ZZ.
Element &	init (Element &x, const int64_t &y) const
	Init from an int64_t.
Element &	init (Element &x, const uint64_t &y) const
	Init from a uint64_t.
Element &	init (Element &x, const integer &y) const
	I don't know how to init from integer efficiently.
integer &	convert (integer &x, const Element &y) const
	Convert y to an Element.
double &	convert (double &x, const Element &y) const
Element &	assign (Element &x, const Element &y) const
	x = y.
bool	areEqual (const Element &x, const Element &y) const
	Test if x == y.
bool	isZero (const Element &x) const
	Test if x == 0.
bool	isOne (const Element &x) const
	Test if x == 1.
bool	isMOne (const Element &x) const
	Test if x == -1.
Element &	add (Element &x, const Element &y, const Element &z) const
	return x = y + z
Element &	sub (Element &x, const Element &y, const Element &z) const
	return x = y - z
template<class Int>
Element &	mul (Element &x, const Element &y, const Int &z) const
	return x = y * z
Element &	div (Element &x, const Element &y, const Element &z) const
	If z divides y, return x = y / z, otherwise, throw an exception.
Element &	inv (Element &x, const Element &y) const
	If y is a unit, return x = 1 / y, otherwsie, throw an exception.
Element &	neg (Element &x, const Element &y) const
	return x = -y;
template<class Int>
Element &	axpy (Element &r, const Element &a, const Int &x, const Element &y) const
	return r = a x + y
Element &	addin (Element &x, const Element &y) const
	return x += y;
Element &	subin (Element &x, const Element &y) const
	return x -= y;
template<class Int>
Element &	mulin (Element &x, const Int &y) const
	return x *= y;
Element &	divin (Element &x, const Element &y) const
	If y divides x, return x /= y, otherwise throw an exception.
Element &	invin (Element &x)
	If x is a unit, x = 1 / x, otherwise, throw an exception.
Element &	negin (Element &x) const
	return x = -x;
template<class Int>
Element &	axpyin (Element &r, const Element &a, const Int &x) const
	return r += a x
std::ostream &	write (std::ostream &out, const Element &y) const
	out << y;
std::istream &	read (std::istream &in, Element &x) const
	read x from istream in
bool	isUnit (const Element &x) const
	some PIR function
Element &	gcd (Element &g, const Element &a, const Element &b) const
	return g = gcd (a, b)
Element &	gcdin (Element &g, const Element &b) const
	return g = gcd (g, b)
Element &	xgcd (Element &g, Element &s, Element &t, const Element &a, const Element &b) const
	g = gcd(a, b) = a*s + b*t.
Element &	lcm (Element &c, const Element &a, const Element &b) const
	c = lcm (a, b)
Element &	lcmin (Element &l, const Element &b) const
	l = lcm (l, b)
Element &	sqrt (Element &x, const Element &y) const
	x = floor ( sqrt(y)).
long	RationalReconstruction (Element &a, Element &b, const Element &x, const Element &m, const Element &a_bound, const Element &b_bound) const
	Requires 0 <= x < m, m > 2 * a_bound * b_bound, a_bound >= 0, b_bound > 0 This routine either returns 0, leaving a and b unchanged, or returns 1 and sets a and b so that (1) a = b x (mod m), (2) |a| <= a_bound, 0 < b <= b_bound, and (3) gcd(m, b) = gcd(a, b).
Element &	quo (Element &q, const Element &a, const Element &b) const
	q = floor (x/y);
Element &	rem (Element &r, const Element &a, const Element &b) const
	r = remindar of a / b
Element &	quoin (Element &a, const Element &b) const
	a = quotient (a, b)
Element &	remin (Element &x, const Element &y) const
	a = quotient (a, b)
void	quoRem (Element &q, Element &r, const Element &a, const Element &b) const
	q = [a/b], r = a - b*q |r| < |b|, and if r != 0, sign(r) = sign(b)
bool	isDivisor (const Element &a, const Element &b) const
	Test if b | a.
long	compare (const Element &a, const Element &b) const
	compare two elements, a and b return 1, if a > b return 0, if a = b; return -1.
Element &	abs (Element &x, const Element &a) const
	return the absolute value x = abs (a);

Static Public Member Functions
static int	maxCardinality ()

Data Fields
Element	zero
Element	one
Element	mOne

Detailed Description

the integer ring.

Member Typedef Documentation

RandIter

typedef NTL_ZZRandIter RandIter

Father_t

typedef NTL_ZZ Father_t

Element

typedef NTL::ZZ Element

Residu_t

typedef NTL::ZZ Residu_t

Constructor & Destructor Documentation

NTL_ZZ()

NTL_ZZ ( int p = 0, int exp = 1 )

inline

Member Function Documentation

cardinality()

integer & cardinality ( integer & c ) const

inline

characteristic() [1/2]

integer & characteristic ( integer & c ) const

inline

characteristic() [2/2]

template<class IntType>

IntType & characteristic ( IntType & c ) const

inline

write() [1/2]

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

inline

read() [1/2]

std::istream & read ( std::istream & in ) const

inline

init() [1/5]

template<class Element2>

Element & init ( Element & x, const Element2 & y ) const

inline

Init x from y.

init() [2/5]

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

inline

Init from a NTL::ZZ.

init() [3/5]

Element & init ( Element & x, const int64_t & y ) const

inline

Init from an int64_t.

init() [4/5]

Element & init ( Element & x, const uint64_t & y ) const

inline

Init from a uint64_t.

init() [5/5]

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

inline

I don't know how to init from integer efficiently.

convert() [1/2]

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

inline

Convert y to an Element.

convert() [2/2]

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

inline

assign()

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

inline

x = y.

areEqual()

bool areEqual ( const Element & x, const Element & y ) const

inline

Test if x == y.

isZero()

bool isZero ( const Element & x ) const

inline

Test if x == 0.

isOne()

bool isOne ( const Element & x ) const

inline

Test if x == 1.

isMOne()

bool isMOne ( const Element & x ) const

inline

Test if x == -1.

add()

Element & add ( Element & x, const Element & y, const Element & z ) const

inline

return x = y + z

sub()

Element & sub ( Element & x, const Element & y, const Element & z ) const

inline

return x = y - z

mul()

template<class Int>

Element & mul ( Element & x, const Element & y, const Int & z ) const

inline

return x = y * z

div()

Element & div ( Element & x, const Element & y, const Element & z ) const

inline

If z divides y, return x = y / z, otherwise, throw an exception.

inv()

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

inline

If y is a unit, return x = 1 / y, otherwsie, throw an exception.

neg()

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

inline

return x = -y;

axpy()

template<class Int>

Element & axpy ( Element & r, const Element & a, const Int & x, const Element & y ) const

inline

return r = a x + y

addin()

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

inline

return x += y;

subin()

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

inline

return x -= y;

mulin()

template<class Int>

Element & mulin ( Element & x, const Int & y ) const

inline

return x *= y;

divin()

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

inline

If y divides x, return x /= y, otherwise throw an exception.

invin()

Element & invin ( Element & x )

inline

If x is a unit, x = 1 / x, otherwise, throw an exception.

negin()

Element & negin ( Element & x ) const

inline

return x = -x;

axpyin()

template<class Int>

Element & axpyin ( Element & r, const Element & a, const Int & x ) const

inline

return r += a x

write() [2/2]

std::ostream & write ( std::ostream & out, const Element & y ) const

inline

out << y;

read() [2/2]

std::istream & read ( std::istream & in, Element & x ) const

inline

read x from istream in

isUnit()

bool isUnit ( const Element & x ) const

inline

some PIR function

Test if x is a unit.

gcd()

Element & gcd ( Element & g, const Element & a, const Element & b ) const

inline

return g = gcd (a, b)

gcdin()

Element & gcdin ( Element & g, const Element & b ) const

inline

return g = gcd (g, b)

xgcd()

Element & xgcd ( Element & g, Element & s, Element & t, const Element & a, const Element & b ) const

inline

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

The coefficients s and t are defined according to the standard Euclidean algorithm applied to |a| and |b|, with the signs then adjusted according to the signs of a and b.

lcm()

Element & lcm ( Element & c, const Element & a, const Element & b ) const

inline

c = lcm (a, b)

lcmin()

Element & lcmin ( Element & l, const Element & b ) const

inline

l = lcm (l, b)

sqrt()

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

inline

x = floor ( sqrt(y)).

RationalReconstruction()

long RationalReconstruction ( Element & a, Element & b, const Element & x, const Element & m, const Element & a_bound, const Element & b_bound ) const

inline

Requires 0 <= x < m, m > 2 * a_bound * b_bound, a_bound >= 0, b_bound > 0 This routine either returns 0, leaving a and b unchanged, or returns 1 and sets a and b so that (1) a = b x (mod m), (2) |a| <= a_bound, 0 < b <= b_bound, and (3) gcd(m, b) = gcd(a, b).

quo()

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

inline

q = floor (x/y);

rem()

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

inline

r = remindar of a / b

quoin()

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

inline

a = quotient (a, b)

remin()

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

inline

a = quotient (a, b)

quoRem()

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

inline

q = [a/b], r = a - b*q |r| < |b|, and if r != 0, sign(r) = sign(b)

isDivisor()

bool isDivisor ( const Element & a, const Element & b ) const

inline

Test if b | a.

compare()

long compare ( const Element & a, const Element & b ) const

inline

compare two elements, a and b return 1, if a > b return 0, if a = b; return -1.

if a < b

abs()

Element & abs ( Element & x, const Element & a ) const

inline

return the absolute value x = abs (a);

maxCardinality()

static int maxCardinality ( )

inlinestatic

Field Documentation

zero

Element zero

one

Element one

mOne

Element mOne

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

• ring/ntl/ntl-zz.h