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NTL_ZZ Class Reference

#include <ntl-ZZ.h>

List of all members.

Public Types

typedef NTL_ZZRandIter RandIter

typedef NTL::ZZ Element

Public Methods

NTL_ZZ (int p=0, int exp=1)

integer & cardinality (integer &c) const

integer & characteristic (integer &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 &y) const

Init from an int64.

Element & init (Element &x, const uint64 &y) const

Init from a uint64.

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

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

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.

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

Test if x is a unit.

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. 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.

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 reconstructRational (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

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

Static Public Methods

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

Convert y to an Element.

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

int getMaxModulus ()

Member Typedef Documentation

typedef NTL::ZZ Element

typedef NTL_ZZRandIter RandIter

Constructor & Destructor Documentation

NTL_ZZ ( int p = 0,

int exp = 1

) [inline]

Member Function Documentation

Element& abs ( Element & x,

const Element & a

) const [inline]

return the absolute value x = abs (a);

Element& add ( Element & x,

const Element & y,

const Element & z

) const [inline]

return x = y + z

Element& addin ( Element & x,

const Element & y

) const [inline]

return x += y;

bool areEqual ( const Element & x,

const Element & y

) const [inline]

Test if x == y.

Element& assign ( Element & x,

const Element & y

) const [inline]

x = y.

Element& axpy ( Element & r,

const Element & a,

const Int & x,

const Element & y

) const [inline]

return r = a x + y

Element& axpyin ( Element & r,

const Element & a,

const Int & x

) const [inline]

return r += a x

integer& cardinality ( integer & c ) const [inline]

integer& characteristic ( integer & c ) const [inline]

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

double& convert ( double & x,

const Element & y

) [inline, static]

integer& convert ( integer & x,

const Element & y

) [inline, static]

Convert y to an Element.

Element& div ( Element & x,

const Element & y,

const Element & z

) const [inline]

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

Element& divin ( Element & x,

const Element & y

) const [inline]

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

Element& gcd ( Element & g,

const Element & a,

const Element & b

) const [inline]

return g = gcd (a, b)

Element& gcdin ( Element & g,

const Element & b

) const [inline]

return g = gcd (g, b)

int getMaxModulus ( ) [inline, static]

Element& init ( Element & x,

const integer & y

) const [inline]

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

Element& init ( Element & x,

const uint64 & y

) const [inline]

Init from a uint64.

Element& init ( Element & x,

const int64 & y

) const [inline]

Init from an int64.

Element& init ( Element & x,

const Element & y

) const [inline]

Init from a NTL::ZZ.

Element& init ( Element & x,

const Element2 & y

) const [inline]

Init x from y.

Element& inv ( Element & x,

const Element & y

) const [inline]

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

Element& invin ( Element & x ) [inline]

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

bool isDivisor ( const Element & a,

const Element & b

) const [inline]

Test if b | a.

bool isOne ( const Element & x ) const [inline]

Test if x == 1.

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

Test if x is a unit.

bool isZero ( const Element & x ) const [inline]

Test if x == 0.

Element& lcm ( Element & c,

const Element & a,

const Element & b

) const [inline]

c = lcm (a, b)

Element& lcmin ( Element & l,

const Element & b

) const [inline]

l = lcm (l, b)

Element& mul ( Element & x,

const Element & y,

const Int & z

) const [inline]

return x = y * z

Element& mulin ( Element & x,

const Int & y

) const [inline]

return x *= y;

Element& neg ( Element & x,

const Element & y

) const [inline]

return x = -y;

Element& negin ( Element & x ) const [inline]

return x = -x;

Element& quo ( Element & q,

const Element & a,

const Element & b

) const [inline]

q = floor (x/y);

Element& quoin ( Element & a,

const Element & b

) const [inline]

a = quotient (a, b)

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)

std::istream& read ( std::istream & in,

Element & x

) const [inline]

read x from istream in

std::istream& read ( std::istream & in ) const [inline]

long reconstructRational ( 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).

Element& rem ( Element & r,

const Element & a,

const Element & b

) const [inline]

r = remindar of a / b

Element& remin ( Element & x,

const Element & y

) const [inline]

a = quotient (a, b)

Element& sqrt ( Element & x,

const Element & y

) const [inline]

x = floor ( sqrt(y)).

Element& sub ( Element & x,

const Element & y,

const Element & z

) const [inline]

return x = y - z

Element& subin ( Element & x,

const Element & y

) const [inline]

return x -= y;

std::ostream& write ( std::ostream & out,

const Element & y

) const [inline]

out << y;

std::ostream& write ( std::ostream & out ) const [inline]

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.

Generated on Mon Jun 20 09:16:55 2005 for linbox by

1.2.18


Public Types
typedef NTL_ZZRandIter	RandIter
typedef NTL::ZZ	Element
Public Methods
	NTL_ZZ (int p=0, int exp=1)
integer &	cardinality (integer &c) const
integer &	characteristic (integer &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 &y) const
	Init from an int64.
Element &	init (Element &x, const uint64 &y) const
	Init from a uint64.
Element &	init (Element &x, const integer &y) const
	I don't know how to init from integer efficiently.
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.
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
	Test if x is a unit.
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) = as + bt. 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.
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	reconstructRational (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 - bq \|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
Element &	abs (Element &x, const Element &a) const
Static Public Methods
integer &	convert (integer &x, const Element &y)
	Convert y to an Element.
double &	convert (double &x, const Element &y)
int	getMaxModulus ()