FermatDom Class Reference

Fermat numbers. More...

#include <givintprime.h>

Inheritance diagram for FermatDom:

Collaboration diagram for FermatDom:

Public Types
using	Self_t = ZRing< Integer >
using	Parent_t = UnparametricZRing< Integer >
typedef Integer	Rep
typedef Rep	Element
typedef RandomIntegerIterator< false, false >	RandIter
typedef GeneralRingNonZeroRandIter< Self_t >	NonZeroRandIter
enum
using	Residu_t = Integer
using	Element_ptr = Element *
using	ConstElement_ptr = const Element *
typedef const Element	ConstElement

Public Member Functions
	FermatDom ()
Rep &	fermat (Rep &, const size_t) const
bool	pepin (const size_t) const
int	operator== (const Self_t &) const
bool	operator== (const Self_t &F) const
int	operator!= (const Self_t &) const
bool	operator!= (const Self_t &F) const
template<class XXX >
XXX &	convert (XXX &x, const Rep &a) const
T &	convert (T &x, const Element &y) const
Rep &	mul (Rep &r, const Rep &a, const Rep &b) const
Rep &	mulin (Rep &r, const Rep &b) const
Rep &	div (Rep &r, const Rep &a, const Rep &b) const
Rep &	divin (Rep &r, const Rep &b) const
Rep &	mod (Rep &r, const Rep &a, const Rep &b) const
Rep &	modin (Rep &r, const Rep &b) const
Rep &	add (Rep &r, const Rep &a, const Rep &b) const
Rep &	addin (Rep &r, const Rep &b) const
Rep &	sub (Rep &r, const Rep &a, const Rep &b) const
Rep &	subin (Rep &r, const Rep &b) const
Rep &	divmod (Rep &q, Rep &r, const Rep &a, const Rep &b) const
Rep &	divexact (Rep &q, const Rep &a, const Rep &b) const
Rep &	axpy (Rep &r, const Rep &a, const Rep &b, const Rep &c) const
Rep &	maxpy (Rep &r, const Rep &a, const Rep &b, const Rep &c) const
Rep &	maxpyin (Rep &r, const Rep &a, const Rep &b) const
Rep &	axmy (Rep &r, const Rep &a, const Rep &b, const Rep &c) const
Rep &	axpyin (Rep &r, const Rep &a, const Rep &b) const
Rep &	axmyin (Rep &r, const Rep &a, const Rep &b) const
Rep &	neg (Rep &r, const Rep &a) const
Rep &	negin (Rep &r) const
Element &	quo (Element &q, const Element &a, const Element &b) const
Element &	rem (Element &r, const Element &a, const Element &b) const
Element &	quoin (Element &a, const Element &b) const
Element &	remin (Element &a, const Element &b) const
void	quoRem (Element &q, Element &r, const Element &a, const Element &b) const
Element &	logtwo (Element &z, const Element &x) const
Rep &	gcd (Rep &g, Rep &u, Rep &v, const Rep &a, const Rep &b) const
Rep &	gcd (Rep &g, const Rep &a, const Rep &b) const
Rep &	gcdin (Rep &g, const Rep &a) const
Rep &	lcm (Rep &l, const Rep &a, const Rep &b) const
Rep &	lcmin (Rep &l, const Rep &a) const
Element &	dxgcd (Element &g, Element &s, Element &t, Element &u, Element &v, const Element &a, const Element &b) const
Rep &	inv (Rep &u, const Rep &a, const Rep &b) const
Rep &	invin (Rep &u, const Rep &b) const
Rep &	invmod (Rep &u, const Rep &a, const Rep &b) const
Rep &	invmodin (Rep &u, const Rep &b) const
bool	ratrecon (Rep &num, Rep &den, const Rep &f, const Rep &m, const Rep &numbound, bool forcereduce=true, bool recurs=true) const
bool	RationalReconstruction (Rep &, Rep &, const Rep &, const Rep &) const
bool	RationalReconstruction (Rep &, Rep &, const Rep &, const Rep &, const Rep &, bool=true, bool=true) const
bool	RationalReconstruction (Rep &, Rep &, const Rep &, const Rep &, const Rep &, const Rep &) const
Rep &	pow (Rep &r, const Rep &n, const int64_t l) const
Rep &	pow (Rep &r, const Rep &n, const uint64_t l) const
Rep &	pow (Rep &r, const Rep &n, const int32_t l) const
Rep &	pow (Rep &r, const Rep &n, const uint32_t l) const
Rep &	sqrt (Rep &s, const Rep &n) const
Rep &	sqrt (Rep &s, Rep &r, const Rep &n) const
int64_t	logp (const Rep &a, const Rep &p) const
Rep &	powmod (Rep &r, const Rep &n, const int64_t e, const Rep &m) const
Rep &	powmod (Rep &r, const Rep &n, const Rep &e, const Rep &m) const
uint64_t	length (const Rep &a) const
int	sign (const Rep &a) const
bool	isZero (const Rep &a) const
bool	isZero (const Element &a) const
bool	isOne (const Rep &a) const
bool	isOne (const Element &a) const
bool	isMOne (const Rep &a) const
bool	isMOne (const Element &a) const
bool	isUnit (const Rep &x) const
	isUnit More...
bool	isUnit (const Element &a) const
bool	isDivisor (const Element &a, const Element &b) const
	isDivisor (a, b) Test if b | a. More...
Element &	abs (Element &x, const Element &a) const
Element	abs (const Element &a) const
Element &	abs (Element &x, const Element &a) const
Element	abs (const Element &a) const
int32_t	compare (const Rep &a, const Rep &b) const
long	compare (const Element &a, const Element &b) const
bool	areEqual (const Rep &a, const Rep &b) const
bool	areNEqual (const Rep &a, const Rep &b) const
bool	areAssociates (const Element &x, const Element &y) const
bool	isgeq (const Rep &a, const Rep &b) const
bool	isgeq (const int64_t b, const Rep &a) const
bool	isgeq (const Rep &a, const int64_t b) const
bool	isleq (const Rep &a, const Rep &b) const
bool	isleq (const int64_t b, const Rep &a) const
bool	isleq (const Rep &a, const int64_t b) const
bool	isgt (const Rep &a, const Rep &b) const
bool	isgt (const int64_t b, const Rep &a) const
bool	isgt (const Rep &a, const int64_t b) const
bool	islt (const Rep &a, const Rep &b) const
bool	islt (const int64_t b, const Rep &a) const
bool	islt (const Rep &a, const int64_t b) const
template<class MyRandIter >
Rep &	random (MyRandIter &, Rep &r, long s=1) const
template<class MyRandIter >
Rep &	random (MyRandIter &, Rep &r, const Rep &b) const
Element &	random (const Random &g, Element &r) const
template<class MyRandIter >
Rep &	nonzerorandom (MyRandIter &, Rep &r, long s=1) const
template<class MyRandIter >
Rep &	nonzerorandom (MyRandIter &, Rep &r, const Rep &b) const
Element &	nonzerorandom (const Random &g, Element &a) const
std::istream &	read (std::istream &i)
std::istream &	read (std::istream &is, Element &a) const
	Read field element. More...
std::ostream &	write (std::ostream &o) const
std::ostream &	write (std::ostream &os, const Element &a) const
	Print field element. More...
Residu_t	residu () const
Residu_t	size () const
Residu_t	cardinality () const
T &	cardinality (T &c) const
Residu_t	characteristic () const
T &	characteristic (T &c) const
Element &	init (Element &x) const
Element &	init (Element &x, const T &s) const
Element &	assign (Element &x, const Element &y) const
Element &	reduce (Element &x, const Element &y) const
Element &	reduce (Element &x) const
Element	minElement () const
Element	maxElement () const
Arithmetic Operations
The first argument is set and is also the return value.
Element &	mul (Element &x, const Element &y, const Element &z) const
	x := y*z More...
Element &	div (Element &x, const Element &y, const Element &z) const
	x := y/z More...
Element &	mod (Element &x, const Element &y, const Element &z) const
	x := y mod z More...
Element &	add (Element &x, const Element &y, const Element &z) const
	x := y + z More...
Element &	sub (Element &x, const Element &y, const Element &z) const
	x := y - z More...
Element &	axpy (Element &z, const Element &a, const Element &x, const Element &y) const
	z := a*x + y More...
Element &	maxpy (Element &z, const Element &a, const Element &x, const Element &y) const
	z := y - a*x More...
Element &	maxpyin (Element &z, const Element &a, const Element &x) const
	z := z - a*x More...
Element &	axmy (Element &z, const Element &a, const Element &x, const Element &y) const
	z := a*x - y More...
Element &	axpyin (Element &z, const Element &a, const Element &x) const
	z := a*x + z More...
Element &	axmyin (Element &z, const Element &a, const Element &x) const
	z := a*x - z More...
Element &	neg (Element &x, const Element &y) const
	x := -y More...
Element &	inv (Element &x, const Element &y) const
	x := 1/y More...
Inplace Arithmetic Operations
The first argument is modified and the result is the return value.
Element &	mulin (Element &x, const Element &y) const
	x := x*y More...
Element &	divin (Element &x, const Element &y) const
	x := x/y More...
Element &	modin (Element &x, const Element &y) const
	x := x mod y More...
Element &	addin (Element &x, const Element &y) const
	x := x + y More...
Element &	subin (Element &x, const Element &y) const
	x := x - y More...
Element &	negin (Element &x) const
	x := -x More...
Element &	invin (Element &x) const
	x := 1/x More...
Comparison Predicates
bool	areEqual (const Element &x, const Element &y) const
	x == y More...
Input/Output Operations
std::istream &	read (std::istream &is) const
	Read field. More...
std::ostream &	write (std::ostream &os, std::string F) const
	Read field. More...

Static Public Member Functions
static Residu_t	maxCardinality ()
static Residu_t	minCardinality ()
static const std::string	type_string ()

Data Fields
const Element	one
const Element	zero
const Element	mOne

Detailed Description

Fermat numbers.

Member Typedef Documentation

Self_t

using Self_t = ZRing<Integer>

inherited

Parent_t

using Parent_t = UnparametricZRing<Integer>

inherited

Rep

typedef Integer Rep

inherited

Examples

examples/Integer/RSA_decipher.C, and examples/Integer/RSA_encipher.C.

Element

typedef Rep Element

inherited

Examples

examples/Integer/isproot.C, examples/Integer/lambda.C, examples/Integer/lambda_inv.C, examples/Integer/phi.C, examples/Integer/primitiveelement.C, examples/Integer/primitiveroot.C, and examples/Integer/probable_primroot.C.

RandIter

typedef RandomIntegerIterator<false,false> RandIter

inherited

NonZeroRandIter

typedef GeneralRingNonZeroRandIter<Self_t> NonZeroRandIter

inherited

Residu_t

using Residu_t = Integer

inherited

Element_ptr

using Element_ptr = Element*

inherited

ConstElement_ptr

using ConstElement_ptr = const Element*

inherited

ConstElement

typedef const Element ConstElement

inherited

Member Enumeration Documentation

anonymous enum

anonymous enum

inherited

Constructor & Destructor Documentation

FermatDom()

FermatDom ( )

inline

Member Function Documentation

fermat()

FermatDom::Rep & fermat	(	Rep &	f,
		const size_t	n
	)		const

pepin()

bool pepin

(

const size_t

n

)

const

operator==() [1/2]

int operator== ( const Self_t &  ) const

inlineinherited

operator==() [2/2]

bool operator== ( const Self_t &  F ) const

inlineinherited

operator!=() [1/2]

int operator!= ( const Self_t &  ) const

inlineinherited

operator!=() [2/2]

bool operator!= ( const Self_t &  F ) const

inlineinherited

convert() [1/2]

XXX& convert ( XXX &  x, const Rep &  a  ) const

inlineinherited

convert() [2/2]

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

inlineinherited

mul() [1/2]

Rep& mul ( Rep &  r, const Rep &  a, const Rep &  b  ) const

inlineinherited

mul() [2/2]

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

inlinevirtualinherited

x := y*z

Implements RingInterface< _Element >.

mulin() [1/2]

Rep& mulin ( Rep &  r, const Rep &  b  ) const

inlineinherited

mulin() [2/2]

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

inlinevirtualinherited

x := x*y

Implements RingInterface< _Element >.

div() [1/2]

Rep& div ( Rep &  r, const Rep &  a, const Rep &  b  ) const

inlineinherited

div() [2/2]

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

inlineinherited

x := y/z

divin() [1/2]

Rep& divin ( Rep &  r, const Rep &  b  ) const

inlineinherited

divin() [2/2]

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

inlineinherited

x := x/y

mod() [1/2]

Rep& mod ( Rep &  r, const Rep &  a, const Rep &  b  ) const

inlineinherited

mod() [2/2]

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

inlineinherited

x := y mod z

modin() [1/2]

Rep& modin ( Rep &  r, const Rep &  b  ) const

inlineinherited

modin() [2/2]

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

inlineinherited

x := x mod y

add() [1/2]

Rep& add ( Rep &  r, const Rep &  a, const Rep &  b  ) const

inlineinherited

add() [2/2]

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

inlinevirtualinherited

x := y + z

Implements RingInterface< _Element >.

addin() [1/2]

Rep& addin ( Rep &  r, const Rep &  b  ) const

inlineinherited

addin() [2/2]

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

inlinevirtualinherited

x := x + y

Implements RingInterface< _Element >.

sub() [1/2]

Rep& sub ( Rep &  r, const Rep &  a, const Rep &  b  ) const

inlineinherited

Examples

examples/Integer/primitiveroot.C.

sub() [2/2]

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

inlinevirtualinherited

x := y - z

Implements RingInterface< _Element >.

subin() [1/2]

Rep& subin ( Rep &  r, const Rep &  b  ) const

inlineinherited

subin() [2/2]

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

inlinevirtualinherited

x := x - y

Implements RingInterface< _Element >.

divmod()

Rep& divmod ( Rep &  q, Rep &  r, const Rep &  a, const Rep &  b  ) const

inlineinherited

divexact()

Rep& divexact ( Rep &  q, const Rep &  a, const Rep &  b  ) const

inlineinherited

axpy() [1/2]

Rep& axpy ( Rep &  r, const Rep &  a, const Rep &  b, const Rep &  c  ) const

inlineinherited

axpy() [2/2]

Element& axpy ( Element &  z, const Element &  a, const Element &  x, const Element &  y  ) const

inlinevirtualinherited

z := a*x + y

Implements RingInterface< _Element >.

maxpy() [1/2]

Rep& maxpy ( Rep &  r, const Rep &  a, const Rep &  b, const Rep &  c  ) const

inlineinherited

maxpy() [2/2]

Element& maxpy ( Element &  z, const Element &  a, const Element &  x, const Element &  y  ) const

inlinevirtualinherited

z := y - a*x

Implements RingInterface< _Element >.

maxpyin() [1/2]

Rep& maxpyin ( Rep &  r, const Rep &  a, const Rep &  b  ) const

inlineinherited

maxpyin() [2/2]

Element& maxpyin ( Element &  z, const Element &  a, const Element &  x  ) const

inlinevirtualinherited

z := z - a*x

Implements RingInterface< _Element >.

axmy() [1/2]

Rep& axmy ( Rep &  r, const Rep &  a, const Rep &  b, const Rep &  c  ) const

inlineinherited

axmy() [2/2]

Element& axmy ( Element &  z, const Element &  a, const Element &  x, const Element &  y  ) const

inlinevirtualinherited

z := a*x - y

Implements RingInterface< _Element >.

axpyin() [1/2]

Rep& axpyin ( Rep &  r, const Rep &  a, const Rep &  b  ) const

inlineinherited

axpyin() [2/2]

Element& axpyin ( Element &  z, const Element &  a, const Element &  x  ) const

inlinevirtualinherited

z := a*x + z

Implements RingInterface< _Element >.

axmyin() [1/2]

Rep& axmyin ( Rep &  r, const Rep &  a, const Rep &  b  ) const

inlineinherited

axmyin() [2/2]

Element& axmyin ( Element &  z, const Element &  a, const Element &  x  ) const

inlinevirtualinherited

z := a*x - z

Implements RingInterface< _Element >.

neg() [1/2]

Rep& neg ( Rep &  r, const Rep &  a  ) const

inlineinherited

neg() [2/2]

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

inlinevirtualinherited

x := -y

Implements RingInterface< _Element >.

negin() [1/2]

Rep& negin ( Rep &  r ) const

inlineinherited

negin() [2/2]

Element& negin ( Element &  x ) const

inlinevirtualinherited

x := -x

Implements RingInterface< _Element >.

quo()

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

inlineinherited

rem()

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

inlineinherited

quoin()

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

inlineinherited

remin()

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

inlineinherited

quoRem()

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

inlineinherited

logtwo()

Element& logtwo ( Element &  z, const Element &  x  ) const

inlineinherited

gcd() [1/2]

Rep& gcd ( Rep &  g, Rep &  u, Rep &  v, const Rep &  a, const Rep &  b  ) const

inlineinherited

Examples

examples/Integer/probable_primroot.C.

gcd() [2/2]

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

inlineinherited

gcdin()

Rep& gcdin ( Rep &  g, const Rep &  a  ) const

inlineinherited

lcm()

Rep& lcm ( Rep &  l, const Rep &  a, const Rep &  b  ) const

inlineinherited

lcmin()

Rep& lcmin ( Rep &  l, const Rep &  a  ) const

inlineinherited

dxgcd()

Element& dxgcd ( Element &  g, Element &  s, Element &  t, Element &  u, Element &  v, const Element &  a, const Element &  b  ) const

inlineinherited

inv() [1/2]

Rep& inv ( Rep &  u, const Rep &  a, const Rep &  b  ) const

inlineinherited

inv() [2/2]

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

inlineinherited

x := 1/y

invin() [1/2]

Rep& invin ( Rep &  u, const Rep &  b  ) const

inlineinherited

invin() [2/2]

Element& invin ( Element &  x ) const

inlineinherited

x := 1/x

invmod()

Rep& invmod ( Rep &  u, const Rep &  a, const Rep &  b  ) const

inlineinherited

invmodin()

Rep& invmodin ( Rep &  u, const Rep &  b  ) const

inlineinherited

ratrecon()

bool ratrecon ( Rep &  num, Rep &  den, const Rep &  f, const Rep &  m, const Rep &  numbound, bool  forcereduce = true, bool  recurs = true  ) const

inherited

RationalReconstruction() [1/3]

bool RationalReconstruction ( Rep &  a, Rep &  b, const Rep &  x, const Rep &  m  ) const

inherited

RationalReconstruction() [2/3]

bool RationalReconstruction ( Rep &  a, Rep &  b, const Rep &  x, const Rep &  m, const Rep &  bound, bool  forcereduce = true, bool  recurs = true  ) const

inherited

RationalReconstruction() [3/3]

bool RationalReconstruction ( Rep &  a, Rep &  b, const Rep &  x, const Rep &  m, const Rep &  a_bound, const Rep &  b_bound  ) const

inherited

pow() [1/4]

Rep& pow ( Rep &  r, const Rep &  n, const int64_t  l  ) const

inlineinherited

pow() [2/4]

Rep& pow ( Rep &  r, const Rep &  n, const uint64_t  l  ) const

inlineinherited

pow() [3/4]

Rep& pow ( Rep &  r, const Rep &  n, const int32_t  l  ) const

inlineinherited

pow() [4/4]

Rep& pow ( Rep &  r, const Rep &  n, const uint32_t  l  ) const

inlineinherited

sqrt() [1/2]

Rep& sqrt ( Rep &  s, const Rep &  n  ) const

inlineinherited

sqrt() [2/2]

Rep& sqrt ( Rep &  s, Rep &  r, const Rep &  n  ) const

inlineinherited

logp()

int64_t logp ( const Rep &  a, const Rep &  p  ) const

inlineinherited

powmod() [1/2]

Rep& powmod ( Rep &  r, const Rep &  n, const int64_t  e, const Rep &  m  ) const

inlineinherited

powmod() [2/2]

Rep& powmod ( Rep &  r, const Rep &  n, const Rep &  e, const Rep &  m  ) const

inlineinherited

length()

uint64_t length ( const Rep &  a ) const

inlineinherited

sign()

int sign ( const Rep &  a ) const

inlineinherited

isZero() [1/2]

bool isZero ( const Rep &  a ) const

inlineinherited

isZero() [2/2]

bool isZero ( const Element &  a ) const

inlinevirtualinherited

Implements RingInterface< _Element >.

isOne() [1/2]

bool isOne ( const Rep &  a ) const

inlineinherited

isOne() [2/2]

bool isOne ( const Element &  a ) const

inlinevirtualinherited

Implements RingInterface< _Element >.

isMOne() [1/2]

bool isMOne ( const Rep &  a ) const

inlineinherited

isMOne() [2/2]

bool isMOne ( const Element &  a ) const

inlinevirtualinherited

Implements RingInterface< _Element >.

isUnit() [1/2]

bool isUnit ( const Rep &  x ) const

inlineinherited

isUnit

isUnit() [2/2]

bool isUnit ( const Element &  a ) const

inlinevirtualinherited

Implements RingInterface< _Element >.

isDivisor()

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

inlineinherited

isDivisor (a, b) Test if b | a.

abs() [1/4]

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

inlineinherited

abs() [2/4]

Element abs ( const Element &  a ) const

inlineinherited

abs() [3/4]

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

inlineinherited

abs() [4/4]

Element abs ( const Element &  a ) const

inlineinherited

compare() [1/2]

int32_t compare ( const Rep &  a, const Rep &  b  ) const

inlineinherited

compare() [2/2]

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

inlineinherited

areEqual() [1/2]

bool areEqual ( const Rep &  a, const Rep &  b  ) const

inlineinherited

areEqual() [2/2]

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

inlinevirtualinherited

x == y

Implements RingInterface< _Element >.

areNEqual()

bool areNEqual ( const Rep &  a, const Rep &  b  ) const

inlineinherited

areAssociates()

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

inlineinherited

isgeq() [1/3]

bool isgeq ( const Rep &  a, const Rep &  b  ) const

inlineinherited

isgeq() [2/3]

bool isgeq ( const int64_t  b, const Rep &  a  ) const

inlineinherited

isgeq() [3/3]

bool isgeq ( const Rep &  a, const int64_t  b  ) const

inlineinherited

isleq() [1/3]

bool isleq ( const Rep &  a, const Rep &  b  ) const

inlineinherited

isleq() [2/3]

bool isleq ( const int64_t  b, const Rep &  a  ) const

inlineinherited

isleq() [3/3]

bool isleq ( const Rep &  a, const int64_t  b  ) const

inlineinherited

isgt() [1/3]

bool isgt ( const Rep &  a, const Rep &  b  ) const

inlineinherited

isgt() [2/3]

bool isgt ( const int64_t  b, const Rep &  a  ) const

inlineinherited

isgt() [3/3]

bool isgt ( const Rep &  a, const int64_t  b  ) const

inlineinherited

islt() [1/3]

bool islt ( const Rep &  a, const Rep &  b  ) const

inlineinherited

islt() [2/3]

bool islt ( const int64_t  b, const Rep &  a  ) const

inlineinherited

islt() [3/3]

bool islt ( const Rep &  a, const int64_t  b  ) const

inlineinherited

random() [1/3]

Rep& random ( MyRandIter &  , Rep &  r, long  s = 1  ) const

inlineinherited

random() [2/3]

Rep& random ( MyRandIter &  , Rep &  r, const Rep &  b  ) const

inlineinherited

random() [3/3]

Element& random ( const Random &  g, Element &  r  ) const

inlineinherited

nonzerorandom() [1/3]

Rep& nonzerorandom ( MyRandIter &  , Rep &  r, long  s = 1  ) const

inlineinherited

nonzerorandom() [2/3]

Rep& nonzerorandom ( MyRandIter &  , Rep &  r, const Rep &  b  ) const

inlineinherited

nonzerorandom() [3/3]

Element& nonzerorandom ( const Random &  g, Element &  a  ) const

inlineinherited

read() [1/3]

std::istream& read ( std::istream &  i )

inlineinherited

read() [2/3]

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

inlinevirtualinherited

Read field element.

Returns

input stream from which field element is read.

Parameters

is	input stream from which field element is read.
x	field element.

Reimplemented from UnparametricOperations< _Element >.

read() [3/3]

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

inlineinherited

Read field.

Returns

input stream from which field is read.

Parameters

is	input stream from which field is read.

write() [1/3]

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

inlinevirtualinherited

Implements RingInterface< _Element >.

Examples

examples/Integer/lambda.C, examples/Integer/lambda_inv.C, examples/Integer/phi.C, examples/Integer/primitiveelement.C, and examples/Integer/probable_primroot.C.

write() [2/3]

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

inlinevirtualinherited

Print field element.

Returns

output stream to which field element is written.

Parameters

os	output stream to which field element is written.
x	field element.

Reimplemented from UnparametricOperations< _Element >.

write() [3/3]

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

inlineinherited

Read field.

Returns

input stream from which field is read.

Parameters

is	input stream from which field is read.

residu()

Residu_t residu ( ) const

inlineinherited

size()

Residu_t size ( ) const

inlineinherited

cardinality() [1/2]

Residu_t cardinality ( ) const

inlineinherited

cardinality() [2/2]

T& cardinality ( T &  c ) const

inlineinherited

characteristic() [1/2]

Residu_t characteristic ( ) const

inlineinherited

characteristic() [2/2]

T& characteristic ( T &  c ) const

inlineinherited

maxCardinality()

static Residu_t maxCardinality ( )

inlinestaticinherited

minCardinality()

static Residu_t minCardinality ( )

inlinestaticinherited

init() [1/2]

Element& init ( Element &  x ) const

inlinevirtualinherited

Reimplemented from UnparametricOperations< _Element >.

init() [2/2]

Element& init ( Element &  x, const T &  s  ) const

inlineinherited

assign()

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

inlinevirtualinherited

Reimplemented from UnparametricOperations< _Element >.

reduce() [1/2]

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

inlineinherited

reduce() [2/2]

Element& reduce ( Element &  x ) const

inlineinherited

minElement()

Element minElement ( ) const

inlineinherited

maxElement()

Element maxElement ( ) const

inlineinherited

type_string()

static const std::string type_string ( )

inlinestaticinherited

Field Documentation

one

const Element one

inherited

Examples

examples/Integer/primitiveroot.C.

zero

const Element zero

inherited

mOne

const Element mOne

inherited

---

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

• givintprime.h
• givintprime.C