#include <givintfactor.h>

Inheritance diagram for IntFactorDom< MyRandIter >:

Public Types
typedef MyRandIter	random_generator

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

using	Residu_t

using	Residu_t

using	Element_ptr

using	Element_ptr

using	ConstElement_ptr

using	ConstElement_ptr

enum

typedef const Element	ConstElement

Public Member Functions
	IntFactorDom (MyRandIter g=MyRandIter())

Rep &	factor (Rep &r, const Rep &n, unsigned long loops=0) const

Rep &	iffactorprime (Rep &r, const Rep &n, unsigned long loops=0) const

Rep &	primefactor (Rep &r, const Rep &n) const

template<class Container1, class Container2>
bool	set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
	Factors with primes.

template<class Container>
void	set (Container &, const Rep &) const

template<class Container>
void	Erathostene (Container &, const Rep &) const

template<class Container, class Cont2, class Cont3>
Container &	divisors (Container &L, const Cont2 &Lf, const Cont3 &Le) const

template<class Container>
Container &	divisors (Container &, const Rep &) const

Rep &	Erathostene (Rep &, const Rep &p) const
	returns a small factor

Rep &	Pollard (const MyRandIter &, Rep &, const Rep &n, unsigned long threshold=0) const

Rep &	Lenstra (const MyRandIter &, Rep &, const Rep &n, const Rep &B1=10000000, const unsigned long curves=30) const

std::ostream &	write (std::ostream &o, const Rep &n) const

template<class Array>
std::ostream &	write (std::ostream &o, Array &, const Rep &n) const

int	isprime (const Rep &n, int r=_GIVARO_ISPRIMETESTS_) const

unsigned int	isprimepower (Rep &, const Rep &) const

template<class MyRandIter>
unsigned int	Miller (MyRandIter &g, const Rep &n=_GIVARO_ISPRIMETESTS_) const

template<class MyRandIter>
Rep &	test_Lehmann (MyRandIter &g, Rep &, const Rep &n=_GIVARO_ISPRIMETESTS_) const

template<class MyRandIter>
int	Lehmann (MyRandIter &g, const Rep &n=_GIVARO_ISPRIMETESTS_) const

int	isprime_Tabule (const int n) const

int	isprime_Tabule2 (const int n) const

Rep &	nextprime (Rep &, const Rep &, int r=_GIVARO_ISPRIMETESTS_) const

Rep &	prevprime (Rep &, const Rep &, int r=_GIVARO_ISPRIMETESTS_) const

Rep &	nextprimein (Rep &, int r=_GIVARO_ISPRIMETESTS_) const

Rep &	prevprimein (Rep &, int r=_GIVARO_ISPRIMETESTS_) const

int	local_prime (const Rep &n, int r=_GIVARO_ISPRIMETESTS_) 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 &	inv (Rep &u, const Rep &a, const Rep &b) const

Rep &	invin (Rep &u) 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

virtual bool	isZero (const Element &a) const =0

bool	isOne (const Rep &a) const

virtual bool	isOne (const Element &a) const =0

bool	isMOne (const Rep &a) const

virtual bool	isMOne (const Element &a) const =0

bool	isUnit (const Rep &x) const
	isUnit

virtual bool	isUnit (const Element &a) const =0

bool	isDivisor (const Element &a, const Element &b) const
	isDivisor (a, b) Test if b \| a.

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

Element	abs (const Element &a) const

int32_t	compare (const Rep &a, const Rep &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 (Random &g, Element &a) const

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

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

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

Residu_t	residu () const

Residu_t	residu () const

Residu_t	size () const

Residu_t	size () const

Residu_t	cardinality () const

T &	cardinality (T &c) const

Residu_t	cardinality () const

T &	cardinality (T &c) const

Residu_t	characteristic () const

T &	characteristic (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 &	init (Element &x) const

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

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

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

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

Element &	reduce (Element &x) const

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

Element &	reduce (Element &x) const

Element	minElement () const

Element	minElement () const

Element	maxElement () 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

Element &	div (Element &x, const Element &y, const Element &z) const
	x := y/z

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

Element &	add (Element &x, const Element &y, const Element &z) const
	x := y + z

Element &	sub (Element &x, const Element &y, const Element &z) const
	x := y - z

Element &	axpy (Element &z, const Element &a, const Element &x, const Element &y) const
	z := a*x + y

Element &	maxpy (Element &z, const Element &a, const Element &x, const Element &y) const
	z := y - a*x

Element &	maxpyin (Element &z, const Element &a, const Element &x) const
	z := z - a*x

Element &	axmy (Element &z, const Element &a, const Element &x, const Element &y) const
	z := a*x - y

Element &	axpyin (Element &z, const Element &a, const Element &x) const
	z := a*x + z

Element &	axmyin (Element &z, const Element &a, const Element &x) const
	z := a*x - z

Element &	neg (Element &x, const Element &y) const
	x := -y

Element &	inv (Element &x, const Element &y) const
	x := 1/y

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

Element &	divin (Element &x, const Element &y) const
	x := x/y

Element &	modin (Element &x, const Element &y) const
	x := x mod y

Element &	addin (Element &x, const Element &y) const
	x := x + y

Element &	subin (Element &x, const Element &y) const
	x := x - y

Element &	negin (Element &x) const
	x := -x

Element &	invin (Element &x) const
	x := 1/x

Comparison Predicates
bool	areEqual (const Element &x, const Element &y) const
	x == y

Input/Output Operations
std::istream &	read (std::istream &is) const
	Read field.

virtual std::istream &	read (std::istream &is, Element &x) const
	Read field element.

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

std::ostream &	write (std::ostream &os, const Element &x) const
	Print field element.

Data Object Management.
first argument is set and the value is also returned.
Element &	init (Element &x) const

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

Static Public Member Functions
static Residu_t	maxCardinality ()

static Residu_t	maxCardinality ()

static Residu_t	minCardinality ()

static Residu_t	minCardinality ()

static const std::string	type_string ()

static const std::string	type_string ()

Data Fields
const Element	one

const Element	one

const Element	zero

const Element	zero

const Element	mOne

const Element	mOne

Protected Attributes
MyRandIter	_g

Detailed Description

template<class MyRandIter = GivRandom>
class Givaro::IntFactorDom< MyRandIter >

Integer Factor Domain.

Examples: examples/Integer/ProbLucas.C, examples/Integer/ifactor.C, and examples/Integer/ifactor_lenstra.C.

Member Typedef Documentation

◆ random_generator

template<class MyRandIter = GivRandom>

typedef MyRandIter random_generator

◆ Self_t

using Self_t = ZRing<Integer>

inherited

◆ Parent_t

using Parent_t = UnparametricZRing<Integer>

inherited

◆ Rep

typedef Integer Rep

inherited

◆ Element

typedef Rep Element

inherited

◆ RandIter

typedef RandomIntegerIterator<false,false> RandIter

inherited

◆ NonZeroRandIter

typedef GeneralRingNonZeroRandIter<Self_t> NonZeroRandIter

inherited

◆ Residu_t [1/2]

using Residu_t

inherited

◆ Residu_t [2/2]

using Residu_t

inherited

◆ Element_ptr [1/2]

using Element_ptr

inherited

◆ Element_ptr [2/2]

using Element_ptr

inherited

◆ ConstElement_ptr [1/2]

using ConstElement_ptr

inherited

◆ ConstElement_ptr [2/2]

using ConstElement_ptr

inherited

◆ ConstElement

template<class _Element>

typedef const Element ConstElement

inherited

Member Enumeration Documentation

◆ anonymous enum

anonymous enum

inherited

Constructor & Destructor Documentation

◆ IntFactorDom()

template<class MyRandIter = GivRandom>

IntFactorDom ( MyRandIter g = MyRandIter() )

inline

Member Function Documentation

◆ factor()

template<class MyRandIter = GivRandom>

Rep & factor	(	Rep &	r,
		const Rep &	n,
		unsigned long	loops = 0 ) const

inline

◆ iffactorprime()

template<class MyRandIter = GivRandom>

Rep & iffactorprime	(	Rep &	r,
		const Rep &	n,
		unsigned long	loops = 0 ) const

inline

◆ primefactor()

template<class MyRandIter = GivRandom>

Rep & primefactor	(	Rep &	r,
		const Rep &	n ) const

inline

◆ set() [1/2]

template<class MyRandIter>

template<class Container1, class Container2>

bool set	(	Container1 &	setint,
		Container2 &	setpwd,
		const Rep &	a,
		unsigned long	loops = 0 ) const

Factors with primes.

◆ set() [2/2]

template<class MyRandIter>

template<class Container>

void set	(	Container &	Lf,
		const Rep &	n ) const

◆ Erathostene() [1/2]

template<class MyRandIter>

template<class Container>

void Erathostene	(	Container &	Lf,
		const Rep &	p ) const

◆ divisors() [1/2]

template<class MyRandIter>

template<class Container, class Cont2, class Cont3>

Container & divisors	(	Container &	L,
		const Cont2 &	Lf,
		const Cont3 &	Le ) const

◆ divisors() [2/2]

template<class MyRandIter>

template<class Container>

Container & divisors	(	Container &	L,
		const Rep &	n ) const

◆ Erathostene() [2/2]

template<class MyRandIter = GivRandom>

Rep & Erathostene	(	Rep &	,
		const Rep &	p ) const

returns a small factor

◆ Pollard()

template<class MyRandIter>

IntFactorDom< MyRandIter >::Rep & Pollard	(	const MyRandIter &	gen,
		Rep &	g,
		const Rep &	n,
		unsigned long	threshold = 0 ) const

◆ Lenstra()

template<class MyRandIter>

IntFactorDom< MyRandIter >::Rep & Lenstra	(	const MyRandIter &	gen,
		Rep &	g,
		const Rep &	n,
		const Rep &	B1 = 10000000,
		const unsigned long	curves = 30 ) const

◆ write() [1/5]

template<class MyRandIter>

std::ostream & write	(	std::ostream &	o,
		const Rep &	n ) const

◆ write() [2/5]

template<class MyRandIter>

template<class Array>

std::ostream & write	(	std::ostream &	o,
		Array &	Lf,
		const Rep &	n ) const

◆ isprime()

int isprime	(	const Rep &	n,
		int	r = _GIVARO_ISPRIMETESTS_ ) const

inlineinherited

Examples: examples/Integer/nb_primes.C.

◆ isprimepower()

unsigned int isprimepower	(	Rep &	q,
		const Rep &	u ) const

inherited

◆ Miller()

template<class MyRandIter>

unsigned int Miller	(	MyRandIter &	g,
		const Rep &	n = _GIVARO_ISPRIMETESTS_ ) const

inherited

◆ test_Lehmann()

template<class MyRandIter>

IntPrimeDom::Rep & test_Lehmann	(	MyRandIter &	g,
		Rep &	r,
		const Rep &	n = _GIVARO_ISPRIMETESTS_ ) const

inherited

◆ Lehmann()

template<class MyRandIter>

int Lehmann	(	MyRandIter &	g,
		const Rep &	n = _GIVARO_ISPRIMETESTS_ ) const

inherited

◆ isprime_Tabule()

int isprime_Tabule ( const int n ) const

inherited

◆ isprime_Tabule2()

int isprime_Tabule2 ( const int n ) const

inherited

◆ nextprime()

IntPrimeDom::Rep & nextprime	(	Rep &	,
		const Rep &	,
		int	r = _GIVARO_ISPRIMETESTS_ ) const

inherited

◆ prevprime()

IntPrimeDom::Rep & prevprime	(	Rep &	n,
		const Rep &	p,
		int	r = _GIVARO_ISPRIMETESTS_ ) const

inherited

◆ nextprimein()

IntPrimeDom::Rep & nextprimein	(	Rep &	,
		int	r = _GIVARO_ISPRIMETESTS_ ) const

inherited

Examples: examples/Integer/nb_primes.C, and examples/Polynomial/PolynomialCRT.C.

◆ prevprimein()

IntPrimeDom::Rep & prevprimein	(	Rep &	n,
		int	r = _GIVARO_ISPRIMETESTS_ ) const

inherited

◆ local_prime()

int local_prime	(	const Rep &	n,
		int	r = _GIVARO_ISPRIMETESTS_ ) const

inlineinherited

◆ 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]

template<class XXX>

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]

template<class _Element>

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]

template<class _Element>

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]

template<class _Element>

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]

template<class _Element>

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]

template<class _Element>

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]

template<class _Element>

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]

template<class _Element>

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]

template<class _Element>

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

◆ sub() [2/2]

template<class _Element>

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]

template<class _Element>

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]

template<class _Element>

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]

template<class _Element>

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]

template<class _Element>

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]

template<class _Element>

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]

template<class _Element>

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]

template<class _Element>

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]

template<class _Element>

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]

template<class _Element>

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

◆ 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() [1/3]

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

inlineinherited

◆ inv() [2/3]

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

inlineinherited

◆ inv() [3/3]

template<class _Element>

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

inlineinherited

x := 1/y

◆ invin() [1/3]

Rep & invin ( Rep & u ) const

inlineinherited

◆ invin() [2/3]

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

inlineinherited

◆ invin() [3/3]

template<class _Element>

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 &	,
		Rep &	,
		const Rep &	,
		const Rep &	) const

inherited

◆ RationalReconstruction() [2/3]

bool RationalReconstruction	(	Rep &	,
		Rep &	,
		const Rep &	,
		const Rep &	,
		const Rep &	,
		bool	= true,
		bool	= true ) const

inherited

◆ RationalReconstruction() [3/3]

bool RationalReconstruction	(	Rep &	,
		Rep &	,
		const Rep &	,
		const Rep &	,
		const Rep &	,
		const Rep &	) 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]

template<class _Element>

virtual bool isZero ( const Element & a ) const

pure virtualinherited

Implemented in UnparametricZRing< _Element >.

◆ isOne() [1/2]

bool isOne ( const Rep & a ) const

inlineinherited

◆ isOne() [2/2]

template<class _Element>

virtual bool isOne ( const Element & a ) const

pure virtualinherited

Implemented in UnparametricZRing< _Element >.

◆ isMOne() [1/2]

bool isMOne ( const Rep & a ) const

inlineinherited

◆ isMOne() [2/2]

template<class _Element>

virtual bool isMOne ( const Element & a ) const

pure virtualinherited

Implemented in UnparametricZRing< _Element >.

◆ isUnit() [1/2]

bool isUnit ( const Rep & x ) const

inlineinherited

isUnit

◆ isUnit() [2/2]

template<class _Element>

virtual bool isUnit ( const Element & a ) const

pure virtualinherited

Implemented in UnparametricZRing< _Element >.

◆ isDivisor()

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

inlineinherited

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

◆ abs() [1/2]

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

inlineinherited

◆ abs() [2/2]

Element abs ( const Element & a ) const

inlineinherited

◆ compare()

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

inlineinherited

◆ areEqual() [1/2]

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

inlineinherited

◆ areEqual() [2/2]

template<class _Element>

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]

template<class MyRandIter>

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

inlineinherited

◆ random() [2/3]

template<class MyRandIter>

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]

template<class MyRandIter>

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

inlineinherited

◆ nonzerorandom() [2/3]

template<class MyRandIter>

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

inlineinherited

◆ nonzerorandom() [3/3]

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

inlineinherited

◆ read() [1/4]

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

inlineinherited

◆ read() [2/4]

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

inlineinherited

◆ read() [3/4]

template<class _Element>

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.

◆ read() [4/4]

template<class _Element>

virtual 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.

Implements RingInterface< _Element >.

Reimplemented in UnparametricZRing< _Element >, UnparametricZRing< Element >, and UnparametricZRing< Element >.

◆ write() [3/5]

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

inlineinherited

◆ write() [4/5]

template<class _Element>

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.

◆ write() [5/5]

template<class _Element>

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.

Implements RingInterface< _Element >.

Reimplemented in UnparametricZRing< _Element >.

◆ residu() [1/2]

Residu_t residu ( ) const

inlineinherited

◆ residu() [2/2]

Residu_t residu ( ) const

inlineinherited

◆ size() [1/2]

Residu_t size ( ) const

inlineinherited

◆ size() [2/2]

Residu_t size ( ) const

inlineinherited

◆ cardinality() [1/4]

Residu_t cardinality ( ) const

inlineinherited

◆ cardinality() [2/4]

T & cardinality ( T & c ) const

inlineinherited

◆ cardinality() [3/4]

Residu_t cardinality ( ) const

inlineinherited

◆ cardinality() [4/4]

T & cardinality ( T & c ) const

inlineinherited

◆ characteristic() [1/4]

Residu_t characteristic ( ) const

inlineinherited

◆ characteristic() [2/4]

T & characteristic ( T & c ) const

inlineinherited

◆ characteristic() [3/4]

Residu_t characteristic ( ) const

inlineinherited

◆ characteristic() [4/4]

T & characteristic ( T & c ) const

inlineinherited

◆ maxCardinality() [1/2]

static Residu_t maxCardinality ( )

inlinestaticinherited

◆ maxCardinality() [2/2]

static Residu_t maxCardinality ( )

inlinestaticinherited

◆ minCardinality() [1/2]

static Residu_t minCardinality ( )

inlinestaticinherited

◆ minCardinality() [2/2]

static Residu_t minCardinality ( )

inlinestaticinherited

◆ init() [1/5]

Element & init ( Element & x ) const

inlineinherited

◆ init() [2/5]

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

inlineinherited

◆ init() [3/5]

Element & init ( Element & x ) const

inlineinherited

◆ init() [4/5]

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

inlineinherited

◆ init() [5/5]

template<class _Element>

Element & init ( Element & x ) const

inlinevirtualinherited

Implements RingInterface< _Element >.

Reimplemented in UnparametricZRing< _Element >.

◆ assign() [1/3]

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

inlineinherited

◆ assign() [2/3]

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

inlineinherited

◆ assign() [3/3]

template<class _Element>

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

inlinevirtualinherited

Implements RingInterface< _Element >.

Reimplemented in UnparametricZRing< _Element >.

◆ reduce() [1/4]

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

inlineinherited

◆ reduce() [2/4]

Element & reduce ( Element & x ) const

inlineinherited

◆ reduce() [3/4]

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

inlineinherited

◆ reduce() [4/4]

Element & reduce ( Element & x ) const

inlineinherited

◆ minElement() [1/2]

Element minElement ( ) const

inlineinherited

◆ minElement() [2/2]

Element minElement ( ) const

inlineinherited

◆ maxElement() [1/2]

Element maxElement ( ) const

inlineinherited

◆ maxElement() [2/2]

Element maxElement ( ) const

inlineinherited

◆ type_string() [1/2]

static const std::string type_string ( )

inlinestaticinherited

◆ type_string() [2/2]

static const std::string type_string ( )

inlinestaticinherited

Field Documentation

◆ _g

template<class MyRandIter = GivRandom>

MyRandIter _g

protected

◆ one [1/2]

const Element one

inherited

◆ one [2/2]

const Element one

inherited

◆ zero [1/2]

const Element zero

inherited

◆ zero [2/2]

const Element zero

inherited

◆ mOne [1/2]

const Element mOne

inherited

◆ mOne [2/2]

const Element mOne

inherited

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

Public Types

Public Member Functions

Static Public Member Functions

Data Fields

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ random_generator

◆ Self_t

◆ Parent_t

◆ Rep

◆ Element

◆ RandIter

◆ NonZeroRandIter

◆ Residu_t [1/2]

◆ Residu_t [2/2]

◆ Element_ptr [1/2]

◆ Element_ptr [2/2]

◆ ConstElement_ptr [1/2]

◆ ConstElement_ptr [2/2]

◆ ConstElement

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ IntFactorDom()

Member Function Documentation

◆ factor()

◆ iffactorprime()

◆ primefactor()

◆ set() [1/2]

◆ set() [2/2]

◆ Erathostene() [1/2]

◆ divisors() [1/2]

◆ divisors() [2/2]

◆ Erathostene() [2/2]

◆ Pollard()

◆ Lenstra()

◆ write() [1/5]

◆ write() [2/5]

◆ isprime()

◆ isprimepower()

◆ Miller()

◆ test_Lehmann()

◆ Lehmann()

◆ isprime_Tabule()

◆ isprime_Tabule2()

◆ nextprime()

◆ prevprime()

◆ nextprimein()

◆ prevprimein()

◆ local_prime()

◆ operator==() [1/2]

◆ operator==() [2/2]

◆ operator!=() [1/2]

◆ operator!=() [2/2]

◆ convert() [1/2]

◆ convert() [2/2]

◆ mul() [1/2]

◆ mul() [2/2]

◆ mulin() [1/2]

◆ mulin() [2/2]

◆ div() [1/2]

◆ div() [2/2]

◆ divin() [1/2]

◆ divin() [2/2]

◆ mod() [1/2]

◆ mod() [2/2]

◆ modin() [1/2]

◆ modin() [2/2]

◆ add() [1/2]

◆ add() [2/2]

◆ addin() [1/2]

◆ addin() [2/2]

◆ sub() [1/2]

◆ sub() [2/2]

◆ subin() [1/2]

◆ subin() [2/2]

◆ divmod()

◆ divexact()

◆ axpy() [1/2]