#include <givintsqrootmod.h>

Inheritance diagram for IntSqrtModDom< MyRandIter >:

Public Types
typedef IntFactorDom< MyRandIter >	Father_t

typedef IntFactorDom< MyRandIter >::Rep	Rep

typedef GivRandom	random_generator

using	Self_t

using	Parent_t

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
	IntSqrtModDom (MyRandIter g=MyRandIter())

Rep &	sqrootmod (Rep &x, const Rep &a, const Rep &n) const

void	Brillhart (Rep &, Rep &, const Rep &) const

void	sumofsquaresmodprime (Rep &, Rep &, const Rep &, const Rep &) const

void	sumofsquaresmodprimeDeterministic (Rep &, Rep &, const Rep &, const Rep &) const

void	sumofsquaresmodprimeMonteCarlo (Rep &, Rep &, const Rep &, const Rep &) const

void	sumofsquaresmodprimeNoERH (Rep &, Rep &, const Rep &, const Rep &) const

void	sumofsquaresmodprimewithnonresidue (Rep &, Rep &, const Rep &, const Rep &, const Rep &) const

Rep &	sqrootmodprime (Rep &x, const Rep &a, const Rep &p) const

Rep &	sqrootmodprimepower (Rep &x, const Rep &a, const Rep &p, const uint64_t k, const Rep &pk) const

Rep &	sqrootmodpoweroftwo (Rep &x, const Rep &a, const uint64_t k, const Rep &pk) const

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

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

void	set (Container &, const Rep &) const

void	Erathostene (Container &, const Rep &) const

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

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

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

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

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

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

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

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

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

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

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

Rep &	test_Lehmann (GivRandom &g, Rep &, const Rep &n=_GIVARO_ISPRIMETESTS_) const

int	Lehmann (GivRandom &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

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

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

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

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

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

Rep &	nonzerorandom (GivRandom &, 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

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

Input/Output Operations
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.

std::istream &	read (std::istream &is) const
	Read field.

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

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 &	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 &	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

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

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

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 Member Functions
Rep &	sqrootlinear (Rep &x, const Rep &a, const Rep &p, const uint64_t k) const

Rep &	sqroottwolinear (Rep &x, const Rep &a, const uint64_t k) const

Rep &	sqroothensellift (Rep &x, const Rep &a, const Rep &p, const uint64_t k, const Rep &pk) const

Rep &	sqrootonemorelift (Rep &x, const Rep &a, const Rep &p, const uint64_t k, const Rep &pk) const

Rep &	sqrootmodtwolift (Rep &x, const Rep &a, const uint64_t k, const Rep &pk) const

Protected Attributes
GivRandom	_g

Detailed Description

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

Modular square roots.

Examples: examples/Integer/ModularSquareRoot.C.

Member Typedef Documentation

◆ Father_t

template<class MyRandIter = GivRandom>

typedef IntFactorDom< MyRandIter > Father_t

◆ Rep

template<class MyRandIter = GivRandom>

typedef IntFactorDom<MyRandIter>::Rep Rep

◆ random_generator

typedef GivRandom random_generator

inherited

◆ Self_t

using Self_t

inherited

◆ Parent_t

using Parent_t

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

typedef const Element ConstElement

inherited

Member Enumeration Documentation

◆ anonymous enum

anonymous enum

inherited

Constructor & Destructor Documentation

◆ IntSqrtModDom()

template<class MyRandIter = GivRandom>

IntSqrtModDom ( MyRandIter g = MyRandIter () )

inline

Member Function Documentation

◆ sqrootmod()

template<class MyRandIter>

IntSqrtModDom< MyRandIter >::Rep & sqrootmod	(	Rep &	x,
		const Rep &	a,
		const Rep &	n ) const

inline

◆ Brillhart()

template<class MyRandIter>

void Brillhart	(	Rep &	a,
		Rep &	b,
		const Rep &	p ) const

inline

◆ sumofsquaresmodprime()

template<class MyRandIter>

void sumofsquaresmodprime	(	Rep &	a,
		Rep &	b,
		const Rep &	k,
		const Rep &	p ) const

inline

◆ sumofsquaresmodprimeDeterministic()

template<class MyRandIter>

void sumofsquaresmodprimeDeterministic	(	Rep &	a,
		Rep &	b,
		const Rep &	k,
		const Rep &	p ) const

inline

◆ sumofsquaresmodprimeMonteCarlo()

template<class MyRandIter>

void sumofsquaresmodprimeMonteCarlo	(	Rep &	a,
		Rep &	b,
		const Rep &	k,
		const Rep &	p ) const

inline

◆ sumofsquaresmodprimeNoERH()

template<class MyRandIter>

void sumofsquaresmodprimeNoERH	(	Rep &	a,
		Rep &	b,
		const Rep &	k,
		const Rep &	p ) const

inline

◆ sumofsquaresmodprimewithnonresidue()

template<class MyRandIter>

void sumofsquaresmodprimewithnonresidue	(	Rep &	a,
		Rep &	b,
		const Rep &	k,
		const Rep &	s,
		const Rep &	p ) const

inline

◆ sqrootmodprime()

template<class MyRandIter>

IntSqrtModDom< MyRandIter >::Rep & sqrootmodprime	(	Rep &	x,
		const Rep &	a,
		const Rep &	p ) const

inline

◆ sqrootmodprimepower()

template<class MyRandIter>

IntSqrtModDom< MyRandIter >::Rep & sqrootmodprimepower	(	Rep &	x,
		const Rep &	a,
		const Rep &	p,
		const uint64_t	k,
		const Rep &	pk ) const

inline

◆ sqrootmodpoweroftwo()

template<class MyRandIter>

IntSqrtModDom< MyRandIter >::Rep & sqrootmodpoweroftwo	(	Rep &	x,
		const Rep &	a,
		const uint64_t	k,
		const Rep &	pk ) const

inline

◆ sqrootlinear()

template<class MyRandIter>

IntSqrtModDom< MyRandIter >::Rep & sqrootlinear	(	Rep &	x,
		const Rep &	a,
		const Rep &	p,
		const uint64_t	k ) const

inlineprotected

◆ sqroottwolinear()

template<class MyRandIter>

IntSqrtModDom< MyRandIter >::Rep & sqroottwolinear	(	Rep &	x,
		const Rep &	a,
		const uint64_t	k ) const

inlineprotected

◆ sqroothensellift()

template<class MyRandIter>

IntSqrtModDom< MyRandIter >::Rep & sqroothensellift	(	Rep &	x,
		const Rep &	a,
		const Rep &	p,
		const uint64_t	k,
		const Rep &	pk ) const

inlineprotected

◆ sqrootonemorelift()

template<class MyRandIter>

IntSqrtModDom< MyRandIter >::Rep & sqrootonemorelift	(	Rep &	x,
		const Rep &	a,
		const Rep &	p,
		const uint64_t	k,
		const Rep &	pk ) const

inlineprotected

◆ sqrootmodtwolift()

template<class MyRandIter>

IntSqrtModDom< MyRandIter >::Rep & sqrootmodtwolift	(	Rep &	x,
		const Rep &	a,
		const uint64_t	k,
		const Rep &	pk ) const

inlineprotected

◆ factor()

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

inlineinherited

◆ iffactorprime()

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

inlineinherited

◆ primefactor()

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

inlineinherited

◆ set() [1/2]

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

inherited

Factors with primes.

◆ set() [2/2]

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

inherited

◆ Erathostene() [1/2]

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

inherited

◆ Erathostene() [2/2]

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

inherited

returns a small factor

◆ divisors() [1/2]

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

inherited

◆ divisors() [2/2]

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

inherited

◆ Pollard()

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

inherited

◆ Lenstra()

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

inherited

◆ write() [1/5]

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

inherited

◆ write() [2/5]

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

inherited

◆ write() [3/5]

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

inlineinherited

◆ write() [4/5]

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]

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

inlineinherited

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.

◆ isprime()

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

inlineinherited

◆ isprimepower()

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

inherited

◆ Miller()

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

inherited

◆ test_Lehmann()

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

inherited

◆ Lehmann()

int Lehmann	(	GivRandom &	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

◆ 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]

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

inlineinherited

x := y*z

◆ mulin() [1/2]

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

inlineinherited

◆ mulin() [2/2]

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

inlineinherited

x := x*y

◆ div() [1/3]

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

inlineinherited

◆ div() [2/3]

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

inlineinherited

x := y/z

◆ div() [3/3]

template<class _Element>

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

inlineinherited

x := y/z

◆ divin() [1/3]

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

inlineinherited

◆ divin() [2/3]

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

inlineinherited

x := x/y

◆ divin() [3/3]

template<class _Element>

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

inlineinherited

x := x/y

◆ mod() [1/3]

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

inlineinherited

◆ mod() [2/3]

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

inlineinherited

x := y mod z

◆ mod() [3/3]

template<class _Element>

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

inlineinherited

x := y mod z

◆ modin() [1/3]

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

inlineinherited

◆ modin() [2/3]

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

inlineinherited

x := x mod y

◆ modin() [3/3]

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]

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

inlineinherited

x := y + z

◆ addin() [1/2]

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

inlineinherited

◆ addin() [2/2]

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

inlineinherited

x := x + y

◆ sub() [1/2]

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

inlineinherited

◆ sub() [2/2]

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

inlineinherited

x := y - z

◆ subin() [1/2]

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

inlineinherited

◆ subin() [2/2]

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

inlineinherited

x := x - y

◆ 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

inlineinherited

z := a*x + y

◆ 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

inlineinherited

z := y - a*x

◆ 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

inlineinherited

z := z - a*x

◆ 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

inlineinherited

z := a*x - y

◆ 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

inlineinherited

z := a*x + z

◆ 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

inlineinherited

z := a*x - z

◆ neg() [1/2]

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

inlineinherited

◆ neg() [2/2]

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

inlineinherited

x := -y

◆ negin() [1/2]

Rep & negin ( Rep & r ) const

inlineinherited

◆ negin() [2/2]

Element & negin ( Element & x ) const

inlineinherited

x := -x

◆ 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() [1/4]

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

inlineinherited

◆ inv() [2/4]

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

inlineinherited

◆ inv() [3/4]

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

inlineinherited

x := 1/y

◆ inv() [4/4]

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]

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]

virtual bool isZero ( const Element & a ) const

pure virtualinherited

◆ isOne() [1/2]

bool isOne ( const Rep & a ) const

inlineinherited

◆ isOne() [2/2]

virtual bool isOne ( const Element & a ) const

pure virtualinherited

◆ isMOne() [1/2]

bool isMOne ( const Rep & a ) const

inlineinherited

◆ isMOne() [2/2]

virtual bool isMOne ( const Element & a ) const

pure virtualinherited

◆ isUnit() [1/2]

bool isUnit ( const Rep & x ) const

inlineinherited

isUnit

◆ isUnit() [2/2]

virtual bool isUnit ( const Element & a ) const

pure virtualinherited

◆ 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]

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

inlineinherited

x == y

◆ 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	(	GivRandom &	,
		Rep &	r,
		long	s = 1 ) const

inlineinherited

◆ random() [2/3]

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

inlineinherited

◆ random() [3/3]

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

inlineinherited

◆ nonzerorandom() [1/3]

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

inlineinherited

◆ nonzerorandom() [2/3]

Rep & nonzerorandom	(	GivRandom &	,
		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]

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]

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.

◆ 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]

Element & init ( Element & x ) const

inlineinherited

◆ 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]

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

inlineinherited

◆ 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

GivRandom _g

protectedinherited

◆ 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 Member Functions

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ Father_t

◆ Rep

◆ random_generator

◆ Self_t

◆ Parent_t

◆ 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

◆ IntSqrtModDom()

Member Function Documentation

◆ sqrootmod()

◆ Brillhart()

◆ sumofsquaresmodprime()

◆ sumofsquaresmodprimeDeterministic()

◆ sumofsquaresmodprimeMonteCarlo()

◆ sumofsquaresmodprimeNoERH()

◆ sumofsquaresmodprimewithnonresidue()

◆ sqrootmodprime()

◆ sqrootmodprimepower()

◆ sqrootmodpoweroftwo()

◆ sqrootlinear()

◆ sqroottwolinear()

◆ sqroothensellift()

◆ sqrootonemorelift()

◆ sqrootmodtwolift()

◆ factor()

◆ iffactorprime()

◆ primefactor()

◆ set() [1/2]

◆ set() [2/2]

◆ Erathostene() [1/2]

◆ Erathostene() [2/2]

◆ divisors() [1/2]

◆ divisors() [2/2]

◆ Pollard()

◆ Lenstra()

◆ write() [1/5]

◆ write() [2/5]

◆ write() [3/5]

◆ write() [4/5]

◆ write() [5/5]

◆ 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]