Arithmetic on GF(p^k), with p a prime number less than 2^15. More...

Data Structures
class	ArrayAllocatort
	ArrayAllocator: class for allocation of arrays. More...
class	Array0Tag
struct	__giv_map_less_ith< T, UNARYOP, 0 >
struct	__giv_map_less_ith< T, UNARYOP, ith >
struct	__giv_map_less_ith_const< T, UNARYOP, 0 >
struct	__giv_map_less_ith_const< T, UNARYOP, ith >
class	Bits
struct	ElemRef
struct	ElemConstRef
struct	Pair
class	Key
	The class Key. More...
class	HashTable
class	List0
class	Stack
class	Integer
	This is the Integer class. More...
class	IntegerDom
class	IntFactorDom
class	IntNumTheoDom
class	FermatDom
class	IntPrimeDom
class	IntRNSsystem
class	IntRSADom
class	IntSqrtModDom
class	GivMMInfo
class	BlocFreeList
class	GivMMFreeList
class	GivMMRefCount
class	GivaroMM
class	RefCountPtr
class	RefCounter
struct	ieee
class	Rational
class	RationalDom
class	Neutral
class	givNoInit
class	givNoCopy
class	givWithCopy
class	GivError
class	GivMathError
class	GivBadFormat
class	GivMathDivZero
struct	__givdom_trait_name
class	BaseDomain
class	GivaroMain
class	GivaroAppli
class	GivaroNoInit
class	InitAfter
class	GivModule
class	ObjectInit
class	GivRandom
class	BaseTimer
	base for class RealTimer; class SysTimer; class UserTimer; More...
class	RealTimer
class	UserTimer
class	SysTimer
class	Timer
class	GIV_randIter
	Random field Element generator. More...
struct	ChineseRemainder
struct	ChineseRemainder< Ring, Domain, false >
class	Extension
class	GIV_ExtensionrandIter
class	GFqDom
class	GFqExtFast
class	GFqExt
struct	GFqKronecker
class	Montgomery< Std32 >
	This class implements the standard arithmetic with Modulo Elements. More...
class	Primes16
class	RNSsystem
	class RNSsystem. More...
class	RNSsystemFixed
	NO DOC. More...
class	AdicSize
class	ZpzDom< Std16 >
	This class implement the standard arithmetic with Modulo Elements. More...
class	ZpzDom< Log16 >
	This class implement the standard arithmetic with Modulo Elements. More...
class	ZpzDom< Std32 >
	This class implement the standard arithmetic with Modulo Elements. More...
class	ZpzDom< Unsigned32 >
	This class implement the standard arithmetic with Modulo Elements. More...
class	ZpzDom< Std64 >
	This class implement the standard arithmetic with Modulo Elements. More...
class	ZpzDom< Integer >
	This class implement the standard arithmetic with Modulo Elements. More...
struct	Std16
struct	Std32
struct	Unsigned32
struct	Log16
struct	Std64
class	StaticElement
class	MatrixDom< Domain, Dense >
class	MatrixDom
class	MatrixDom< Domain, Sparse >
struct	RetMatrixStorage
struct	RetMatrix2Storage
struct	RetMatrixStorage< T, Dense >
struct	RetMatrixStorage< T, Sparse >
class	Degree
class	Indeter
struct	Interpolation
struct	NewtonInterpGeomMultip
struct	NewtonInterpGeom
class	Poly1CRT
class	givvector
class	Poly1Dom< Domain, Dense >
class	Poly1FactorDom
class	Poly1PadicDom< Domain, Dense >
struct	KSpace
class	Undefined
struct	IsEqual
struct	IsEqual< A, A >
struct	IsNotEqual
class	Sporadic
class	Dense
class	Sparse
struct	Sparsity_Trait
class	DefaultFormat
struct	StructFormat
class	FixedTruncDom
struct	Frac
struct	FracDom
struct	HighOrder
class	isUndefinedIterator
class	isForwardIterator
class	isBidirectionalIterator
class	isRandomIterator
struct	IteratorTraits
struct	IteratorInterface
struct	BaseOP
struct	CopyOp
struct	MulOp
struct	DivOp
struct	ModOp
struct	AddOp
struct	SubOp
struct	NegOp
struct	MulAddOp
struct	Curried1
struct	Curried2
struct	QuotientDom
class	TruncDom
struct	RetVectorStorage
struct	RetVector2Storage
struct	RetVectorStorage< T, Dense >
class	VectorDom
	VectorDom<Domain,StorageTag> More...
class	VectorDom< Domain, Sparse >
Typedefs
typedef BaseDomain< char >	CharDom
typedef BaseDomain< short >	ShortDom
typedef BaseDomain< int >	IntDom
typedef BaseDomain< long >	LongDom
typedef BaseDomain< float >	FloatDom
typedef BaseDomain< double >	DoubleDom
Functions
template<class T >
class Array0	GIVARO_PERF_INEHERIT (Array0, T)
template<class T , size_t SIZE>
class ArrayFixed	GIVARO_PERF_INEHERIT (ArrayFixed, T)
std::ostream &	operator<< (std::ostream &o, const Bits &a)
template<class T1 , class T2 >
ostream &	operator<< (ostream &o, const Pair< T1, T2 > &p)
template<class T1 , class T2 >
istream &	operator>> (istream &fin, Pair< T1, T2 > &p)
int	compare (const Integer &a, const Integer &b)
int	absCompare (const Integer &a, const Integer &b)
Integer &	inv (Integer &u, const Integer &a, const Integer &b)
Integer &	invin (Integer &u, const Integer &b)
Integer	gcd (const Integer &a, const Integer &b)
Integer	gcd (const Integer &a, const Integer &b, Integer &u, Integer &v)
Integer &	gcd (Integer &g, const Integer &a, const Integer &b)
Integer &	gcd (Integer &g, const Integer &a, const Integer &b, Integer &u, Integer &v)
Integer	pp (const Integer &P, const Integer &Q)
Integer &	lcm (Integer &g, const Integer &a, const Integer &b)
Integer	lcm (const Integer &a, const Integer &b)
Integer &	pow (Integer &Res, const Integer &n, const long l)
Integer &	pow (Integer &Res, const unsigned long n, const unsigned long l)
Integer &	pow (Integer &Res, const Integer &n, const unsigned long l)
Integer &	pow (Integer &Res, const Integer &n, const int l)
Integer &	pow (Integer &Res, const Integer &n, const unsigned int l)
Integer	pow (const Integer &n, const long l)
Integer	pow (const Integer &n, const unsigned long l)
Integer	pow (const Integer &n, const int l)
Integer	pow (const Integer &n, const unsigned int l)
Integer &	powmod (Integer &Res, const Integer &n, const unsigned long e, const Integer &m)
Integer &	powmod (Integer &Res, const Integer &n, const long e, const Integer &m)
Integer &	powmod (Integer &Res, const Integer &n, const unsigned int e, const Integer &m)
Integer &	powmod (Integer &Res, const Integer &n, const int e, const Integer &m)
Integer &	powmod (Integer &Res, const Integer &n, const Integer &e, const Integer &m)
Integer	powmod (const Integer &n, const unsigned long e, const Integer &m)
Integer	powmod (const Integer &n, const long e, const Integer &m)
Integer	powmod (const Integer &n, const unsigned int e, const Integer &m)
Integer	powmod (const Integer &n, const int e, const Integer &m)
Integer	powmod (const Integer &n, const Integer &e, const Integer &m)
Integer	fact (unsigned long l)
Integer	sqrt (const Integer &p)
Integer	sqrtrem (const Integer &p, Integer &rem)
Integer &	sqrt (Integer &r, const Integer &p)
Integer &	sqrtrem (Integer &r, const Integer &p, Integer &rem)
bool	root (Integer &q, const Integer &, unsigned int n)
long	logp (const Integer &a, const Integer &p)
double	logtwo (const Integer &a)
double	naturallog (const Integer &a)
void	swap (Integer &, Integer &)
int	sign (const Integer &a)
int	isZero (const Integer &a)
int	isOne (const Integer &a)
int	isperfectpower (const Integer &)
Integer	abs (const Integer &n)
Integer &	prevprime (Integer &, const Integer &p)
Integer &	nextprime (Integer &, const Integer &p)
int	probab_prime (const Integer &p)
int	probab_prime (const Integer &p, int r)
int	jacobi (const Integer &u, const Integer &v)
int	legendre (const Integer &u, const Integer &v)
unsigned long	length (const Integer &a)
std::istream &	operator>> (std::istream &i, Integer &n)
std::ostream &	operator<< (std::ostream &o, const Integer &n)
std::ostream &	absOutput (std::ostream &o, const Integer &n)
void	importWords (Integer &, size_t, int, int, int, size_t, const void *)
int	operator!= (const Integer &a, const Integer &b)
int	operator!= (int l, const Integer &n)
int	operator!= (long l, const Integer &n)
int	operator!= (unsigned long l, const Integer &n)
int	operator== (const Integer &a, const Integer &b)
int	operator== (int l, const Integer &n)
int	operator== (long l, const Integer &n)
int	operator== (unsigned long l, const Integer &n)
int	operator== (const Integer &n, unsigned long l)
int	operator== (const Integer &n, int l)
int	operator== (const Integer &n, long l)
int	operator< (const Integer &a, const Integer &b)
int	operator< (const int l, const Integer &n)
int	operator< (const long l, const Integer &n)
int	operator< (const unsigned long l, const Integer &n)
int	operator<= (const Integer &n, unsigned long l)
int	operator<= (unsigned long l, const Integer &n)
int	operator>= (unsigned long l, const Integer &n)
int	operator>= (const Integer &n, unsigned long l)
int	operator> (int l, const Integer &n)
int	operator> (long l, const Integer &n)
int	operator> (unsigned long l, const Integer &n)
int	operator> (const Integer &a, const Integer &b)
int	operator<= (const Integer &a, const Integer &b)
int	operator<= (const Integer &n, int l)
int	operator<= (const Integer &n, long l)
int	operator<= (int l, const Integer &n)
int	operator<= (long l, const Integer &n)
int	operator>= (const Integer &a, const Integer &b)
int	operator>= (int l, const Integer &n)
int	operator>= (long l, const Integer &n)
int	operator>= (const Integer &n, int l)
int	operator>= (const Integer &n, long l)
Integer	operator+ (const int l, const Integer &n)
Integer	operator+ (const unsigned int l, const Integer &n)
Integer	operator+ (const long l, const Integer &n)
Integer	operator+ (const unsigned long l, const Integer &n)
Integer	operator+ (const Integer &n, const int l)
Integer	operator+ (const Integer &n, const unsigned int l)
Integer &	operator+= (Integer &n, const int l)
Integer &	operator+= (Integer &n, const unsigned int l)
Integer	operator- (const int l, const Integer &n)
Integer	operator- (const unsigned int l, const Integer &n)
Integer	operator- (const long l, const Integer &n)
Integer	operator- (const unsigned long l, const Integer &n)
Integer	operator- (const Integer &n, const int l)
Integer	operator- (const Integer &n, const unsigned int l)
Integer &	operator-= (Integer &n, const int l)
Integer &	operator-= (Integer &n, const unsigned int l)
Integer	operator* (const int l, const Integer &n)
Integer	operator* (const unsigned int l, const Integer &n)
Integer	operator* (const long l, const Integer &n)
Integer	operator* (const unsigned long l, const Integer &n)
Integer	operator* (const Integer &n, const int l)
Integer	operator* (const Integer &n, const unsigned int l)
Integer &	operator*= (Integer &n, const int l)
Integer &	operator*= (Integer &n, const unsigned int l)
Integer	operator/ (const int l, const Integer &n)
Integer	operator/ (const long l, const Integer &n)
Integer	operator/ (const Integer &n, const int l)
Integer	operator/ (const Integer &n, const unsigned int l)
Integer &	operator/= (Integer &n, const int l)
Integer &	operator/= (Integer &n, const long l)
Integer &	operator/= (Integer &n, const unsigned int l)
Integer	operator% (const int l, const Integer &n)
Integer	operator% (const long l, const Integer &n)
Integer	operator% (const Integer &n, const int l)
Integer	operator% (const Integer &n, const unsigned int l)
Integer &	operator%= (Integer &n, const int l)
Integer &	operator%= (Integer &n, const unsigned int l)
int	isZero (const short int a)
int	isZero (const int a)
int	isZero (const long a)
int	isZero (const unsigned short int a)
int	isZero (const unsigned int a)
int	isZero (const unsigned long a)
void	Add_Curve (const Integer &n, const Integer A, const Integer &ax, const Integer &az, Integer &cx, Integer &cz)
void	one_Mul_Curve (const Integer &n, const Integer A, const Integer &mm, const Integer &nn, const Integer &px, const Integer &pz, Integer &ax, Integer &az)
void	one_Mul_Curve2 (const Integer &n, const Integer A, const Integer &mm, const Integer &nn, const Integer &px, const Integer &pz, Integer &aax, Integer &aaz)
void	Mul_Curve (const Integer &n, Integer &Ai, const Integer &mm, const Integer &nn, const Integer &B1, Integer &Xi, Integer &Zi)
Integer &	ppin (Integer &res, const Integer &prime)
std::ostream &	operator<< (std::ostream &o, const GivMMInfo &T)
int	compare (const Rational &a, const Rational &b)
int	absCompare (const Rational &a, const Rational &b)
template double	power (double x, unsigned int p)
std::istream &	operator>> (std::istream &in, Rational &r)
const Rational	pow (const Rational &r, const long l)
const Integer	floor (const Rational &r)
const Integer	ceil (const Rational &r)
const Integer	round (const Rational &r)
const Integer	trunc (const Rational &r)
const Rational	abs (const Rational &r)
const Rational	pow (const Rational &n, unsigned int l)
const Rational	pow (const Rational &n, unsigned long l)
unsigned long	length (const Rational &r)
int	sign (const Rational &r)
int	isZero (const Rational &r)
int	isOne (const Rational &r)
int	isInteger (const Rational &r)
int	operator!= (const Rational &a, const Rational &b)
int	operator== (const Rational &a, const Rational &b)
int	operator< (const Rational &a, const Rational &b)
int	operator> (const Rational &a, const Rational &b)
int	operator<= (const Rational &a, const Rational &b)
int	operator>= (const Rational &a, const Rational &b)
const Rational	operator+ (const Rational &r, const int i)
const Rational	operator- (const Rational &r, const int i)
const Rational	operator* (const Rational &r, const int i)
const Rational	operator/ (const Rational &r, const int i)
const Rational	operator+ (const int i, const Rational &r)
const Rational	operator- (const int i, const Rational &r)
const Rational	operator* (const int i, const Rational &r)
const Rational	operator/ (const int i, const Rational &r)
std::ostream &	operator<< (std::ostream &o, const Rational &a)
std::ostream &	operator<< (std::ostream &o, const GivError &E)
template<typename T >
unsigned	GIVINTLOG (const T &a)
template<class TT , class UU >
TT	power (const TT n, const UU l)
template<class D , class TT >
TT &	dom_power (TT &res, const TT &n, long l, const D &F)
std::ostream &	operator<< (std::ostream &o, const BaseTimer &BT)
std::ostream &	operator<< (std::ostream &o, const Timer &T)
template<class Rt >
Rt	FF_EXPONENT_MAX (const Rt p, const Rt e=1)
template<typename Field >
unsigned long	Exponent_Trait (const Field &F)
template<>
unsigned long	Exponent_Trait (const GFqDom< long > &F)
template<typename BaseField >
unsigned long	Exponent_Trait (const Extension< BaseField > &F)
long	value (const Degree &d)
std::ostream &	operator<< (std::ostream &o, const Indeter &X)
std::istream &	operator>> (std::istream &s_in, Indeter &X)
int	operator== (const Indeter &i1, const Indeter &i2)
int	operator!= (const Indeter &i1, const Indeter &i2)
int	operator<= (const Indeter &i1, const Indeter &i2)
int	operator< (const Indeter &i1, const Indeter &i2)
int	operator>= (const Indeter &i1, const Indeter &i2)
int	operator> (const Indeter &i1, const Indeter &i2)
template<class T >
const Poly1< T >	Karatsuba (const Poly1< T > &P, const Poly1< T > &Q)
template<class Domain >
KSpace< Domain >	operator* (const typename KSpace< Domain >::Scalar_t &v, const KSpace< Domain > &U)
template<class Domain >
void	dotprod (typename Domain::Scalar_t &dot, const KSpace< Domain > &U, const KSpace< Domain > &V)
template<class Domain >
ostream &	operator<< (ostream &sout, const KSpace< Domain > &U)
template<class Domain >
istream &	operator>> (istream &sin, KSpace< Domain > &U)
template<class T , class Tag >
StructFormat< T, Tag >	Formatted (const T &val, Tag xx)

Detailed Description

Arithmetic on GF(p^k), with p a prime number less than 2^15.

Specialized for fast conversions to floating point numbers. Main difference in interface is init/convert.

Bibliography:: [JG Dumas, Q-adic Transform Revisited, ISSAC 2008]

Warning:: k strictly greater than 1

Todo:: use NTL if available ?

Typedef Documentation

typedef BaseDomain<char> CharDom

typedef BaseDomain<short> ShortDom

typedef BaseDomain<int> IntDom

typedef BaseDomain<long> LongDom

typedef BaseDomain<float> FloatDom

typedef BaseDomain<double> DoubleDom

Function Documentation

class Array0 Givaro::GIVARO_PERF_INEHERIT	(	Array0	,
		T
	)

class ArrayFixed Givaro::GIVARO_PERF_INEHERIT	(	ArrayFixed	,
		T
	)

std::ostream& Givaro::operator<<	(	std::ostream &	o,
		const Bits &	a
	)		`[inline]`

Examples:: examples/Rational/polydouble.C.

ostream& Givaro::operator<<	(	ostream &	o,
		const Pair< T1, T2 > &	p
	)

istream& Givaro::operator>>	(	istream &	fin,
		Pair< T1, T2 > &	p
	)

int compare	(	const Integer &	a,
		const Integer &	b
	)

int absCompare	(	const Integer &	a,
		const Integer &	b
	)

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

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

Integer gcd	(	const Integer &	a,
		const Integer &	b
	)

Examples:: examples/Integer/ProbLucas.C.

Integer gcd	(	const Integer &	a,
		const Integer &	b,
		Integer &	u,
		Integer &	v
	)

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

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

Integer pp	(	const Integer &	P,
		const Integer &	Q
	)

Integer & lcm	(	Integer &	g,
		const Integer &	a,
		const Integer &	b
	)

Integer lcm	(	const Integer &	a,
		const Integer &	b
	)

Integer & pow	(	Integer &	Res,
		const Integer &	n,
		const long	l
	)

Examples:: examples/Integer/ProbLucas.C.

Integer & pow	(	Integer &	Res,
		const unsigned long	n,
		const unsigned long	l
	)

Integer & pow	(	Integer &	Res,
		const Integer &	n,
		const unsigned long	l
	)

Integer& Givaro::pow	(	Integer &	Res,
		const Integer &	n,
		const int	l
	)

Integer& Givaro::pow	(	Integer &	Res,
		const Integer &	n,
		const unsigned int	l
	)

Integer pow	(	const Integer &	n,
		const long	l
	)

Integer pow	(	const Integer &	n,
		const unsigned long	l
	)

Integer Givaro::pow	(	const Integer &	n,
		const int	l
	)

Integer Givaro::pow	(	const Integer &	n,
		const unsigned int	l
	)

Integer & powmod	(	Integer &	Res,
		const Integer &	n,
		const unsigned long	e,
		const Integer &	m
	)

Integer & powmod	(	Integer &	Res,
		const Integer &	n,
		const long	e,
		const Integer &	m
	)

Integer& Givaro::powmod	(	Integer &	Res,
		const Integer &	n,
		const unsigned int	e,
		const Integer &	m
	)

Integer& Givaro::powmod	(	Integer &	Res,
		const Integer &	n,
		const int	e,
		const Integer &	m
	)

Integer & powmod	(	Integer &	Res,
		const Integer &	n,
		const Integer &	e,
		const Integer &	m
	)

Integer powmod	(	const Integer &	n,
		const unsigned long	e,
		const Integer &	m
	)

Integer powmod	(	const Integer &	n,
		const long	e,
		const Integer &	m
	)

Integer Givaro::powmod	(	const Integer &	n,
		const unsigned int	e,
		const Integer &	m
	)

Integer Givaro::powmod	(	const Integer &	n,
		const int	e,
		const Integer &	m
	)

Integer powmod	(	const Integer &	n,
		const Integer &	e,
		const Integer &	m
	)

Integer fact ( unsigned long l )

Integer sqrt ( const Integer & p )

Examples:: examples/Integer/ProbLucas.C.

Integer sqrtrem	(	const Integer &	p,
		Integer &	rem
	)

Integer & sqrt	(	Integer &	r,
		const Integer &	p
	)

Integer & sqrtrem	(	Integer &	r,
		const Integer &	p,
		Integer &	rem
	)

bool root	(	Integer &	q,
		const Integer &	a,
		unsigned int	n
	)

Examples:: examples/Integer/ProbLucas.C.

long logp	(	const Integer &	a,
		const Integer &	p
	)

double logtwo ( const Integer & a )

Examples:: examples/Integer/ProbLucas.C.

double naturallog ( const Integer & a )

void swap	(	Integer &	a,
		Integer &	b
	)

int sign ( const Integer & a ) [inline]

int isZero ( const Integer & a ) [inline]

int isOne ( const Integer & a ) [inline]

int isperfectpower ( const Integer & n )

Examples:: examples/Integer/ispower.C.

Integer abs ( const Integer & n ) [inline]

Integer & prevprime	(	Integer &	r,
		const Integer &	p
	)

Integer & nextprime	(	Integer &	r,
		const Integer &	p
	)

int probab_prime ( const Integer & p )

int probab_prime	(	const Integer &	p,
		int	r
	)

int jacobi	(	const Integer &	u,
		const Integer &	v
	)

int legendre	(	const Integer &	u,
		const Integer &	v
	)

unsigned long length ( const Integer & a ) [inline]

std::istream & operator>>	(	std::istream &	i,
		Integer &	n
	)

std::ostream & operator<<	(	std::ostream &	o,
		const Integer &	n
	)		`[inline]`

std::ostream & absOutput	(	std::ostream &	o,
		const Integer &	n
	)

void importWords	(	Integer &	x,
		size_t	count,
		int	order,
		int	size,
		int	endian,
		size_t	nails,
		const void *	op
	)

int Givaro::operator!=	(	const Integer &	a,
		const Integer &	b
	)		`[inline]`

int Givaro::operator!=	(	int	l,
		const Integer &	n
	)		`[inline]`

int Givaro::operator!=	(	long	l,
		const Integer &	n
	)		`[inline]`

int Givaro::operator!=	(	unsigned long	l,
		const Integer &	n
	)		`[inline]`

int Givaro::operator==	(	const Integer &	a,
		const Integer &	b
	)		`[inline]`

int Givaro::operator==	(	int	l,
		const Integer &	n
	)		`[inline]`

int Givaro::operator==	(	long	l,
		const Integer &	n
	)		`[inline]`

int Givaro::operator==	(	unsigned long	l,
		const Integer &	n
	)		`[inline]`

int Givaro::operator==	(	const Integer &	n,
		unsigned long	l
	)		`[inline]`

int Givaro::operator==	(	const Integer &	n,
		int	l
	)		`[inline]`

int Givaro::operator==	(	const Integer &	n,
		long	l
	)		`[inline]`

int Givaro::operator<	(	const Integer &	a,
		const Integer &	b
	)		`[inline]`

int Givaro::operator<	(	const int	l,
		const Integer &	n
	)		`[inline]`

int Givaro::operator<	(	const long	l,
		const Integer &	n
	)		`[inline]`

int Givaro::operator<	(	const unsigned long	l,
		const Integer &	n
	)		`[inline]`

int Givaro::operator<=	(	const Integer &	n,
		unsigned long	l
	)		`[inline]`

int Givaro::operator<=	(	unsigned long	l,
		const Integer &	n
	)		`[inline]`

int Givaro::operator>=	(	unsigned long	l,
		const Integer &	n
	)		`[inline]`

int Givaro::operator>=	(	const Integer &	n,
		unsigned long	l
	)		`[inline]`

int Givaro::operator>	(	int	l,
		const Integer &	n
	)		`[inline]`

int Givaro::operator>	(	long	l,
		const Integer &	n
	)		`[inline]`

int Givaro::operator>	(	unsigned long	l,
		const Integer &	n
	)		`[inline]`

int Givaro::operator>	(	const Integer &	a,
		const Integer &	b
	)		`[inline]`

int Givaro::operator<=	(	const Integer &	a,
		const Integer &	b
	)		`[inline]`

int Givaro::operator<=	(	const Integer &	n,
		int	l
	)		`[inline]`

int Givaro::operator<=	(	const Integer &	n,
		long	l
	)		`[inline]`

int Givaro::operator<=	(	int	l,
		const Integer &	n
	)		`[inline]`

int Givaro::operator<=	(	long	l,
		const Integer &	n
	)		`[inline]`

int Givaro::operator>=	(	const Integer &	a,
		const Integer &	b
	)		`[inline]`

int Givaro::operator>=	(	int	l,
		const Integer &	n
	)		`[inline]`

int Givaro::operator>=	(	long	l,
		const Integer &	n
	)		`[inline]`

int Givaro::operator>=	(	const Integer &	n,
		int	l
	)		`[inline]`

int Givaro::operator>=	(	const Integer &	n,
		long	l
	)		`[inline]`

Integer Givaro::operator+	(	const int	l,
		const Integer &	n
	)		`[inline]`

Integer Givaro::operator+	(	const unsigned int	l,
		const Integer &	n
	)		`[inline]`

Integer Givaro::operator+	(	const long	l,
		const Integer &	n
	)		`[inline]`

Integer Givaro::operator+	(	const unsigned long	l,
		const Integer &	n
	)		`[inline]`

Integer Givaro::operator+	(	const Integer &	n,
		const int	l
	)		`[inline]`

Integer Givaro::operator+	(	const Integer &	n,
		const unsigned int	l
	)		`[inline]`

Integer& Givaro::operator+=	(	Integer &	n,
		const int	l
	)		`[inline]`

Integer& Givaro::operator+=	(	Integer &	n,
		const unsigned int	l
	)		`[inline]`

Integer Givaro::operator-	(	const int	l,
		const Integer &	n
	)		`[inline]`

Integer Givaro::operator-	(	const unsigned int	l,
		const Integer &	n
	)		`[inline]`

Integer Givaro::operator-	(	const long	l,
		const Integer &	n
	)		`[inline]`

Integer Givaro::operator-	(	const unsigned long	l,
		const Integer &	n
	)		`[inline]`

Integer Givaro::operator-	(	const Integer &	n,
		const int	l
	)		`[inline]`

Integer Givaro::operator-	(	const Integer &	n,
		const unsigned int	l
	)		`[inline]`

Integer& Givaro::operator-=	(	Integer &	n,
		const int	l
	)		`[inline]`

Integer& Givaro::operator-=	(	Integer &	n,
		const unsigned int	l
	)		`[inline]`

Integer Givaro::operator*	(	const int	l,
		const Integer &	n
	)		`[inline]`

Integer Givaro::operator*	(	const unsigned int	l,
		const Integer &	n
	)		`[inline]`

Integer Givaro::operator*	(	const long	l,
		const Integer &	n
	)		`[inline]`

Integer Givaro::operator*	(	const unsigned long	l,
		const Integer &	n
	)		`[inline]`

Integer Givaro::operator*	(	const Integer &	n,
		const int	l
	)		`[inline]`

Integer Givaro::operator*	(	const Integer &	n,
		const unsigned int	l
	)		`[inline]`

Integer& Givaro::operator*=	(	Integer &	n,
		const int	l
	)		`[inline]`

Integer& Givaro::operator*=	(	Integer &	n,
		const unsigned int	l
	)		`[inline]`

Integer Givaro::operator/	(	const int	l,
		const Integer &	n
	)		`[inline]`

Integer Givaro::operator/	(	const long	l,
		const Integer &	n
	)		`[inline]`

Integer Givaro::operator/	(	const Integer &	n,
		const int	l
	)		`[inline]`

Integer Givaro::operator/	(	const Integer &	n,
		const unsigned int	l
	)		`[inline]`

Integer& Givaro::operator/=	(	Integer &	n,
		const int	l
	)		`[inline]`

Integer& Givaro::operator/=	(	Integer &	n,
		const long	l
	)		`[inline]`

Integer& Givaro::operator/=	(	Integer &	n,
		const unsigned int	l
	)		`[inline]`

Integer Givaro::operator%	(	const int	l,
		const Integer &	n
	)		`[inline]`

Integer Givaro::operator%	(	const long	l,
		const Integer &	n
	)		`[inline]`

Integer Givaro::operator%	(	const Integer &	n,
		const int	l
	)		`[inline]`

Integer Givaro::operator%	(	const Integer &	n,
		const unsigned int	l
	)		`[inline]`

Integer& Givaro::operator%=	(	Integer &	n,
		const int	l
	)		`[inline]`

Integer& Givaro::operator%=	(	Integer &	n,
		const unsigned int	l
	)		`[inline]`

int Givaro::isZero ( const short int a ) [inline]

int Givaro::isZero ( const int a ) [inline]

int Givaro::isZero ( const long a ) [inline]

int Givaro::isZero ( const unsigned short int a ) [inline]

int Givaro::isZero ( const unsigned int a ) [inline]

int Givaro::isZero ( const unsigned long a ) [inline]

void Givaro::Add_Curve	(	const Integer &	n,
		const Integer	A,
		const Integer &	ax,
		const Integer &	az,
		Integer &	cx,
		Integer &	cz
	)		`[inline]`

void Givaro::one_Mul_Curve	(	const Integer &	n,
		const Integer	A,
		const Integer &	mm,
		const Integer &	nn,
		const Integer &	px,
		const Integer &	pz,
		Integer &	ax,
		Integer &	az
	)		`[inline]`

void Givaro::one_Mul_Curve2	(	const Integer &	n,
		const Integer	A,
		const Integer &	mm,
		const Integer &	nn,
		const Integer &	px,
		const Integer &	pz,
		Integer &	aax,
		Integer &	aaz
	)		`[inline]`

void Givaro::Mul_Curve	(	const Integer &	n,
		Integer &	Ai,
		const Integer &	mm,
		const Integer &	nn,
		const Integer &	B1,
		Integer &	Xi,
		Integer &	Zi
	)		`[inline]`

Integer& Givaro::ppin	(	Integer &	res,
		const Integer &	prime
	)		`[inline]`

std::ostream& Givaro::operator<<	(	std::ostream &	o,
		const GivMMInfo &	T
	)		`[inline]`

int compare	(	const Rational &	a,
		const Rational &	b
	)

int absCompare	(	const Rational &	a,
		const Rational &	b
	)

template double Givaro::power	(	double	x,
		unsigned int	p
	)

Examples:: examples/FiniteField/GFirreducible.C.

std::istream & operator>>	(	std::istream &	in,
		Rational &	r
	)

const Rational pow	(	const Rational &	r,
		const long	l
	)

const Integer floor ( const Rational & r )

const Integer ceil ( const Rational & r )

const Integer round ( const Rational & r )

const Integer trunc ( const Rational & r )

const Rational abs ( const Rational & r ) [inline]

const Rational Givaro::pow	(	const Rational &	n,
		unsigned int	l
	)

const Rational Givaro::pow	(	const Rational &	n,
		unsigned long	l
	)

unsigned long length ( const Rational & r ) [inline]

int sign ( const Rational & r ) [inline]

int isZero ( const Rational & r ) [inline]

int isOne ( const Rational & r ) [inline]

int isInteger ( const Rational & r ) [inline]

int Givaro::operator!=	(	const Rational &	a,
		const Rational &	b
	)		`[inline]`

int Givaro::operator==	(	const Rational &	a,
		const Rational &	b
	)		`[inline]`

int Givaro::operator<	(	const Rational &	a,
		const Rational &	b
	)		`[inline]`

int Givaro::operator>	(	const Rational &	a,
		const Rational &	b
	)		`[inline]`

int Givaro::operator<=	(	const Rational &	a,
		const Rational &	b
	)		`[inline]`

int Givaro::operator>=	(	const Rational &	a,
		const Rational &	b
	)		`[inline]`

const Rational Givaro::operator+	(	const Rational &	r,
		const int	i
	)		`[inline]`

const Rational Givaro::operator-	(	const Rational &	r,
		const int	i
	)		`[inline]`

const Rational Givaro::operator*	(	const Rational &	r,
		const int	i
	)		`[inline]`

const Rational Givaro::operator/	(	const Rational &	r,
		const int	i
	)		`[inline]`

const Rational Givaro::operator+	(	const int	i,
		const Rational &	r
	)		`[inline]`

const Rational Givaro::operator-	(	const int	i,
		const Rational &	r
	)		`[inline]`

const Rational Givaro::operator*	(	const int	i,
		const Rational &	r
	)		`[inline]`

const Rational Givaro::operator/	(	const int	i,
		const Rational &	r
	)		`[inline]`

std::ostream& Givaro::operator<<	(	std::ostream &	o,
		const Rational &	a
	)		`[inline]`

std::ostream& Givaro::operator<<	(	std::ostream &	o,
		const GivError &	E
	)

unsigned Givaro::GIVINTLOG ( const T & a ) [inline]

TT Givaro::power	(	const TT	n,
		const UU	l
	)

TT& Givaro::dom_power	(	TT &	res,
		const TT &	n,
		long	l,
		const D &	F
	)

Examples:: examples/Integer/iexponentiation.C.

std::ostream& Givaro::operator<<	(	std::ostream &	o,
		const BaseTimer &	BT
	)		`[inline]`

std::ostream& Givaro::operator<<	(	std::ostream &	o,
		const Timer &	T
	)		`[inline]`

Rt Givaro::FF_EXPONENT_MAX	(	const Rt	p,
		const Rt	e = `1`
	)

Examples:: examples/FiniteField/Test_Extension.C.

unsigned long Givaro::Exponent_Trait ( const Field & F )

unsigned long Givaro::Exponent_Trait ( const GFqDom< long > & F )

unsigned long Givaro::Exponent_Trait ( const Extension< BaseField > & F )

long Givaro::value ( const Degree & d ) [inline]

std::ostream& Givaro::operator<<	(	std::ostream &	o,
		const Indeter &	X
	)

std::istream& Givaro::operator>>	(	std::istream &	s_in,
		Indeter &	X
	)

int Givaro::operator==	(	const Indeter &	i1,
		const Indeter &	i2
	)		`[inline]`

int Givaro::operator!=	(	const Indeter &	i1,
		const Indeter &	i2
	)		`[inline]`

int Givaro::operator<=	(	const Indeter &	i1,
		const Indeter &	i2
	)		`[inline]`

int Givaro::operator<	(	const Indeter &	i1,
		const Indeter &	i2
	)		`[inline]`

int Givaro::operator>=	(	const Indeter &	i1,
		const Indeter &	i2
	)		`[inline]`

int Givaro::operator>	(	const Indeter &	i1,
		const Indeter &	i2
	)		`[inline]`

const Poly1<T> Givaro::Karatsuba	(	const Poly1< T > &	P,
		const Poly1< T > &	Q
	)

KSpace<Domain> Givaro::operator*	(	const typename KSpace< Domain >::Scalar_t &	v,
		const KSpace< Domain > &	U
	)

void Givaro::dotprod	(	typename Domain::Scalar_t &	dot,
		const KSpace< Domain > &	U,
		const KSpace< Domain > &	V
	)		`[inline]`

ostream& Givaro::operator<<	(	ostream &	sout,
		const KSpace< Domain > &	U
	)		`[inline]`

istream& Givaro::operator>>	(	istream &	sin,
		KSpace< Domain > &	U
	)		`[inline]`

StructFormat<T,Tag> Givaro::Formatted	(	const T &	val,
		Tag	xx
	)

Data Structures

Typedefs

Functions

Detailed Description

Typedef Documentation

Function Documentation