carl::GaloisField< IntegerType > Class Template Reference

A finite field. More...

#include <GaloisField.h>

Inheritance diagram for carl::GaloisField< IntegerType >:

Public Types
using	BaseIntType = unsigned

Public Member Functions
	GaloisField (BaseIntType p, BaseIntType k=1)
	Creating the field Z_{p^k}. More...
BaseIntType	p () const noexcept
	Returns the p from Z_{p^k}. More...
BaseIntType	k () const noexcept
	Returns the k from Z_{p^k}. More...
const IntegerType &	size () const noexcept
IntegerType	modulo (const IntegerType &n) const
IntegerType	symmetric_modulo (const IntegerType &n) const

Private Attributes
const BaseIntType	mP
const BaseIntType	mK
const IntegerType	mPK
const IntegerType	mMaxValue
const IntegerType	mModulus

Friends
bool	operator== (const GaloisField &lhs, const GaloisField &rhs)
std::ostream &	operator<< (std::ostream &os, const GaloisField &rhs)

Detailed Description

template<typename IntegerType>
class carl::GaloisField< IntegerType >

A finite field.

Definition at line 32 of file GaloisField.h.

Member Typedef Documentation

BaseIntType

template<typename IntegerType >

using carl::GaloisField< IntegerType >::BaseIntType = unsigned

Definition at line 34 of file GaloisField.h.

Constructor & Destructor Documentation

GaloisField()

template<typename IntegerType >

carl::GaloisField< IntegerType >::GaloisField ( BaseIntType  p, BaseIntType  k = 1  )

inlineexplicit

Creating the field Z_{p^k}.

Parameters

p	A prime number
k	A exponent

See also

GaloisFieldManager where the overhead of creating several GFs is prevented by storing them.

Definition at line 49 of file GaloisField.h.

Member Function Documentation

k()

template<typename IntegerType >

BaseIntType carl::GaloisField< IntegerType >::k ( ) const

inlinenoexcept

Returns the k from Z_{p^k}.

Returns

A positive integer

Definition at line 69 of file GaloisField.h.

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modulo()

template<typename IntegerType >

IntegerType carl::GaloisField< IntegerType >::modulo ( const IntegerType &  n ) const

inline

Definition at line 77 of file GaloisField.h.

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p()

template<typename IntegerType >

BaseIntType carl::GaloisField< IntegerType >::p ( ) const

inlinenoexcept

Returns the p from Z_{p^k}.

Returns

a prime

Definition at line 61 of file GaloisField.h.

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size()

template<typename IntegerType >

const IntegerType& carl::GaloisField< IntegerType >::size ( ) const

inlinenoexcept

Definition at line 73 of file GaloisField.h.

symmetric_modulo()

template<typename IntegerType >

IntegerType carl::GaloisField< IntegerType >::symmetric_modulo ( const IntegerType &  n ) const

inline

Definition at line 81 of file GaloisField.h.

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Friends And Related Function Documentation

operator<<

template<typename IntegerType >

std::ostream& operator<< ( std::ostream &  os, const GaloisField< IntegerType > &  rhs  )

friend

Definition at line 93 of file GaloisField.h.

operator==

template<typename IntegerType >

bool operator== ( const GaloisField< IntegerType > &  lhs, const GaloisField< IntegerType > &  rhs  )

friend

Definition at line 89 of file GaloisField.h.

Field Documentation

mK

template<typename IntegerType >

const BaseIntType carl::GaloisField< IntegerType >::mK

private

Definition at line 37 of file GaloisField.h.

mMaxValue

template<typename IntegerType >

const IntegerType carl::GaloisField< IntegerType >::mMaxValue

private

Definition at line 39 of file GaloisField.h.

mModulus

template<typename IntegerType >

const IntegerType carl::GaloisField< IntegerType >::mModulus

private

Definition at line 40 of file GaloisField.h.

mP

template<typename IntegerType >

const BaseIntType carl::GaloisField< IntegerType >::mP

private

Definition at line 36 of file GaloisField.h.

mPK

template<typename IntegerType >

const IntegerType carl::GaloisField< IntegerType >::mPK

private

Definition at line 38 of file GaloisField.h.

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

• carl-arith/numbers/GaloisField.h