Copyright	(c) Masahiro Sakai 2013
License	BSD-style
Maintainer	masahiro.sakai@gmail.com
Stability	provisional
Portability	portable
Safe Haskell	Safe
Language	Haskell2010

Data.FiniteField.Base

Description

Synopsis

class Fractional k => FiniteField k where
- order :: k -> Integer
- char :: k -> Integer
- pthRoot :: k -> k
- allValues :: [k]

Documentation

class Fractional k => FiniteField k where Source #

Type class for finite fields

Methods

order :: k -> Integer Source #

The order is number of elements of a finite field k. It of the form p^n, where p is prime number called the characteristic of the field, and n is a positive integer.

char :: k -> Integer Source #

The characteristic of a field, p.

pthRoot :: k -> k Source #

The inverse of Frobenius endomorphism x ↦ x^p.

allValues :: [k] Source #

All values of a field

Instances

KnownNat p => FiniteField (PrimeField p) Source #
Instance details Defined in Data.FiniteField.PrimeField Methods order :: PrimeField p -> Integer Source # char :: PrimeField p -> Integer Source # pthRoot :: PrimeField p -> PrimeField p Source # allValues :: [PrimeField p] Source #