GaloisField

Documentation

class (Arbitrary k, Eq k, Fractional k, Pretty k, Random k, Show k) => GaloisField k where

Galois fields GF(p^q) for p prime and q non-negative

Minimal complete definition

char, deg, pow, rnd

Methods

char

Arguments

:: k

-> Integer

Characteristic q of field

deg

Arguments

:: k

-> Int

Degree q of field

order

Arguments

:: k

-> Integer

Order p^q of field

pow :: k -> Integer -> k

rnd

Arguments

:: MonadRandom m

=> m k

Random element of field

Instances

KnownNat p => GaloisField (PrimeField p)

Prime fields are Galois fields

Defined in PrimeField

Methods

char :: PrimeField p -> Integer

deg :: PrimeField p -> Int

order :: PrimeField p -> Integer

pow :: PrimeField p -> Integer -> PrimeField p

rnd :: MonadRandom m => m (PrimeField p)

(GaloisField k, IrreducibleMonic k im) => GaloisField (ExtensionField k im)

Extension fields are Galois fields

Defined in ExtensionField

Methods

char :: ExtensionField k im -> Integer

deg :: ExtensionField k im -> Int

order :: ExtensionField k im -> Integer

pow :: ExtensionField k im -> Integer -> ExtensionField k im

rnd :: MonadRandom m => m (ExtensionField k im)