Safe Haskell	None
Language	Haskell2010

ExtensionField

Synopsis

data ExtensionField k im
class IrreducibleMonic k im where
- split :: (k, im) -> Polynomial k
fromField :: ExtensionField k im -> [k]
fromList :: forall k im. (GaloisField k, IrreducibleMonic k im) => [k] -> ExtensionField k im
t :: Polynomial k -> Polynomial (ExtensionField k im)
x :: GaloisField k => Polynomial k

Documentation

data ExtensionField k im Source #

Extension fields GF(p^q)[X]/f(X) for p prime, q positive, and f(X) irreducible monic in GF(p^q)[X]

Instances

Eq k => Eq (ExtensionField k im) Source #
Instance details Defined in ExtensionField Methods (==) :: ExtensionField k im -> ExtensionField k im -> Bool # (/=) :: ExtensionField k im -> ExtensionField k im -> Bool #
(GaloisField k, IrreducibleMonic k im) => Fractional (ExtensionField k im) Source #	Extension fields are fields
Instance details Defined in ExtensionField Methods (/) :: ExtensionField k im -> ExtensionField k im -> ExtensionField k im # recip :: ExtensionField k im -> ExtensionField k im # fromRational :: Rational -> ExtensionField k im #
(GaloisField k, IrreducibleMonic k im) => Num (ExtensionField k im) Source #	Extension fields are rings
Instance details Defined in ExtensionField Methods (+) :: ExtensionField k im -> ExtensionField k im -> ExtensionField k im # (-) :: ExtensionField k im -> ExtensionField k im -> ExtensionField k im # (*) :: ExtensionField k im -> ExtensionField k im -> ExtensionField k im # negate :: ExtensionField k im -> ExtensionField k im # abs :: ExtensionField k im -> ExtensionField k im # signum :: ExtensionField k im -> ExtensionField k im # fromInteger :: Integer -> ExtensionField k im #
Show k => Show (ExtensionField k im) Source #
Instance details Defined in ExtensionField Methods showsPrec :: Int -> ExtensionField k im -> ShowS # show :: ExtensionField k im -> String # showList :: [ExtensionField k im] -> ShowS #
Generic (ExtensionField k im) Source #
Instance details Defined in ExtensionField Associated Types type Rep (ExtensionField k im) :: Type -> Type # Methods from :: ExtensionField k im -> Rep (ExtensionField k im) x # to :: Rep (ExtensionField k im) x -> ExtensionField k im #
NFData k => NFData (ExtensionField k im) Source #
Instance details Defined in ExtensionField Methods rnf :: ExtensionField k im -> () #
(GaloisField k, IrreducibleMonic k im) => GaloisField (ExtensionField k im) Source #	Extension fields are Galois fields
Instance details Defined in ExtensionField Methods char :: ExtensionField k im -> Integer Source #
type Rep (ExtensionField k im) Source #
Instance details Defined in ExtensionField type Rep (ExtensionField k im)

class IrreducibleMonic k im where Source #

Irreducible monic splitting polynomial of extension field

Methods

split :: (k, im) -> Polynomial k Source #

fromField :: ExtensionField k im -> [k] Source #

List from field

fromList :: forall k im. (GaloisField k, IrreducibleMonic k im) => [k] -> ExtensionField k im Source #

Field from list

t :: Polynomial k -> Polynomial (ExtensionField k im) Source #

Descend variable tower

x :: GaloisField k => Polynomial k Source #

Current indeterminate variable