Safe Haskell	None
Language	Haskell2010

PrimeField

Synopsis

data PrimeField (p :: Nat)
toInt :: PrimeField p -> Integer

Documentation

data PrimeField (p :: Nat) Source #

Prime fields GF(p) for p prime.

Instances

Eq (PrimeField p) Source #
Instance details Defined in PrimeField Methods (==) :: PrimeField p -> PrimeField p -> Bool # (/=) :: PrimeField p -> PrimeField p -> Bool #
KnownNat p => Fractional (PrimeField p) Source #
Instance details Defined in PrimeField Methods (/) :: PrimeField p -> PrimeField p -> PrimeField p # recip :: PrimeField p -> PrimeField p # fromRational :: Rational -> PrimeField p #
KnownNat p => Num (PrimeField p) Source #
Instance details Defined in PrimeField Methods (+) :: PrimeField p -> PrimeField p -> PrimeField p # (-) :: PrimeField p -> PrimeField p -> PrimeField p # (*) :: PrimeField p -> PrimeField p -> PrimeField p # negate :: PrimeField p -> PrimeField p # abs :: PrimeField p -> PrimeField p # signum :: PrimeField p -> PrimeField p # fromInteger :: Integer -> PrimeField p #
Ord (PrimeField p) Source #
Instance details Defined in PrimeField Methods compare :: PrimeField p -> PrimeField p -> Ordering # (<) :: PrimeField p -> PrimeField p -> Bool # (<=) :: PrimeField p -> PrimeField p -> Bool # (>) :: PrimeField p -> PrimeField p -> Bool # (>=) :: PrimeField p -> PrimeField p -> Bool # max :: PrimeField p -> PrimeField p -> PrimeField p # min :: PrimeField p -> PrimeField p -> PrimeField p #
Show (PrimeField p) Source #
Instance details Defined in PrimeField Methods showsPrec :: Int -> PrimeField p -> ShowS # show :: PrimeField p -> String # showList :: [PrimeField p] -> ShowS #
Generic (PrimeField p) Source #
Instance details Defined in PrimeField Associated Types type Rep (PrimeField p) :: Type -> Type # Methods from :: PrimeField p -> Rep (PrimeField p) x # to :: Rep (PrimeField p) x -> PrimeField p #
KnownNat p => Random (PrimeField p) Source #
Instance details Defined in PrimeField Methods randomR :: RandomGen g => (PrimeField p, PrimeField p) -> g -> (PrimeField p, g) # random :: RandomGen g => g -> (PrimeField p, g) # randomRs :: RandomGen g => (PrimeField p, PrimeField p) -> g -> [PrimeField p] # randoms :: RandomGen g => g -> [PrimeField p] # randomRIO :: (PrimeField p, PrimeField p) -> IO (PrimeField p) # randomIO :: IO (PrimeField p) #
KnownNat p => Arbitrary (PrimeField p) Source #
Instance details Defined in PrimeField Methods arbitrary :: Gen (PrimeField p) # shrink :: PrimeField p -> [PrimeField p] #
Bits (PrimeField p) Source #
Instance details Defined in PrimeField Methods (.&.) :: PrimeField p -> PrimeField p -> PrimeField p # (.\|.) :: PrimeField p -> PrimeField p -> PrimeField p # xor :: PrimeField p -> PrimeField p -> PrimeField p # complement :: PrimeField p -> PrimeField p # shift :: PrimeField p -> Int -> PrimeField p # rotate :: PrimeField p -> Int -> PrimeField p # zeroBits :: PrimeField p # bit :: Int -> PrimeField p # setBit :: PrimeField p -> Int -> PrimeField p # clearBit :: PrimeField p -> Int -> PrimeField p # complementBit :: PrimeField p -> Int -> PrimeField p # testBit :: PrimeField p -> Int -> Bool # bitSizeMaybe :: PrimeField p -> Maybe Int # bitSize :: PrimeField p -> Int # isSigned :: PrimeField p -> Bool # shiftL :: PrimeField p -> Int -> PrimeField p # unsafeShiftL :: PrimeField p -> Int -> PrimeField p # shiftR :: PrimeField p -> Int -> PrimeField p # unsafeShiftR :: PrimeField p -> Int -> PrimeField p # rotateL :: PrimeField p -> Int -> PrimeField p # rotateR :: PrimeField p -> Int -> PrimeField p # popCount :: PrimeField p -> Int #
KnownNat p => GcdDomain (PrimeField p) Source #
Instance details Defined in PrimeField Methods divide :: PrimeField p -> PrimeField p -> Maybe (PrimeField p) # gcd :: PrimeField p -> PrimeField p -> PrimeField p # lcm :: PrimeField p -> PrimeField p -> PrimeField p # coprime :: PrimeField p -> PrimeField p -> Bool #
KnownNat p => Euclidean (PrimeField p) Source #
Instance details Defined in PrimeField Methods quotRem :: PrimeField p -> PrimeField p -> (PrimeField p, PrimeField p) # quot :: PrimeField p -> PrimeField p -> PrimeField p # rem :: PrimeField p -> PrimeField p -> PrimeField p # degree :: PrimeField p -> Natural #
KnownNat p => Semiring (PrimeField p) Source #
Instance details Defined in PrimeField Methods plus :: PrimeField p -> PrimeField p -> PrimeField p # zero :: PrimeField p # times :: PrimeField p -> PrimeField p -> PrimeField p # one :: PrimeField p # fromNatural :: Natural -> PrimeField p #
KnownNat p => Ring (PrimeField p) Source #
Instance details Defined in PrimeField Methods negate :: PrimeField p -> PrimeField p #
KnownNat p => Pretty (PrimeField p) Source #
Instance details Defined in PrimeField Methods pretty :: PrimeField p -> Doc # prettyList :: [PrimeField p] -> Doc #
KnownNat p => GaloisField (PrimeField p) Source #
Instance details Defined in PrimeField Methods char :: PrimeField p -> Integer Source # deg :: PrimeField p -> Int Source # order :: PrimeField p -> Integer Source # frob :: PrimeField p -> PrimeField p Source # pow :: PrimeField p -> Integer -> PrimeField p Source # qnr :: PrimeField p Source # qr :: PrimeField p -> Bool Source # quad :: PrimeField p -> PrimeField p -> PrimeField p -> Maybe (PrimeField p) Source # rnd :: MonadRandom m => m (PrimeField p) Source # sr :: PrimeField p -> Maybe (PrimeField p) Source #
KnownNat p => Field (PrimeField p) Source #
Instance details Defined in PrimeField Methods divide :: PrimeField p -> PrimeField p -> PrimeField p Source # invert :: PrimeField p -> PrimeField p Source # minus :: PrimeField p -> PrimeField p -> PrimeField p Source #
type Rep (PrimeField p) Source #
Instance details Defined in PrimeField type Rep (PrimeField p) = D1 (MetaData "PrimeField" "PrimeField" "galois-field-0.4.0-728POA9oIqrGokqiBM9ptF" True) (C1 (MetaCons "PF" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Integer)))

toInt :: PrimeField p -> Integer Source #

Embed field element to integers.