Safe Haskell	Safe
Language	Haskell2010

Math.Algebra.ModP

Description

Prime fields.

TODO: do it properly; and fast implementation for specialized prime fields

Synopsis

Documentation

2^31-1 is a prime (in practice this seems to be significantly faster than 2^63-25)

newtype Zp Source #

Constructors

Instances

Eq Zp Source #
Methods (==) :: Zp -> Zp -> Bool # (/=) :: Zp -> Zp -> Bool #
Fractional Zp Source #
Methods (/) :: Zp -> Zp -> Zp # recip :: Zp -> Zp # fromRational :: Rational -> Zp #
Num Zp Source #
Methods (+) :: Zp -> Zp -> Zp # (-) :: Zp -> Zp -> Zp # (*) :: Zp -> Zp -> Zp # negate :: Zp -> Zp # abs :: Zp -> Zp # signum :: Zp -> Zp # fromInteger :: Integer -> Zp #
Show Zp Source #
Methods showsPrec :: Int -> Zp -> ShowS # show :: Zp -> String # showList :: [Zp] -> ShowS #
Determinant Zp Source #
Methods determinant :: Matrix Zp -> Zp Source #
CoeffRing Zp Source #
Associated Types type FieldOfFractions Zp :: * Source # Methods embed :: Zp -> FieldOfFractions Zp Source # project :: Proxy * Zp -> FieldOfFractions Zp -> Maybe Zp Source # toBigInt :: Proxy * Zp -> FieldOfFractions Zp -> Maybe Integer Source #
(Pretty b, Ord b) => Pretty (FreeMod b Zp) Source #
Methods pretty :: FreeMod b Zp -> String Source #
type FieldOfFractions Zp Source #
type FieldOfFractions Zp = Zp

Inverse using the binary Euclidean algorithm