Arithmetic.Quadratic

Documentation

rootFloor :: Natural -> Natural

rootCeiling :: Natural -> Natural

destSquare :: Natural -> Maybe Natural

isSquare :: Natural -> Bool

rootContinuedFraction :: Natural -> ContinuedFraction

rootContinuedFractionPeriodic :: Natural -> [Natural]

rootContinuedFractionPeriodicTail :: Natural -> Natural -> [Natural]

data Residue

Constructors

Residue

NonResidue

Zero

Instances

Eq Residue

Defined in Arithmetic.Quadratic

Methods

(==) :: Residue -> Residue -> Bool

(/=) :: Residue -> Residue -> Bool

Ord Residue

Defined in Arithmetic.Quadratic

Methods

compare :: Residue -> Residue -> Ordering

(<) :: Residue -> Residue -> Bool

(<=) :: Residue -> Residue -> Bool

(>) :: Residue -> Residue -> Bool

(>=) :: Residue -> Residue -> Bool

max :: Residue -> Residue -> Residue

min :: Residue -> Residue -> Residue

Show Residue

Defined in Arithmetic.Quadratic

Methods

showsPrec :: Int -> Residue -> ShowS

show :: Residue -> String

showList :: [Residue] -> ShowS

jacobiSymbol :: Natural -> Natural -> Residue

isResidue :: Natural -> Natural -> Bool

isNonResidue :: Natural -> Natural -> Bool

nextResidue :: Natural -> Natural -> Natural

nextNonResidue :: Natural -> Natural -> Natural

rootModuloPrime3Mod4 :: Natural -> Natural -> Natural

rootModuloPrime5Mod8 :: Natural -> Natural -> Natural

rootModuloPrime :: Natural -> Natural -> Natural