module Number.ResidueClass.Maybe where
import qualified Number.ResidueClass as Res
import qualified Algebra.IntegralDomain as Integral
import qualified Algebra.Ring as Ring
import qualified Algebra.Additive as Additive
import qualified Algebra.ZeroTestable as ZeroTestable
import Algebra.ZeroTestable(isZero)
import PreludeBase
import NumericPrelude
infix 7 /:, `Cons`
data T a
= Cons {modulus :: !(Maybe a)
,representative :: !a
}
deriving (Show, Read)
(/:) :: (Integral.C a) => a -> a -> T a
(/:) r m = Cons (Just m) (mod r m)
matchMaybe :: Maybe a -> Maybe a -> Maybe a
matchMaybe Nothing y = y
matchMaybe x _ = x
isCompatibleMaybe :: (Eq a) => Maybe a -> Maybe a -> Bool
isCompatibleMaybe Nothing _ = True
isCompatibleMaybe _ Nothing = True
isCompatibleMaybe (Just x) (Just y) = x == y
isCompatible :: (Eq a) => T a -> T a -> Bool
isCompatible x y = isCompatibleMaybe (modulus x) (modulus y)
lift2 :: (Eq a) => (a -> a -> a -> a) -> (a -> a -> a) -> (T a -> T a -> T a)
lift2 f g x y =
if isCompatible x y
then let m = matchMaybe (modulus x) (modulus y)
in Cons m
(maybe g f m (representative x) (representative y))
else error "ResidueClass: Incompatible operands"
instance (Eq a, ZeroTestable.C a, Integral.C a) => Eq (T a) where
(==) x y =
if isCompatible x y
then maybe (==)
(\m x' y' -> isZero (mod (x'y') m))
(matchMaybe (modulus x) (modulus y))
(representative x) (representative y)
else error "ResidueClass.(==): Incompatible operands"
instance (Eq a, Integral.C a) => Additive.C (T a) where
zero = Cons Nothing zero
(+) = lift2 Res.add (+)
() = lift2 Res.sub ()
negate (Cons m r) = Cons m (negate r)
instance (Eq a, Integral.C a) => Ring.C (T a) where
one = Cons Nothing one
(*) = lift2 Res.mul (*)
fromInteger = Cons Nothing . fromInteger