Safe Haskell	None
Language	Haskell98

Number.ResidueClass.Maybe

Synopsis

data T a = Cons {
- modulus :: !(Maybe a)
- representative :: !a
}
(/:) :: C a => a -> a -> T a
matchMaybe :: Maybe a -> Maybe a -> Maybe a
isCompatibleMaybe :: Eq a => Maybe a -> Maybe a -> Bool
isCompatible :: Eq a => T a -> T a -> Bool
lift2 :: Eq a => (a -> a -> a -> a) -> (a -> a -> a) -> T a -> T a -> T a

Documentation

data T a Source #

Here we try to provide implementations for zero and one by making the modulus optional. We have to provide non-modulus operations for the cases where both operands have Nothing modulus. This is problematic since operations like (\/) depend essentially on the modulus.

A working version with disabled zero and one can be found ResidueClass.

Constructors

Cons infix 7
Fields modulus :: !(Maybe a) the modulus can be Nothing to denote a generic constant like `zero` and `one` which could not be bound to a specific modulus so far representative :: !a

Instances

Instances details

(Eq a, C a, C a) => Eq (T a) Source #
Instance details Defined in Number.ResidueClass.Maybe Methods (==) :: T a -> T a -> Bool # (/=) :: T a -> T a -> Bool #
Read a => Read (T a) Source #
Instance details Defined in Number.ResidueClass.Maybe Methods readsPrec :: Int -> ReadS (T a) # readList :: ReadS [T a] # readPrec :: ReadPrec (T a) # readListPrec :: ReadPrec [T a] #
Show a => Show (T a) Source #
Instance details Defined in Number.ResidueClass.Maybe Methods showsPrec :: Int -> T a -> ShowS # show :: T a -> String # showList :: [T a] -> ShowS #
(Eq a, C a) => C (T a) Source #
Instance details Defined in Number.ResidueClass.Maybe Methods zero :: T a Source # (+) :: T a -> T a -> T a Source # (-) :: T a -> T a -> T a Source # negate :: T a -> T a Source #
(Eq a, C a) => C (T a) Source #
Instance details Defined in Number.ResidueClass.Maybe Methods (*) :: T a -> T a -> T a Source # one :: T a Source # fromInteger :: Integer -> T a Source # (^) :: T a -> Integer -> T a Source #

(/:) :: C a => a -> a -> T a infix 7 Source #

r /: m is the residue class containing r with respect to the modulus m

matchMaybe :: Maybe a -> Maybe a -> Maybe a Source #

isCompatibleMaybe :: Eq a => Maybe a -> Maybe a -> Bool Source #

isCompatible :: Eq a => T a -> T a -> Bool Source #

Check if two residue classes share the same modulus

lift2 :: Eq a => (a -> a -> a -> a) -> (a -> a -> a) -> T a -> T a -> T a Source #