Number.ResidueClass.Maybe

Documentation

data T a

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

(Eq a, C a, C a) => Eq (T a)

Defined in Number.ResidueClass.Maybe

Methods

(==) :: T a -> T a -> Bool

(/=) :: T a -> T a -> Bool

Read a => Read (T a)

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)

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)

Defined in Number.ResidueClass.Maybe

Methods

zero :: T a

(+) :: T a -> T a -> T a

(-) :: T a -> T a -> T a

negate :: T a -> T a

(Eq a, C a) => C (T a)

Defined in Number.ResidueClass.Maybe

Methods

(*) :: T a -> T a -> T a

one :: T a

fromInteger :: Integer -> T a

(^) :: T a -> Integer -> T a

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

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

matchMaybe :: Maybe a -> Maybe a -> Maybe a

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

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

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