numeric-prelude-0.4.3: An experimental alternative hierarchy of numeric type classes

Number.ResidueClass.Maybe

Synopsis

# 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 Fieldsmodulus :: !(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 farrepresentative :: !a

Instances

 (Eq a, C a, C a) => Eq (T a) Source # Methods(==) :: T a -> T a -> Bool #(/=) :: T a -> T a -> Bool # Read a => Read (T a) Source # MethodsreadsPrec :: Int -> ReadS (T a) #readList :: ReadS [T a] #readPrec :: ReadPrec (T a) # Show a => Show (T a) Source # MethodsshowsPrec :: Int -> T a -> ShowS #show :: T a -> String #showList :: [T a] -> ShowS # (Eq a, C a) => C (T a) Source # Methodszero :: 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 # Methods(*) :: T a -> T a -> T a Source #one :: 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

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 #