Safe Haskell	None
Language	Haskell98

Data.Field

Contents

Field typeclass

Description

A Field is a Ring in which all nonzero elements have a multiplicative inverse.

Synopsis

class (Euclidean a, Ring a) => Field a
divide :: Field a => a -> a -> a
fromRational :: Field a => Rational -> a
recip :: Field a => a -> a
(/) :: Field a => a -> a -> a

Field typeclass

class (Euclidean a, Ring a) => Field a Source #

Field represents a field, a ring with a multiplicative inverse for any non-zero element.

Instances

Instances details

Field Double Source #
Instance details Defined in Data.Euclidean
Field Float Source #
Instance details Defined in Data.Euclidean
Field () Source #
Instance details Defined in Data.Euclidean
Field CFloat Source #
Instance details Defined in Data.Euclidean
Field CDouble Source #
Instance details Defined in Data.Euclidean
Field Mod2 Source #
Instance details Defined in Data.Euclidean
Integral a => Field (Ratio a) Source #
Instance details Defined in Data.Euclidean
Field a => Field (Complex a) Source #
Instance details Defined in Data.Euclidean
Fractional a => Field (WrappedFractional a) Source #
Instance details Defined in Data.Euclidean

divide :: Field a => a -> a -> a infixl 7 Source #

Divide two elements of a Field. For any Fractional type, this is the same as (/).

x divide y = x times recip y

fromRational :: Field a => Rational -> a Source #

Convert from rational to field.

When {-# LANGUAGE RebindableSyntax #-} is enabled, this function is used for desugaring rational literals (like, 2.37). This may be used to facilitate transition from Fractional to Field, because less casts are now required.

recip :: Field a => a -> a Source #

Invert an element of a Field. For any Fractional type, this is the same as recip.

recip x times x = one

(/) :: Field a => a -> a -> a infixl 7 Source #

Infix shorthand for divide.