Modulesemirings-0.7Haskell98

Data.Field

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

Contents

Field typeclass

Synopsis

class Field
value divide
value fromRational
value recip
value /

Packagesemirings-0.7
Exports5
LanguageHaskell98
LicenceBSD-3-Clause
SourceField.hs

Field typeclass

classclass (Euclidean a, Ring a) => Field a

Source#

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

Instances9Field, …

Field CDoubleDefined in semirings-0.7 · Data.Euclidean
Field CFloatDefined in semirings-0.7 · Data.Euclidean
Field DoubleDefined in semirings-0.7 · Data.Euclidean
Field FloatDefined in semirings-0.7 · Data.Euclidean
Field Mod2Defined in semirings-0.7 · Data.Euclidean
Field ()Defined in semirings-0.7 · Data.Euclidean
Fractional a => Field (WrappedFractional a)Defined in semirings-0.7 · Data.Euclidean
Integral a => Field (Ratio a)Defined in semirings-0.7 · Data.Euclidean
Field a => Field (Complex a)Defined in semirings-0.7 · Data.Euclidean

valuedivide :: Field a => a -> a -> a

Source#

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

x divide y = x times recip y

valuefromRational :: 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.

valuerecip :: 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

value(/) :: Field a => a -> a -> a

Source#

Infix shorthand for divide.