Data.Field

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

Field typeclass

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

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

Instances

Field Double

Defined in Data.Euclidean

Field Float

Defined in Data.Euclidean

Field ()

Defined in Data.Euclidean

Field CFloat

Defined in Data.Euclidean

Field CDouble

Defined in Data.Euclidean

Field Mod2

Defined in Data.Euclidean

Integral a => Field (Ratio a)

Defined in Data.Euclidean

Field a => Field (Complex a)

Defined in Data.Euclidean

Fractional a => Field (WrappedFractional a)

Defined in Data.Euclidean

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

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

x divide y = x times recip y

fromRational :: Field a => Rational -> a

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

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

Infix shorthand for divide.