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

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

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.

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.