Safe Haskell	Safe
Language	Haskell2010

Data.Semifield

Synopsis

(/) :: (Multiplicative - Group) a => a -> a -> a
(^^) :: (Multiplicative - Group) a => a -> Integer -> a
recip :: (Multiplicative - Group) a => a -> a
anan :: Semifield a => a
pinf :: Semifield a => a
ninf :: Field a => a
type SemifieldLaw a = ((Additive - Monoid) a, (Multiplicative - Group) a)
class (Semiring a, SemifieldLaw a) => Semifield a
type FieldLaw a = ((Additive - Group) a, (Multiplicative - Group) a)
class (Ring a, Semifield a, FieldLaw a) => Field a

Documentation

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

(^^) :: (Multiplicative - Group) a => a -> Integer -> a infixr 8 Source #

recip :: (Multiplicative - Group) a => a -> a Source #

Take the reciprocal of a multiplicative group element.

>>> recip (3 :+ 4) :: Complex Rational
3 % 25 :+ (-4) % 25
>>> recip (3 :+ 4) :: Complex Double
0.12 :+ (-0.16)
>>> recip (3 :+ 4) :: Complex Pico
0.120000000000 :+ -0.160000000000

anan :: Semifield a => a Source #

pinf :: Semifield a => a Source #

ninf :: Field a => a Source #

type SemifieldLaw a = ((Additive - Monoid) a, (Multiplicative - Group) a) Source #

class (Semiring a, SemifieldLaw a) => Semifield a Source #

A semifield, near-field, division ring, or associative division algebra.

Instances needn't have commutative multiplication or additive inverses.

See also the wikipedia definitions of semifield, near-field, division ring, and division algebra.

Instances

Semifield Double Source #
Instance details Defined in Data.Semifield
Semifield Float Source #
Instance details Defined in Data.Semifield
Semifield Rational Source #
Instance details Defined in Data.Semifield
Semifield () Source #
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Semifield Uni Source #
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Semifield Deci Source #
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Semifield Centi Source #
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Semifield Milli Source #
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Semifield Micro Source #
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Semifield Nano Source #
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Semifield Pico Source #
Instance details Defined in Data.Semifield
Semifield CFloat Source #
Instance details Defined in Data.Semifield
Semifield CDouble Source #
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Semifield (Ratio Natural) Source #
Instance details Defined in Data.Semifield
Field a => Semifield (Complex a) Source #
Instance details Defined in Data.Semifield

type FieldLaw a = ((Additive - Group) a, (Multiplicative - Group) a) Source #

class (Ring a, Semifield a, FieldLaw a) => Field a Source #

Instances

Field Double Source #
Instance details Defined in Data.Semifield
Field Float Source #
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Field Rational Source #
Instance details Defined in Data.Semifield
Field () Source #
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Field Uni Source #
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Field Deci Source #
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Field Centi Source #
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Field Milli Source #
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Field Micro Source #
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Field Nano Source #
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Field Pico Source #
Instance details Defined in Data.Semifield
Field CFloat Source #
Instance details Defined in Data.Semifield
Field CDouble Source #
Instance details Defined in Data.Semifield
Field a => Field (Complex a) Source #
Instance details Defined in Data.Semifield