Safe Haskell | Safe |
---|---|
Language | Haskell2010 |
Synopsis
- type SemifieldLaw a = ((Additive - Monoid) a, (Multiplicative - Group) a)
- class (Semiring a, SemifieldLaw a) => Semifield a
- anan :: Semifield a => a
- pinf :: Semifield a => a
- (/) :: (Multiplicative - Group) a => a -> a -> a
- (\\) :: (Multiplicative - Group) a => a -> a -> a
- recip :: (Multiplicative - Group) a => a -> a
- type FieldLaw a = ((Additive - Group) a, (Multiplicative - Group) a)
- class (Ring a, Semifield a, FieldLaw a) => Field a
- class Field a => Real a
- ninf :: Field a => a
- (^^) :: (Multiplicative - Group) a => a -> Integer -> a
Semifields
type SemifieldLaw a = ((Additive - Monoid) a, (Multiplicative - Group) a) Source #
class (Semiring a, SemifieldLaw a) => Semifield a Source #
A semifield, near-field, or division ring.
Instances needn't have commutative multiplication or additive inverses, however addition must be commutative, and addition and multiplication must be associative as usual.
See also the wikipedia definitions of:
Instances
Semifield Double Source # | |
Defined in Data.Semifield | |
Semifield Float Source # | |
Defined in Data.Semifield | |
Semifield Rational Source # | |
Defined in Data.Semifield | |
Semifield () Source # | |
Defined in Data.Semifield | |
Semifield Uni Source # | |
Defined in Data.Semifield | |
Semifield Deci Source # | |
Defined in Data.Semifield | |
Semifield Centi Source # | |
Defined in Data.Semifield | |
Semifield Milli Source # | |
Defined in Data.Semifield | |
Semifield Micro Source # | |
Defined in Data.Semifield | |
Semifield Nano Source # | |
Defined in Data.Semifield | |
Semifield Pico Source # | |
Defined in Data.Semifield | |
Semifield CFloat Source # | |
Defined in Data.Semifield | |
Semifield CDouble Source # | |
Defined in Data.Semifield | |
Semifield (Ratio Natural) Source # | |
Defined in Data.Semifield |
(/) :: (Multiplicative - Group) a => a -> a -> a infixl 7 Source #
Right division by a multiplicative group element.
Fields
class (Ring a, Semifield a, FieldLaw a) => Field a Source #
A field.
Instances
Field Double Source # | |
Defined in Data.Semifield | |
Field Float Source # | |
Defined in Data.Semifield | |
Field Rational Source # | |
Defined in Data.Semifield | |
Field () Source # | |
Defined in Data.Semifield | |
Field Uni Source # | |
Defined in Data.Semifield | |
Field Deci Source # | |
Defined in Data.Semifield | |
Field Centi Source # | |
Defined in Data.Semifield | |
Field Milli Source # | |
Defined in Data.Semifield | |
Field Micro Source # | |
Defined in Data.Semifield | |
Field Nano Source # | |
Defined in Data.Semifield | |
Field Pico Source # | |
Defined in Data.Semifield | |
Field CFloat Source # | |
Defined in Data.Semifield | |
Field CDouble Source # | |
Defined in Data.Semifield |
class Field a => Real a Source #
A type modeling the real numbers.
Instances
Real Double Source # | |
Defined in Data.Semifield | |
Real Float Source # | |
Defined in Data.Semifield | |
Real Rational Source # | |
Defined in Data.Semifield | |
Real Uni Source # | |
Defined in Data.Semifield | |
Real Deci Source # | |
Defined in Data.Semifield | |
Real Centi Source # | |
Defined in Data.Semifield | |
Real Milli Source # | |
Defined in Data.Semifield | |
Real Micro Source # | |
Defined in Data.Semifield | |
Real Nano Source # | |
Defined in Data.Semifield | |
Real Pico Source # | |
Defined in Data.Semifield | |
Real CFloat Source # | |
Defined in Data.Semifield | |
Real CDouble Source # | |
Defined in Data.Semifield |