Safe Haskell	Safe
Language	Haskell2010

Math.Number.Group

Synopsis

class Monoid g => Group g where
- ginvert :: g -> g
group_power :: (Group g, Ord z, Num z) => g -> z -> g
class SetLike s where
- sintersection :: s -> s -> s
- sunion :: s -> s -> s
- scomplement :: s -> s
class Monoid g => AbelianGroup g where
- gnegate :: g -> g
subgroup :: Group a => Prop a -> Prop (a, a)
subgroup_identity :: Group a => Prop a -> Prop a
subgroup_inverse :: Group a => Prop a -> Prop a
subgroup_closure :: Group a => Prop a -> Prop (a, a)
data SubGroup a b = SubGroup {
- subgroup_part :: a -> b
- subgroup_restriction :: Prop a
}
automorphism :: Group g => g -> Endo g
left_coset :: Monoid m => m -> Prop m -> Prop m
right_coset :: Monoid m => m -> Prop m -> Prop m
group_commutator :: Group g => g -> g -> g
data GroupRing r g = GroupRing {
- groupring_apply :: g -> r
}
groupring_element :: (Universe g, VectorSpace g) => GroupRing (Scalar g) g -> g

Documentation

class Monoid g => Group g where Source #

https://en.wikipedia.org/wiki/Group_(mathematics)

Methods

ginvert :: g -> g Source #

Instances

Instances details

Group All Source #
Instance details Defined in Math.Number.Group Methods ginvert :: All -> All Source #
Group Any Source #
Instance details Defined in Math.Number.Group Methods ginvert :: Any -> Any Source #
Group Dimension Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods ginvert :: Dimension -> Dimension Source #
Group Ordering Source #
Instance details Defined in Math.Number.Group Methods ginvert :: Ordering -> Ordering Source #
Group () Source #
Instance details Defined in Math.Number.Group Methods ginvert :: () -> () Source #
Group b => Group (Endo b) Source #
Instance details Defined in Math.Number.Group Methods ginvert :: Endo b -> Endo b Source #
Fractional a => Group (Product a) Source #
Instance details Defined in Math.Number.Group Methods ginvert :: Product a -> Product a Source #
Num s => Group (Vector3 s) Source #
Instance details Defined in Math.Matrix.Vector3 Methods ginvert :: Vector3 s -> Vector3 s Source #
(Group a, Group b) => Group (a, b) Source #
Instance details Defined in Math.Number.Group Methods ginvert :: (a, b) -> (a, b) Source #
Group b => Group (a -> b) Source #
Instance details Defined in Math.Number.Group Methods ginvert :: (a -> b) -> a -> b Source #
Group (Four Bool Bool) Source #
Instance details Defined in Math.Graph.GraphMonoid Methods ginvert :: Four Bool Bool -> Four Bool Bool Source #
Group (Three Bool Bool) Source #
Instance details Defined in Math.Graph.GraphMonoid Methods ginvert :: Three Bool Bool -> Three Bool Bool Source #
(Group a, Group b, Group c) => Group (a, b, c) Source #
Instance details Defined in Math.Number.Group Methods ginvert :: (a, b, c) -> (a, b, c) Source #
(Group a, Group b, Group c, Group d) => Group (a, b, c, d) Source #
Instance details Defined in Math.Number.Group Methods ginvert :: (a, b, c, d) -> (a, b, c, d) Source #
(Fractional a, ConjugateSymmetric a) => Group ((Vector2 :*: Vector2) a) Source #
Instance details Defined in Math.Matrix.Vector2 Methods ginvert :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a Source #
(Fractional a, ConjugateSymmetric a) => Group ((Vector3 :*: Vector3) a) Source #
Instance details Defined in Math.Matrix.Vector3 Methods ginvert :: (Vector3 :: Vector3) a -> (Vector3 :: Vector3) a Source #
(Fractional a, ConjugateSymmetric a) => Group ((Vector4 :*: Vector4) a) Source #
Instance details Defined in Math.Matrix.Vector4 Methods ginvert :: (Vector4 :: Vector4) a -> (Vector4 :: Vector4) a Source #

group_power :: (Group g, Ord z, Num z) => g -> z -> g Source #

class SetLike s where Source #

Methods

sintersection :: s -> s -> s Source #

sunion :: s -> s -> s Source #

scomplement :: s -> s Source #

Instances

Instances details

(Ord a, Show a, Show (m Bool Bool), ReversibleGraphMonoid m Bool) => SetLike (Graph m a) Source #
Instance details Defined in Math.Graph.Reversible Methods sintersection :: Graph m a -> Graph m a -> Graph m a Source # sunion :: Graph m a -> Graph m a -> Graph m a Source # scomplement :: Graph m a -> Graph m a Source #

class Monoid g => AbelianGroup g where Source #

Abelian groups are required to be commutative with respect to mappend.

Methods

gnegate :: g -> g Source #

Instances

Instances details

Num a => AbelianGroup (Sum a) Source #
Instance details Defined in Math.Number.Group Methods gnegate :: Sum a -> Sum a Source #

subgroup :: Group a => Prop a -> Prop (a, a) Source #

subgroup_identity :: Group a => Prop a -> Prop a Source #

subgroup_inverse :: Group a => Prop a -> Prop a Source #

subgroup_closure :: Group a => Prop a -> Prop (a, a) Source #

data SubGroup a b Source #

Constructors

SubGroup
Fields subgroup_part :: a -> b subgroup_restriction :: Prop a

Instances

Instances details

Category SubGroup Source #
Instance details Defined in Math.Number.Group Methods id :: forall (a :: k). SubGroup a a # (.) :: forall (b :: k) (c :: k) (a :: k). SubGroup b c -> SubGroup a b -> SubGroup a c #

automorphism :: Group g => g -> Endo g Source #

left_coset :: Monoid m => m -> Prop m -> Prop m Source #

https://en.wikipedia.org/wiki/Coset

right_coset :: Monoid m => m -> Prop m -> Prop m Source #

group_commutator :: Group g => g -> g -> g Source #

https://en.wikipedia.org/wiki/Commutator

data GroupRing r g Source #

https://en.wikipedia.org/wiki/Group_ring

Constructors

GroupRing
Fields groupring_apply :: g -> r

Instances

Instances details

(Num r, Group g, Universe g) => Num (GroupRing r g) Source #
Instance details Defined in Math.Number.Group Methods (+) :: GroupRing r g -> GroupRing r g -> GroupRing r g # (-) :: GroupRing r g -> GroupRing r g -> GroupRing r g # (*) :: GroupRing r g -> GroupRing r g -> GroupRing r g # negate :: GroupRing r g -> GroupRing r g # abs :: GroupRing r g -> GroupRing r g # signum :: GroupRing r g -> GroupRing r g # fromInteger :: Integer -> GroupRing r g #
Num r => VectorSpace (GroupRing r g) Source #
Instance details Defined in Math.Number.Group Associated Types type Scalar (GroupRing r g) Source # Methods vzero :: GroupRing r g Source # vnegate :: GroupRing r g -> GroupRing r g Source # (%+) :: GroupRing r g -> GroupRing r g -> GroupRing r g Source # (%*) :: Scalar (GroupRing r g) -> GroupRing r g -> GroupRing r g Source #
type Scalar (GroupRing r g) Source #
Instance details Defined in Math.Number.Group type Scalar (GroupRing r g) = r

groupring_element :: (Universe g, VectorSpace g) => GroupRing (Scalar g) g -> g Source #