HLearn.Algebra.Structures.Modules

Modules are a generalization of vector spaces

Documentation

class (LeftOperator r m, RightOperator r m) => Operator r m

Instances

(LeftOperator r m, RightOperator r m) => Operator r m

class LeftOperator r m | m -> r where

Methods

(.*) :: r -> m -> m

Instances

LeftOperator Double Double

LeftOperator Float Float

LeftOperator Int Int

LeftOperator Integer Integer

LeftOperator a b => LeftOperator a [b]

(LeftOperator r sg, RegularSemigroup sg) => LeftOperator r (RegSG2Group sg)

(Num r, Ord a) => LeftOperator r (FreeMod r a)

class RightOperator r m | m -> r where

Methods

(*.) :: m -> r -> m

Instances

RightOperator Double Double

RightOperator Float Float

RightOperator Int Int

RightOperator Integer Integer

RightOperator a b => RightOperator a [b]

(RightOperator r sg, RegularSemigroup sg) => RightOperator r (RegSG2Group sg)

(Num r, Ord a) => RightOperator r (FreeMod r a)

class (LeftModule r g, RightModule r g) => Module r g

Bug: Technically, the free operator should just require that r be a semigroup and use () to chain the r's together. But this would make things awkward because the number types aren't instances of semigroup. Constraining r to be of type Num reduces our generality but makes FreeOp easier to work with in most practical use cases.

Bug: The module classes have the constraint that r be of type Num. Technically, this should be a Ring. But creating a Ring class would be awkward because it would conflict with the Num class and require importing a different Prelude.

Instances

(LeftModule r g, RightModule r g) => Module r g

class (LeftOperator r g, Num r, Group g, Abelian g) => LeftModule r g

Instances

(LeftOperator r g, Num r, Group g, Abelian g) => LeftModule r g

(LeftOperator r (FreeMod r a), Group (FreeMod r a), Abelian (FreeMod r a), Num r, Ord a) => LeftModule r (FreeMod r a)

class (RightOperator r g, Num r, Group g, Abelian g) => RightModule r g

Instances

(RightOperator r g, Num r, Group g, Abelian g) => RightModule r g

(RightOperator r (FreeMod r a), Group (FreeMod r a), Abelian (FreeMod r a), Num r, Ord a) => RightModule r (FreeMod r a)

data FreeModParams

Constructors

FreeModParams

newtype (Num r, Ord a) => FreeMod r a

Constructors

FreeMod (Map a r)

Instances

(RightOperator r (FreeMod r a), Group (FreeMod r a), Abelian (FreeMod r a), Num r, Ord a) => RightModule r (FreeMod r a)

(LeftOperator r (FreeMod r a), Group (FreeMod r a), Abelian (FreeMod r a), Num r, Ord a) => LeftModule r (FreeMod r a)

(Num r, Ord a) => RightOperator r (FreeMod r a)

(Num r, Ord a) => LeftOperator r (FreeMod r a)

Foldable (FreeMod r)

Functor (FreeMod r)

(Eq r, Eq a) => Eq (FreeMod r a)

(Num r, Ord a, Read r, Read a) => Read (FreeMod r a)

(Num r, Ord a, Show r, Show a) => Show (FreeMod r a)

(Num r, Ord a) => Monoid (FreeMod r a)

(Num r, Ord a) => Semigroup (FreeMod r a)

(Semigroup (FreeMod r a), Num r, Ord a) => RegularSemigroup (FreeMod r a)

(Semigroup (FreeMod r a), Num r, Ord a) => Abelian (FreeMod r a)

list2module :: (Num r, Ord r, Ord a) => [a] -> FreeMod r a