Copyright	(c) Erich Gut
License	BSD3
Maintainer	zerich.gut@gmail.com
Safe Haskell	Safe-Inferred
Language	Haskell2010

OAlg.Structure.Algebraic.Definition

Contents

Algebraic

Description

definition of algebraic structures, i.e. Distributive structures with a suitable Vectorial structure.

Synopsis

class (Distributive a, Vectorial a) => Algebraic a
data Alg k
class (ForgetfulOrt (s k), ForgetfulMlt (s k), ForgetfulFbr (s k), ForgetfulFbrOrt (s k), ForgetfulAdd (s k), ForgetfulDst (s k), ForgetfulVec k s, Transformable (s k) (Alg k)) => ForgetfulAlg k s

Algebraic

class (Distributive a, Vectorial a) => Algebraic a Source #

Distributive structures with a suitable Vectorial structure.

Property Let a be a Algebraic structure, then holds:

For all r in Scalar a and a, b in a with start a == end b holds: r!(a*b) == (r!a)*b and r!(a*b) == a*(r!b).

Instances

Instances details

Algebraic N Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition
Algebraic Q Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition
Algebraic Z Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition
Algebraic Integer Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition
Algebraic () Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition
Algebraic Int Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition
Algebraic a => Algebraic (Op a) Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition
Algebraic x => Algebraic (Matrix x) Source #
Instance details Defined in OAlg.Entity.Matrix.Definition
Entity p => Algebraic (Orientation p) Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition
(Algebraic a, Typeable t, Typeable n, Typeable m) => Algebraic (Transformation t n m a) Source #
Instance details Defined in OAlg.Entity.Diagram.Transformation

data Alg k Source #

type representing the class of k-Algebraic structures.

Instances

Instances details

ForgetfulAlg k Alg Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition
ForgetfulVec k Alg Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition
Transformable1 Op (Alg k) Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition Methods tau1 :: Struct (Alg k) x -> Struct (Alg k) (Op x) Source #
ForgetfulAdd (Alg k) Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition
ForgetfulTyp (Alg k) Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition
ForgetfulDst (Alg k) Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition
ForgetfulFbr (Alg k) Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition
ForgetfulFbrOrt (Alg k) Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition
ForgetfulMlt (Alg k) Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition
ForgetfulOrt (Alg k) Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition
Transformable (Alg k) Ent Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition Methods tau :: Struct (Alg k) x -> Struct Ent x Source #
Transformable (Alg k) Add Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition Methods tau :: Struct (Alg k) x -> Struct Add x Source #
Transformable (Alg k) Typ Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition Methods tau :: Struct (Alg k) x -> Struct Typ x Source #
Transformable (Alg k) Dst Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition Methods tau :: Struct (Alg k) x -> Struct Dst x Source #
Transformable (Alg k) Fbr Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition Methods tau :: Struct (Alg k) x -> Struct Fbr x Source #
Transformable (Alg k) FbrOrt Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition Methods tau :: Struct (Alg k) x -> Struct FbrOrt x Source #
Transformable (Alg k) Mlt Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition Methods tau :: Struct (Alg k) x -> Struct Mlt x Source #
Transformable (Alg k) Ort Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition Methods tau :: Struct (Alg k) x -> Struct Ort x Source #
Transformable (Alg k) (Vec k) Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition Methods tau :: Struct (Alg k) x -> Struct (Vec k) x Source #
type Hom (Alg k) h Source #
Instance details Defined in OAlg.Hom.Algebraic type Hom (Alg k) h = HomAlgebraic k h
type Structure (Alg k) x Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition type Structure (Alg k) x = (Algebraic x, k ~ Scalar x)

class (ForgetfulOrt (s k), ForgetfulMlt (s k), ForgetfulFbr (s k), ForgetfulFbrOrt (s k), ForgetfulAdd (s k), ForgetfulDst (s k), ForgetfulVec k s, Transformable (s k) (Alg k)) => ForgetfulAlg k s Source #

transformable to k-Algebraic structure.

Instances

Instances details

ForgetfulAlg k Alg Source #
Instance details Defined in OAlg.Structure.Algebraic.Definition