Copyright	(c) Erich Gut
License	BSD3
Maintainer	zerich.gut@gmail.com
Safe Haskell	None
Language	Haskell2010

OAlg.Data.Canonical

Contents

Canonical Mappings

Description

canonical mappings between two types.

Synopsis

class Embeddable a b where
- inj :: a -> b
class Projectible a b where
- prj :: b -> a

Canonical Mappings

class Embeddable a b where Source #

canonical embedding from a in to b.

Property

inj is injective.
if the two types a and b are also Projectible a b then prj . inj is the identical mapping.

Methods

inj :: a -> b Source #

canonical injetion from a in to b.

Instances

Instances details

Embeddable N Q Source #
Instance details Defined in OAlg.Data.Number Methods inj :: N -> Q Source #
Embeddable N Z Source #
Instance details Defined in OAlg.Data.Number Methods inj :: N -> Z Source #
Embeddable N Integer Source #
Instance details Defined in OAlg.Data.Number Methods inj :: N -> Integer Source #
Embeddable Z Q Source #
Instance details Defined in OAlg.Data.Number Methods inj :: Z -> Q Source #
Embeddable Integer Z Source #
Instance details Defined in OAlg.Data.Number Methods inj :: Integer -> Z Source #
Boolean b => Embeddable Bool b Source #
Instance details Defined in OAlg.Data.Canonical Methods inj :: Bool -> b Source #
Embeddable Int Z Source #
Instance details Defined in OAlg.Data.Number Methods inj :: Int -> Z Source #
Fibred f => Embeddable f (Sheaf f) Source #
Instance details Defined in OAlg.Structure.Fibred.Definition Methods inj :: f -> Sheaf f Source #
Oriented q => Embeddable q (Path q) Source #
Instance details Defined in OAlg.Structure.Oriented.Path Methods inj :: q -> Path q Source #
(Oriented a, Integral r) => Embeddable a (Product r a) Source #
Instance details Defined in OAlg.Entity.Product.Definition Methods inj :: a -> Product r a Source #
Embeddable a (ProductForm r a) Source #
Instance details Defined in OAlg.Entity.Product.Definition Methods inj :: a -> ProductForm r a Source #
Embeddable (Inv c) c Source #
Instance details Defined in OAlg.Structure.Multiplicative.Definition Methods inj :: Inv c -> c Source #
Embeddable (GLT x) (ProductForm N (Transformation x)) Source #
Instance details Defined in OAlg.Entity.Matrix.GeneralLinearGroup Methods inj :: GLT x -> ProductForm N (Transformation x) Source #
(Oriented a, Integral r) => Embeddable (Path a) (Product r a) Source #
Instance details Defined in OAlg.Entity.Product.Definition Methods inj :: Path a -> Product r a Source #
Embeddable (Path a) (ProductForm r a) Source #
Instance details Defined in OAlg.Entity.Product.Definition Methods inj :: Path a -> ProductForm r a Source #
Embeddable [x] (PSequence N x) Source #
Instance details Defined in OAlg.Entity.Sequence.PSequence Methods inj :: [x] -> PSequence N x Source #
Integral r => Embeddable (ProductForm N a) (ProductForm r a) Source #
Instance details Defined in OAlg.Entity.Product.Definition Methods inj :: ProductForm N a -> ProductForm r a Source #
(Embeddable a a', Embeddable b b') => Embeddable (a, b) (a', b') Source #
Instance details Defined in OAlg.Data.Canonical Methods inj :: (a, b) -> (a', b') Source #
(Embeddable a a', Embeddable b b', Embeddable c c') => Embeddable (a, b, c) (a', b', c') Source #
Instance details Defined in OAlg.Data.Canonical Methods inj :: (a, b, c) -> (a', b', c') Source #

class Projectible a b where Source #

canonical projection from b on to a.

Property

prj is surjective.
if the two types a and b are also Projectible a b then prj . inj is the identical mapping.

Methods

prj :: b -> a Source #

canonical projection from b on to a

Instances

Instances details

Projectible N Q Source #
Instance details Defined in OAlg.Data.Number Methods prj :: Q -> N Source #
Projectible N Z Source #
Instance details Defined in OAlg.Data.Number Methods prj :: Z -> N Source #
Projectible N Integer Source #
Instance details Defined in OAlg.Data.Number Methods prj :: Integer -> N Source #
Projectible Z Q Source #
Instance details Defined in OAlg.Data.Number Methods prj :: Q -> Z Source #
Projectible Integer Z Source #
Instance details Defined in OAlg.Data.Number Methods prj :: Z -> Integer Source #
Projectible Bool Valid Source #
Instance details Defined in OAlg.Data.Statement.Definition Methods prj :: Valid -> Bool Source #
Projectible Int Z Source #
Instance details Defined in OAlg.Data.Number Methods prj :: Z -> Int Source #
Entity x => Projectible (ProductSymbol x) [x] Source #
Instance details Defined in OAlg.Entity.Product.ProductSymbol Methods prj :: [x] -> ProductSymbol x Source #
Entity x => Projectible (ProductSymbol x) (Word N x) Source #
Instance details Defined in OAlg.Entity.Product.ProductSymbol Methods prj :: Word N x -> ProductSymbol x Source #
Oriented a => Projectible (Path a) (Product N a) Source #
Instance details Defined in OAlg.Entity.Product.Definition Methods prj :: Product N a -> Path a Source #
Oriented a => Projectible (Path a) (ProductForm N a) Source #
Instance details Defined in OAlg.Entity.Product.Definition Methods prj :: ProductForm N a -> Path a Source #
Projectible [x] (PSequence N x) Source #
Instance details Defined in OAlg.Entity.Sequence.PSequence Methods prj :: PSequence N x -> [x] Source #
(Oriented a, Integral r) => Projectible (Product r a) (Path a) Source #
Instance details Defined in OAlg.Entity.Product.Definition Methods prj :: Path a -> Product r a Source #
(Fibred a, Ord a, Semiring r, Commutative r) => Projectible (Sum r a) (Sheaf a) Source #
Instance details Defined in OAlg.Entity.Sum.Definition Methods prj :: Sheaf a -> Sum r a Source #
(Fibred a, Ord a, Scalar a ~ r, Semiring r, Commutative r) => Projectible (Sum r a) (VectorSheaf a) Source #
Instance details Defined in OAlg.Entity.Sum.Definition Methods prj :: VectorSheaf a -> Sum r a Source #
(Entity a, Ord a, Semiring r, Commutative r) => Projectible (SumSymbol r a) [a] Source #
Instance details Defined in OAlg.Entity.Sum.SumSymbol Methods prj :: [a] -> SumSymbol r a Source #
(Oriented a, Total a, Integral r) => Projectible (Product r a) (Word r a) Source #
Instance details Defined in OAlg.Entity.Product.Definition Methods prj :: Word r a -> Product r a Source #
Integral r => Projectible (ProductForm N a) (ProductForm r a) Source #
Instance details Defined in OAlg.Entity.Product.Definition Methods prj :: ProductForm r a -> ProductForm N a Source #
(Entity a, Ord a, Semiring r, Commutative r) => Projectible (SumSymbol r a) (LinearCombination r (SumSymbol r a)) Source #
Instance details Defined in OAlg.Entity.Sum.SumSymbol Methods prj :: LinearCombination r (SumSymbol r a) -> SumSymbol r a Source #
(Entity a, Ord a, Semiring r, Commutative r) => Projectible (SumSymbol r a) (LinearCombination r a) Source #
Instance details Defined in OAlg.Entity.Sum.SumSymbol Methods prj :: LinearCombination r a -> SumSymbol r a Source #
(Projectible a a', Projectible b b') => Projectible (a, b) (a', b') Source #
Instance details Defined in OAlg.Data.Canonical Methods prj :: (a', b') -> (a, b) Source #
(Projectible a a', Projectible b b', Projectible c c') => Projectible (a, b, c) (a', b', c') Source #
Instance details Defined in OAlg.Data.Canonical Methods prj :: (a', b', c') -> (a, b, c) Source #