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

OAlg.Entity.Matrix.Dim

Description

dimension for matrices of x as a complete sequence of Point x.

Synopsis

data Dim x p where
- Dim :: CSequence (Point x) -> Dim x (Point x)
type Dim' x = Dim x (Point x)
fromDim :: Dim x p -> ProductSymbol p
dim :: (Entity p, p ~ Point x) => p -> Dim x p
productDim :: (Entity p, p ~ Point x) => [p] -> Dim x p
dimxs :: p ~ Point x => Dim x p -> [(p, N)]
dimwrd :: (Entity p, p ~ Point x) => Dim x p -> Word N p
dimMap :: (Entity q, q ~ Point y) => (p -> q) -> Dim x p -> Dim y q

Documentation

data Dim x p where Source #

dimension of x as a complete sequence of Point x.

Constructors

Dim :: CSequence (Point x) -> Dim x (Point x)

Instances

Instances details

Sequence (Dim x) N p Source #
Instance details Defined in OAlg.Entity.Matrix.Dim Methods graph :: p0 N -> Dim x p -> Graph N p Source # list :: p0 N -> Dim x p -> [(p, N)] Source # (??) :: Dim x p -> N -> Maybe p Source #
(Oriented x, Entity p) => PermutableSequence (Dim x) N p Source #
Instance details Defined in OAlg.Entity.Matrix.Dim Methods permuteBy :: p0 N -> (w -> w -> Ordering) -> (p -> w) -> Dim x p -> (Dim x p, Permutation N) Source #
Entity p => Opr (Permutation N) (Dim x p) Source #
Instance details Defined in OAlg.Entity.Matrix.Dim Methods (<*) :: Dim x p -> Permutation N -> Dim x p Source #
(Oriented x, Entity p) => TotalOpr (Permutation N) (Dim x p) Source #
Instance details Defined in OAlg.Entity.Matrix.Dim
Oriented x => Show (Dim x p) Source #
Instance details Defined in OAlg.Entity.Matrix.Dim Methods showsPrec :: Int -> Dim x p -> ShowS # show :: Dim x p -> String # showList :: [Dim x p] -> ShowS #
Oriented x => Eq (Dim x p) Source #
Instance details Defined in OAlg.Entity.Matrix.Dim Methods (==) :: Dim x p -> Dim x p -> Bool # (/=) :: Dim x p -> Dim x p -> Bool #
(Oriented x, OrdPoint x) => Ord (Dim x p) Source #
Instance details Defined in OAlg.Entity.Matrix.Dim Methods compare :: Dim x p -> Dim x p -> Ordering # (<) :: Dim x p -> Dim x p -> Bool # (<=) :: Dim x p -> Dim x p -> Bool # (>) :: Dim x p -> Dim x p -> Bool # (>=) :: Dim x p -> Dim x p -> Bool # max :: Dim x p -> Dim x p -> Dim x p # min :: Dim x p -> Dim x p -> Dim x p #
LengthN (Dim x p) Source #
Instance details Defined in OAlg.Entity.Matrix.Dim Methods lengthN :: Dim x p -> N Source #
Oriented x => Validable (Dim x p) Source #
Instance details Defined in OAlg.Entity.Matrix.Dim Methods valid :: Dim x p -> Statement Source #
(Oriented x, () ~ Point x) => XStandard (Dim x ()) Source #
Instance details Defined in OAlg.Entity.Matrix.Dim Methods xStandard :: X (Dim x ()) Source #
(Oriented x, Typeable p) => Entity (Dim x p) Source #
Instance details Defined in OAlg.Entity.Matrix.Dim
(Oriented x, Typeable p, p ~ Point x) => Exponential (Dim x p) Source #
Instance details Defined in OAlg.Entity.Matrix.Dim Associated Types type Exponent (Dim x p) Source # Methods (^) :: Dim x p -> Exponent (Dim x p) -> Dim x p Source #
(Oriented x, Typeable p, p ~ Point x) => Multiplicative (Dim x p) Source #
Instance details Defined in OAlg.Entity.Matrix.Dim Methods one :: Point (Dim x p) -> Dim x p Source # (*) :: Dim x p -> Dim x p -> Dim x p Source # npower :: Dim x p -> N -> Dim x p Source #
(Oriented x, Typeable p) => Oriented (Dim x p) Source #
Instance details Defined in OAlg.Entity.Matrix.Dim Associated Types type Point (Dim x p) Source # Methods orientation :: Dim x p -> Orientation (Point (Dim x p)) Source # start :: Dim x p -> Point (Dim x p) Source # end :: Dim x p -> Point (Dim x p) Source #
Total (Dim x p) Source #
Instance details Defined in OAlg.Entity.Matrix.Dim
type Exponent (Dim x p) Source #
Instance details Defined in OAlg.Entity.Matrix.Dim type Exponent (Dim x p) = N
type Point (Dim x p) Source #
Instance details Defined in OAlg.Entity.Matrix.Dim type Point (Dim x p) = ()

type Dim' x = Dim x (Point x) Source #

abbreviation for Dim x (Point x).

fromDim :: Dim x p -> ProductSymbol p Source #

the underlying product.

dim :: (Entity p, p ~ Point x) => p -> Dim x p Source #

constructing a dimension form a point.

productDim :: (Entity p, p ~ Point x) => [p] -> Dim x p Source #

constructing a dimension from a list of points.

dimxs :: p ~ Point x => Dim x p -> [(p, N)] Source #

the indexed listing of the points.

dimwrd :: (Entity p, p ~ Point x) => Dim x p -> Word N p Source #

the underlying word.

dimMap :: (Entity q, q ~ Point y) => (p -> q) -> Dim x p -> Dim y q Source #

mapping a dimension.