Copyright	(c) Justus Sagemüller 2016
License	GPL v3
Maintainer	(@) sagemueller $ geo.uni-koeln.de
Stability	experimental
Portability	portable
Safe Haskell	Safe
Language	Haskell2010

Math.Manifold.VectorSpace.ZeroDimensional

Description

Documentation

data ZeroDim s Source #

Constructors

Origin

Instances

Eq (ZeroDim s) Source #
Instance details Defined in Math.Manifold.VectorSpace.ZeroDimensional Methods (==) :: ZeroDim s -> ZeroDim s -> Bool # (/=) :: ZeroDim s -> ZeroDim s -> Bool #
Show (ZeroDim s) Source #
Instance details Defined in Math.Manifold.VectorSpace.ZeroDimensional Methods showsPrec :: Int -> ZeroDim s -> ShowS # show :: ZeroDim s -> String # showList :: [ZeroDim s] -> ShowS #
Semigroup (ZeroDim s) Source #
Instance details Defined in Math.Manifold.VectorSpace.ZeroDimensional Methods (<>) :: ZeroDim s -> ZeroDim s -> ZeroDim s # sconcat :: NonEmpty (ZeroDim s) -> ZeroDim s # stimes :: Integral b => b -> ZeroDim s -> ZeroDim s #
Monoid (ZeroDim s) Source #
Instance details Defined in Math.Manifold.VectorSpace.ZeroDimensional Methods mempty :: ZeroDim s # mappend :: ZeroDim s -> ZeroDim s -> ZeroDim s # mconcat :: [ZeroDim s] -> ZeroDim s #
AffineSpace (ZeroDim s) Source #
Instance details Defined in Math.Manifold.VectorSpace.ZeroDimensional Associated Types type Diff (ZeroDim s) :: Type # Methods (.-.) :: ZeroDim s -> ZeroDim s -> Diff (ZeroDim s) # (.+^) :: ZeroDim s -> Diff (ZeroDim s) -> ZeroDim s #
HasBasis (ZeroDim s) Source #
Instance details Defined in Math.Manifold.VectorSpace.ZeroDimensional Associated Types type Basis (ZeroDim s) :: Type # Methods basisValue :: Basis (ZeroDim s) -> ZeroDim s # decompose :: ZeroDim s -> [(Basis (ZeroDim s), Scalar (ZeroDim s))] # decompose' :: ZeroDim s -> Basis (ZeroDim s) -> Scalar (ZeroDim s) #
VectorSpace (ZeroDim s) Source #
Instance details Defined in Math.Manifold.VectorSpace.ZeroDimensional Associated Types type Scalar (ZeroDim s) :: Type # Methods (*^) :: Scalar (ZeroDim s) -> ZeroDim s -> ZeroDim s #
AdditiveGroup s => InnerSpace (ZeroDim s) Source #
Instance details Defined in Math.Manifold.VectorSpace.ZeroDimensional Methods (<.>) :: ZeroDim s -> ZeroDim s -> Scalar (ZeroDim s) #
AdditiveGroup (ZeroDim s) Source #
Instance details Defined in Math.Manifold.VectorSpace.ZeroDimensional Methods zeroV :: ZeroDim s # (^+^) :: ZeroDim s -> ZeroDim s -> ZeroDim s # negateV :: ZeroDim s -> ZeroDim s # (^-^) :: ZeroDim s -> ZeroDim s -> ZeroDim s #
PseudoAffine (ZeroDim k) Source #
Instance details Defined in Math.Manifold.Core.PseudoAffine Methods (.-~.) :: ZeroDim k -> ZeroDim k -> Maybe (Needle (ZeroDim k)) Source # (.-~!) :: ZeroDim k -> ZeroDim k -> Needle (ZeroDim k) Source # pseudoAffineWitness :: PseudoAffineWitness (ZeroDim k) Source #
Semimanifold (ZeroDim k) Source #
Instance details Defined in Math.Manifold.Core.PseudoAffine Associated Types type Needle (ZeroDim k) :: Type Source # type Interior (ZeroDim k) :: Type Source # Methods (.+~^) :: Interior (ZeroDim k) -> Needle (ZeroDim k) -> ZeroDim k Source # fromInterior :: Interior (ZeroDim k) -> ZeroDim k Source # toInterior :: ZeroDim k -> Maybe (Interior (ZeroDim k)) Source # translateP :: Tagged (ZeroDim k) (Interior (ZeroDim k) -> Needle (ZeroDim k) -> Interior (ZeroDim k)) Source # (.-~^) :: Interior (ZeroDim k) -> Needle (ZeroDim k) -> ZeroDim k Source # semimanifoldWitness :: SemimanifoldWitness (ZeroDim k) Source #
type Diff (ZeroDim s) Source #
Instance details Defined in Math.Manifold.VectorSpace.ZeroDimensional type Diff (ZeroDim s) = ZeroDim s
type Basis (ZeroDim s) Source #
Instance details Defined in Math.Manifold.VectorSpace.ZeroDimensional type Basis (ZeroDim s) = Void
type Scalar (ZeroDim s) Source #
Instance details Defined in Math.Manifold.VectorSpace.ZeroDimensional type Scalar (ZeroDim s) = s
type Needle (ZeroDim k) Source #
Instance details Defined in Math.Manifold.Core.PseudoAffine type Needle (ZeroDim k) = ZeroDim k
type Interior (ZeroDim k) Source #
Instance details Defined in Math.Manifold.Core.PseudoAffine type Interior (ZeroDim k) = ZeroDim k