Copyright	(c) Justus Sagemüller 2020
License	GPL v3
Maintainer	(@) jsag $ hvl.no
Stability	experimental
Portability	portable
Safe Haskell	Safe-Inferred
Language	Haskell2010

Data.Manifold.WithBoundary

Contents

Orphan instances

Description

Synopsis

class SemimanifoldWithBoundary m where
- type Interior m :: Type
- type Boundary m :: Type
- type HalfNeedle m :: Type
- (.+^|) :: m -> Needle (Interior m) -> Either (Boundary m, Scalar (Needle (Interior m))) (Interior m)
- fromInterior :: Interior m -> m
- fromBoundary :: Boundary m -> m
- (|+^) :: Boundary m -> HalfNeedle m -> m
- separateInterior :: m -> Either (Boundary m) (Interior m)
- toInterior :: m -> Maybe (Interior m)
- extendToBoundary :: Interior m -> Needle (Interior m) -> Maybe (Boundary m)
- smfdWBoundWitness :: SmfdWBoundWitness m
- needleIsOpenMfd :: (OpenManifold (Needle (Interior m)) => r) -> r
- scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior m))) => r) -> r
- boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary m)), Scalar (Needle (Boundary m)) ~ Scalar (Needle (Interior m))) => r) -> r
class (SemimanifoldWithBoundary m, PseudoAffine (Interior m), PseudoAffine (Boundary m)) => PseudoAffineWithBoundary m where
- (.--!) :: m -> m -> Needle (Interior m)
- (.-|) :: m -> Boundary m -> Maybe (HalfNeedle m)
- (!-|) :: m -> Boundary m -> HalfNeedle m
- (.--.) :: m -> m -> Maybe (Needle (Interior m))
class PseudoAffineWithBoundary m => ProjectableBoundary m where
- projectToBoundary :: m -> Boundary m -> Maybe (Needle (Boundary m), Scalar (Needle (Interior m)))
- marginFromBoundary :: Boundary m -> Scalar (Needle (Interior m)) -> m
- needleBoundaryIsTriviallyProjectible :: forall r. (ProjectableBoundary (Needle (Interior m)) => r) -> r
- scalarBoundaryIsTriviallyProjectible :: forall r. (ProjectableBoundary (Scalar (Needle (Interior m))) => r) -> r
data SmfdWBoundWitness m where
- OpenManifoldWitness :: forall m. OpenManifold m => SmfdWBoundWitness m
- SmfdWBoundWitness :: forall m. (OpenManifold (Interior m), OpenManifold (Boundary m), FullSubspace (HalfNeedle m) ~ Needle (Boundary m)) => SmfdWBoundWitness m
class AdditiveMonoid h where
- zeroHV :: h
- addHVs :: h -> h -> h
class AdditiveMonoid h => HalfSpace h where
- type FullSubspace h
- type Ray h
- type MirrorJoin h
- scaleNonNeg :: Ray h -> h -> h
- fromFullSubspace :: FullSubspace h -> h
- projectToFullSubspace :: h -> FullSubspace h
- fullSubspaceIsVectorSpace :: ((VectorSpace (FullSubspace h), ScalarSpace (Scalar (FullSubspace h)), Scalar (FullSubspace h) ~ MirrorJoin (Ray h)) => r) -> r
- rayIsHalfSpace :: (HalfSpace (Ray h) => r) -> r
- mirrorJoinIsVectorSpace :: ((VectorSpace (MirrorJoin h), Scalar (MirrorJoin h) ~ MirrorJoin (Ray h)) => r) -> r
- fromPositiveHalf :: h -> MirrorJoin h
- fromNegativeHalf :: h -> MirrorJoin h

Documentation

class SemimanifoldWithBoundary m where Source #

The class of spaces with a displacement operation like Semimanifold, but there may be a limited range how far it is possible to move before leaving the space.

Such spaces decompose into two Semimanifold spaces: the Interior and the Boundary.

Minimal complete definition

(.+^|), fromInterior, fromBoundary, (|+^)

Associated Types

type Interior m :: Type Source #

Subspace of m representing the set of points where it is possible to move at least a small distance in any direction (with .+^|) without leaving m.

type Boundary m :: Type Source #

The set of points where an infinitesimal movement is sufficient to leave m.

type HalfNeedle m :: Type Source #

Methods

(.+^|) Source #

Arguments

:: m	Starting point `p`
-> Needle (Interior m)	Displacement `v`
-> Either (Boundary m, Scalar (Needle (Interior m))) (Interior m)	If `v` is enough to leave `m`, yield the point where it does and what fraction of the length is still left (i.e. how much of `v` “pokes out of the space”). If it stays within the space, just give back the result.

Boundary-aware pendant to .+~^.

fromInterior :: Interior m -> m Source #

fromBoundary :: Boundary m -> m Source #

(|+^) :: Boundary m -> HalfNeedle m -> m Source #

separateInterior :: m -> Either (Boundary m) (Interior m) Source #

toInterior :: m -> Maybe (Interior m) Source #

extendToBoundary :: Interior m -> Needle (Interior m) -> Maybe (Boundary m) Source #

default extendToBoundary :: (VectorSpace (Needle (Interior m)), Num (Scalar (Needle (Interior m)))) => Interior m -> Needle (Interior m) -> Maybe (Boundary m) Source #

smfdWBoundWitness :: SmfdWBoundWitness m Source #

default smfdWBoundWitness :: (OpenManifold (Interior m), OpenManifold (Boundary m), FullSubspace (HalfNeedle m) ~ Needle (Boundary m)) => SmfdWBoundWitness m Source #

needleIsOpenMfd :: (OpenManifold (Needle (Interior m)) => r) -> r Source #

default needleIsOpenMfd :: OpenManifold (Needle (Interior m)) => (OpenManifold (Needle (Interior m)) => r) -> r Source #

scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior m))) => r) -> r Source #

default scalarIsOpenMfd :: OpenManifold (Scalar (Needle (Interior m))) => (OpenManifold (Scalar (Needle (Interior m))) => r) -> r Source #

boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary m)), Scalar (Needle (Boundary m)) ~ Scalar (Needle (Interior m))) => r) -> r Source #

default boundaryHasSameScalar :: (LinearSpace (Needle (Boundary m)), Scalar (Needle (Boundary m)) ~ Scalar (Needle (Interior m))) => ((LinearSpace (Needle (Boundary m)), Scalar (Needle (Boundary m)) ~ Scalar (Needle (Interior m))) => r) -> r Source #

Instances

Instances details

SemimanifoldWithBoundary ℝay Source #
Instance details Defined in Data.Manifold.Cone Associated Types type Interior ℝay Source # type Boundary ℝay Source # type HalfNeedle ℝay Source # Methods (.+^\|) :: ℝay -> Needle (Interior ℝay) -> Either (Boundary ℝay, Scalar (Needle (Interior ℝay))) (Interior ℝay) Source # fromInterior :: Interior ℝay -> ℝay Source # fromBoundary :: Boundary ℝay -> ℝay Source # (\|+^) :: Boundary ℝay -> HalfNeedle ℝay -> ℝay Source # separateInterior :: ℝay -> Either (Boundary ℝay) (Interior ℝay) Source # toInterior :: ℝay -> Maybe (Interior ℝay) Source # extendToBoundary :: Interior ℝay -> Needle (Interior ℝay) -> Maybe (Boundary ℝay) Source # smfdWBoundWitness :: SmfdWBoundWitness ℝay Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior ℝay)) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior ℝay))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary ℝay)), Scalar (Needle (Boundary ℝay)) ~ Scalar (Needle (Interior ℝay))) => r) -> r Source #
(Num' ℝ, Eq ℝ, OpenManifold ℝ, ProjectableBoundary ℝ) => SemimanifoldWithBoundary ℝ Source #
Instance details Defined in Data.Manifold.WithBoundary Associated Types type Interior ℝ Source # type Boundary ℝ Source # type HalfNeedle ℝ Source # Methods (.+^\|) :: ℝ -> Needle (Interior ℝ) -> Either (Boundary ℝ, Scalar (Needle (Interior ℝ))) (Interior ℝ) Source # fromInterior :: Interior ℝ -> ℝ Source # fromBoundary :: Boundary ℝ -> ℝ Source # (\|+^) :: Boundary ℝ -> HalfNeedle ℝ -> ℝ Source # separateInterior :: ℝ -> Either (Boundary ℝ) (Interior ℝ) Source # toInterior :: ℝ -> Maybe (Interior ℝ) Source # extendToBoundary :: Interior ℝ -> Needle (Interior ℝ) -> Maybe (Boundary ℝ) Source # smfdWBoundWitness :: SmfdWBoundWitness ℝ Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior ℝ)) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior ℝ))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary ℝ)), Scalar (Needle (Boundary ℝ)) ~ Scalar (Needle (Interior ℝ))) => r) -> r Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => SemimanifoldWithBoundary (V0 s) Source #
Instance details Defined in Data.Manifold.WithBoundary Associated Types type Interior (V0 s) Source # type Boundary (V0 s) Source # type HalfNeedle (V0 s) Source # Methods (.+^\|) :: V0 s -> Needle (Interior (V0 s)) -> Either (Boundary (V0 s), Scalar (Needle (Interior (V0 s)))) (Interior (V0 s)) Source # fromInterior :: Interior (V0 s) -> V0 s Source # fromBoundary :: Boundary (V0 s) -> V0 s Source # (\|+^) :: Boundary (V0 s) -> HalfNeedle (V0 s) -> V0 s Source # separateInterior :: V0 s -> Either (Boundary (V0 s)) (Interior (V0 s)) Source # toInterior :: V0 s -> Maybe (Interior (V0 s)) Source # extendToBoundary :: Interior (V0 s) -> Needle (Interior (V0 s)) -> Maybe (Boundary (V0 s)) Source # smfdWBoundWitness :: SmfdWBoundWitness (V0 s) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (V0 s))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (V0 s)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (V0 s))), Scalar (Needle (Boundary (V0 s))) ~ Scalar (Needle (Interior (V0 s)))) => r) -> r Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => SemimanifoldWithBoundary (V1 s) Source #
Instance details Defined in Data.Manifold.WithBoundary Associated Types type Interior (V1 s) Source # type Boundary (V1 s) Source # type HalfNeedle (V1 s) Source # Methods (.+^\|) :: V1 s -> Needle (Interior (V1 s)) -> Either (Boundary (V1 s), Scalar (Needle (Interior (V1 s)))) (Interior (V1 s)) Source # fromInterior :: Interior (V1 s) -> V1 s Source # fromBoundary :: Boundary (V1 s) -> V1 s Source # (\|+^) :: Boundary (V1 s) -> HalfNeedle (V1 s) -> V1 s Source # separateInterior :: V1 s -> Either (Boundary (V1 s)) (Interior (V1 s)) Source # toInterior :: V1 s -> Maybe (Interior (V1 s)) Source # extendToBoundary :: Interior (V1 s) -> Needle (Interior (V1 s)) -> Maybe (Boundary (V1 s)) Source # smfdWBoundWitness :: SmfdWBoundWitness (V1 s) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (V1 s))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (V1 s)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (V1 s))), Scalar (Needle (Boundary (V1 s))) ~ Scalar (Needle (Interior (V1 s)))) => r) -> r Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => SemimanifoldWithBoundary (V2 s) Source #
Instance details Defined in Data.Manifold.WithBoundary Associated Types type Interior (V2 s) Source # type Boundary (V2 s) Source # type HalfNeedle (V2 s) Source # Methods (.+^\|) :: V2 s -> Needle (Interior (V2 s)) -> Either (Boundary (V2 s), Scalar (Needle (Interior (V2 s)))) (Interior (V2 s)) Source # fromInterior :: Interior (V2 s) -> V2 s Source # fromBoundary :: Boundary (V2 s) -> V2 s Source # (\|+^) :: Boundary (V2 s) -> HalfNeedle (V2 s) -> V2 s Source # separateInterior :: V2 s -> Either (Boundary (V2 s)) (Interior (V2 s)) Source # toInterior :: V2 s -> Maybe (Interior (V2 s)) Source # extendToBoundary :: Interior (V2 s) -> Needle (Interior (V2 s)) -> Maybe (Boundary (V2 s)) Source # smfdWBoundWitness :: SmfdWBoundWitness (V2 s) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (V2 s))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (V2 s)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (V2 s))), Scalar (Needle (Boundary (V2 s))) ~ Scalar (Needle (Interior (V2 s)))) => r) -> r Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => SemimanifoldWithBoundary (V3 s) Source #
Instance details Defined in Data.Manifold.WithBoundary Associated Types type Interior (V3 s) Source # type Boundary (V3 s) Source # type HalfNeedle (V3 s) Source # Methods (.+^\|) :: V3 s -> Needle (Interior (V3 s)) -> Either (Boundary (V3 s), Scalar (Needle (Interior (V3 s)))) (Interior (V3 s)) Source # fromInterior :: Interior (V3 s) -> V3 s Source # fromBoundary :: Boundary (V3 s) -> V3 s Source # (\|+^) :: Boundary (V3 s) -> HalfNeedle (V3 s) -> V3 s Source # separateInterior :: V3 s -> Either (Boundary (V3 s)) (Interior (V3 s)) Source # toInterior :: V3 s -> Maybe (Interior (V3 s)) Source # extendToBoundary :: Interior (V3 s) -> Needle (Interior (V3 s)) -> Maybe (Boundary (V3 s)) Source # smfdWBoundWitness :: SmfdWBoundWitness (V3 s) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (V3 s))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (V3 s)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (V3 s))), Scalar (Needle (Boundary (V3 s))) ~ Scalar (Needle (Interior (V3 s)))) => r) -> r Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => SemimanifoldWithBoundary (V4 s) Source #
Instance details Defined in Data.Manifold.WithBoundary Associated Types type Interior (V4 s) Source # type Boundary (V4 s) Source # type HalfNeedle (V4 s) Source # Methods (.+^\|) :: V4 s -> Needle (Interior (V4 s)) -> Either (Boundary (V4 s), Scalar (Needle (Interior (V4 s)))) (Interior (V4 s)) Source # fromInterior :: Interior (V4 s) -> V4 s Source # fromBoundary :: Boundary (V4 s) -> V4 s Source # (\|+^) :: Boundary (V4 s) -> HalfNeedle (V4 s) -> V4 s Source # separateInterior :: V4 s -> Either (Boundary (V4 s)) (Interior (V4 s)) Source # toInterior :: V4 s -> Maybe (Interior (V4 s)) Source # extendToBoundary :: Interior (V4 s) -> Needle (Interior (V4 s)) -> Maybe (Boundary (V4 s)) Source # smfdWBoundWitness :: SmfdWBoundWitness (V4 s) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (V4 s))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (V4 s)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (V4 s))), Scalar (Needle (Boundary (V4 s))) ~ Scalar (Needle (Interior (V4 s)))) => r) -> r Source #
(AffineSpace x, Manifold x, Diff x ~ Needle x, Atlas x, HasTrie (ChartIndex x), LinearSpace (Needle x), LinearSpace (Needle' x), Num' (Scalar (Needle x))) => SemimanifoldWithBoundary (Shade x) Source #
Instance details Defined in Data.Manifold.Shade Associated Types type Interior (Shade x) Source # type Boundary (Shade x) Source # type HalfNeedle (Shade x) Source # Methods (.+^\|) :: Shade x -> Needle (Interior (Shade x)) -> Either (Boundary (Shade x), Scalar (Needle (Interior (Shade x)))) (Interior (Shade x)) Source # fromInterior :: Interior (Shade x) -> Shade x Source # fromBoundary :: Boundary (Shade x) -> Shade x Source # (\|+^) :: Boundary (Shade x) -> HalfNeedle (Shade x) -> Shade x Source # separateInterior :: Shade x -> Either (Boundary (Shade x)) (Interior (Shade x)) Source # toInterior :: Shade x -> Maybe (Interior (Shade x)) Source # extendToBoundary :: Interior (Shade x) -> Needle (Interior (Shade x)) -> Maybe (Boundary (Shade x)) Source # smfdWBoundWitness :: SmfdWBoundWitness (Shade x) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (Shade x))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (Shade x)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (Shade x))), Scalar (Needle (Boundary (Shade x))) ~ Scalar (Needle (Interior (Shade x)))) => r) -> r Source #
(AffineSpace x, Manifold x, Diff x ~ Needle x, Atlas' x, LinearSpace (Needle x), LinearSpace (Needle' x)) => SemimanifoldWithBoundary (Shade' x) Source #
Instance details Defined in Data.Manifold.Shade Associated Types type Interior (Shade' x) Source # type Boundary (Shade' x) Source # type HalfNeedle (Shade' x) Source # Methods (.+^\|) :: Shade' x -> Needle (Interior (Shade' x)) -> Either (Boundary (Shade' x), Scalar (Needle (Interior (Shade' x)))) (Interior (Shade' x)) Source # fromInterior :: Interior (Shade' x) -> Shade' x Source # fromBoundary :: Boundary (Shade' x) -> Shade' x Source # (\|+^) :: Boundary (Shade' x) -> HalfNeedle (Shade' x) -> Shade' x Source # separateInterior :: Shade' x -> Either (Boundary (Shade' x)) (Interior (Shade' x)) Source # toInterior :: Shade' x -> Maybe (Interior (Shade' x)) Source # extendToBoundary :: Interior (Shade' x) -> Needle (Interior (Shade' x)) -> Maybe (Boundary (Shade' x)) Source # smfdWBoundWitness :: SmfdWBoundWitness (Shade' x) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (Shade' x))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (Shade' x)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (Shade' x))), Scalar (Needle (Boundary (Shade' x))) ~ Scalar (Needle (Interior (Shade' x)))) => r) -> r Source #
SemimanifoldWithBoundary (CD¹ ℝ⁰) Source #
Instance details Defined in Data.Manifold.Cone Associated Types type Interior (CD¹ ℝ⁰) Source # type Boundary (CD¹ ℝ⁰) Source # type HalfNeedle (CD¹ ℝ⁰) Source # Methods (.+^\|) :: CD¹ ℝ⁰ -> Needle (Interior (CD¹ ℝ⁰)) -> Either (Boundary (CD¹ ℝ⁰), Scalar (Needle (Interior (CD¹ ℝ⁰)))) (Interior (CD¹ ℝ⁰)) Source # fromInterior :: Interior (CD¹ ℝ⁰) -> CD¹ ℝ⁰ Source # fromBoundary :: Boundary (CD¹ ℝ⁰) -> CD¹ ℝ⁰ Source # (\|+^) :: Boundary (CD¹ ℝ⁰) -> HalfNeedle (CD¹ ℝ⁰) -> CD¹ ℝ⁰ Source # separateInterior :: CD¹ ℝ⁰ -> Either (Boundary (CD¹ ℝ⁰)) (Interior (CD¹ ℝ⁰)) Source # toInterior :: CD¹ ℝ⁰ -> Maybe (Interior (CD¹ ℝ⁰)) Source # extendToBoundary :: Interior (CD¹ ℝ⁰) -> Needle (Interior (CD¹ ℝ⁰)) -> Maybe (Boundary (CD¹ ℝ⁰)) Source # smfdWBoundWitness :: SmfdWBoundWitness (CD¹ ℝ⁰) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (CD¹ ℝ⁰))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (CD¹ ℝ⁰)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (CD¹ ℝ⁰))), Scalar (Needle (Boundary (CD¹ ℝ⁰))) ~ Scalar (Needle (Interior (CD¹ ℝ⁰)))) => r) -> r Source #
SemimanifoldWithBoundary (Cℝay S⁰) Source #
Instance details Defined in Data.Manifold.Cone Associated Types type Interior (Cℝay S⁰) Source # type Boundary (Cℝay S⁰) Source # type HalfNeedle (Cℝay S⁰) Source # Methods (.+^\|) :: Cℝay S⁰ -> Needle (Interior (Cℝay S⁰)) -> Either (Boundary (Cℝay S⁰), Scalar (Needle (Interior (Cℝay S⁰)))) (Interior (Cℝay S⁰)) Source # fromInterior :: Interior (Cℝay S⁰) -> Cℝay S⁰ Source # fromBoundary :: Boundary (Cℝay S⁰) -> Cℝay S⁰ Source # (\|+^) :: Boundary (Cℝay S⁰) -> HalfNeedle (Cℝay S⁰) -> Cℝay S⁰ Source # separateInterior :: Cℝay S⁰ -> Either (Boundary (Cℝay S⁰)) (Interior (Cℝay S⁰)) Source # toInterior :: Cℝay S⁰ -> Maybe (Interior (Cℝay S⁰)) Source # extendToBoundary :: Interior (Cℝay S⁰) -> Needle (Interior (Cℝay S⁰)) -> Maybe (Boundary (Cℝay S⁰)) Source # smfdWBoundWitness :: SmfdWBoundWitness (Cℝay S⁰) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (Cℝay S⁰))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (Cℝay S⁰)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (Cℝay S⁰))), Scalar (Needle (Boundary (Cℝay S⁰))) ~ Scalar (Needle (Interior (Cℝay S⁰)))) => r) -> r Source #
(Semimanifold a, Semimanifold (VRep a), Needle a ~ GenericNeedle a, OpenManifold (Scalar (Needle (Rep a Void))), LinearSpace (Needle (Rep a Void)), Num' (Scalar (Needle (Rep a Void)))) => SemimanifoldWithBoundary (GenericNeedle a) Source #
Instance details Defined in Data.Manifold.WithBoundary Associated Types type Interior (GenericNeedle a) Source # type Boundary (GenericNeedle a) Source # type HalfNeedle (GenericNeedle a) Source # Methods (.+^\|) :: GenericNeedle a -> Needle (Interior (GenericNeedle a)) -> Either (Boundary (GenericNeedle a), Scalar (Needle (Interior (GenericNeedle a)))) (Interior (GenericNeedle a)) Source # fromInterior :: Interior (GenericNeedle a) -> GenericNeedle a Source # fromBoundary :: Boundary (GenericNeedle a) -> GenericNeedle a Source # (\|+^) :: Boundary (GenericNeedle a) -> HalfNeedle (GenericNeedle a) -> GenericNeedle a Source # separateInterior :: GenericNeedle a -> Either (Boundary (GenericNeedle a)) (Interior (GenericNeedle a)) Source # toInterior :: GenericNeedle a -> Maybe (Interior (GenericNeedle a)) Source # extendToBoundary :: Interior (GenericNeedle a) -> Needle (Interior (GenericNeedle a)) -> Maybe (Boundary (GenericNeedle a)) Source # smfdWBoundWitness :: SmfdWBoundWitness (GenericNeedle a) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (GenericNeedle a))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (GenericNeedle a)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (GenericNeedle a))), Scalar (Needle (Boundary (GenericNeedle a))) ~ Scalar (Needle (Interior (GenericNeedle a)))) => r) -> r Source #
RealFloat'' s => SemimanifoldWithBoundary (D¹_ s) Source #
Instance details Defined in Data.Manifold.WithBoundary Associated Types type Interior (D¹_ s) Source # type Boundary (D¹_ s) Source # type HalfNeedle (D¹_ s) Source # Methods (.+^\|) :: D¹_ s -> Needle (Interior (D¹_ s)) -> Either (Boundary (D¹_ s), Scalar (Needle (Interior (D¹_ s)))) (Interior (D¹_ s)) Source # fromInterior :: Interior (D¹_ s) -> D¹_ s Source # fromBoundary :: Boundary (D¹_ s) -> D¹_ s Source # (\|+^) :: Boundary (D¹_ s) -> HalfNeedle (D¹_ s) -> D¹_ s Source # separateInterior :: D¹_ s -> Either (Boundary (D¹_ s)) (Interior (D¹_ s)) Source # toInterior :: D¹_ s -> Maybe (Interior (D¹_ s)) Source # extendToBoundary :: Interior (D¹_ s) -> Needle (Interior (D¹_ s)) -> Maybe (Boundary (D¹_ s)) Source # smfdWBoundWitness :: SmfdWBoundWitness (D¹_ s) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (D¹_ s))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (D¹_ s)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (D¹_ s))), Scalar (Needle (Boundary (D¹_ s))) ~ Scalar (Needle (Interior (D¹_ s)))) => r) -> r Source #
(LinearSpace k, OpenManifold k, OpenManifold (Scalar k)) => SemimanifoldWithBoundary (EmptyMfd k) Source #
Instance details Defined in Data.Manifold.WithBoundary.Class Associated Types type Interior (EmptyMfd k) Source # type Boundary (EmptyMfd k) Source # type HalfNeedle (EmptyMfd k) Source # Methods (.+^\|) :: EmptyMfd k -> Needle (Interior (EmptyMfd k)) -> Either (Boundary (EmptyMfd k), Scalar (Needle (Interior (EmptyMfd k)))) (Interior (EmptyMfd k)) Source # fromInterior :: Interior (EmptyMfd k) -> EmptyMfd k Source # fromBoundary :: Boundary (EmptyMfd k) -> EmptyMfd k Source # (\|+^) :: Boundary (EmptyMfd k) -> HalfNeedle (EmptyMfd k) -> EmptyMfd k Source # separateInterior :: EmptyMfd k -> Either (Boundary (EmptyMfd k)) (Interior (EmptyMfd k)) Source # toInterior :: EmptyMfd k -> Maybe (Interior (EmptyMfd k)) Source # extendToBoundary :: Interior (EmptyMfd k) -> Needle (Interior (EmptyMfd k)) -> Maybe (Boundary (EmptyMfd k)) Source # smfdWBoundWitness :: SmfdWBoundWitness (EmptyMfd k) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (EmptyMfd k))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (EmptyMfd k)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (EmptyMfd k))), Scalar (Needle (Boundary (EmptyMfd k))) ~ Scalar (Needle (Interior (EmptyMfd k)))) => r) -> r Source #
RealFloat'' s => SemimanifoldWithBoundary (S²_ s) Source #
Instance details Defined in Data.Manifold.WithBoundary Associated Types type Interior (S²_ s) Source # type Boundary (S²_ s) Source # type HalfNeedle (S²_ s) Source # Methods (.+^\|) :: S²_ s -> Needle (Interior (S²_ s)) -> Either (Boundary (S²_ s), Scalar (Needle (Interior (S²_ s)))) (Interior (S²_ s)) Source # fromInterior :: Interior (S²_ s) -> S²_ s Source # fromBoundary :: Boundary (S²_ s) -> S²_ s Source # (\|+^) :: Boundary (S²_ s) -> HalfNeedle (S²_ s) -> S²_ s Source # separateInterior :: S²_ s -> Either (Boundary (S²_ s)) (Interior (S²_ s)) Source # toInterior :: S²_ s -> Maybe (Interior (S²_ s)) Source # extendToBoundary :: Interior (S²_ s) -> Needle (Interior (S²_ s)) -> Maybe (Boundary (S²_ s)) Source # smfdWBoundWitness :: SmfdWBoundWitness (S²_ s) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (S²_ s))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (S²_ s)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (S²_ s))), Scalar (Needle (Boundary (S²_ s))) ~ Scalar (Needle (Interior (S²_ s)))) => r) -> r Source #
RealFloat'' s => SemimanifoldWithBoundary (S¹_ s) Source #
Instance details Defined in Data.Manifold.WithBoundary Associated Types type Interior (S¹_ s) Source # type Boundary (S¹_ s) Source # type HalfNeedle (S¹_ s) Source # Methods (.+^\|) :: S¹_ s -> Needle (Interior (S¹_ s)) -> Either (Boundary (S¹_ s), Scalar (Needle (Interior (S¹_ s)))) (Interior (S¹_ s)) Source # fromInterior :: Interior (S¹_ s) -> S¹_ s Source # fromBoundary :: Boundary (S¹_ s) -> S¹_ s Source # (\|+^) :: Boundary (S¹_ s) -> HalfNeedle (S¹_ s) -> S¹_ s Source # separateInterior :: S¹_ s -> Either (Boundary (S¹_ s)) (Interior (S¹_ s)) Source # toInterior :: S¹_ s -> Maybe (Interior (S¹_ s)) Source # extendToBoundary :: Interior (S¹_ s) -> Needle (Interior (S¹_ s)) -> Maybe (Boundary (S¹_ s)) Source # smfdWBoundWitness :: SmfdWBoundWitness (S¹_ s) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (S¹_ s))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (S¹_ s)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (S¹_ s))), Scalar (Needle (Boundary (S¹_ s))) ~ Scalar (Needle (Interior (S¹_ s)))) => r) -> r Source #
RealFloat'' s => SemimanifoldWithBoundary (S⁰_ s) Source #
Instance details Defined in Data.Manifold.WithBoundary Associated Types type Interior (S⁰_ s) Source # type Boundary (S⁰_ s) Source # type HalfNeedle (S⁰_ s) Source # Methods (.+^\|) :: S⁰_ s -> Needle (Interior (S⁰_ s)) -> Either (Boundary (S⁰_ s), Scalar (Needle (Interior (S⁰_ s)))) (Interior (S⁰_ s)) Source # fromInterior :: Interior (S⁰_ s) -> S⁰_ s Source # fromBoundary :: Boundary (S⁰_ s) -> S⁰_ s Source # (\|+^) :: Boundary (S⁰_ s) -> HalfNeedle (S⁰_ s) -> S⁰_ s Source # separateInterior :: S⁰_ s -> Either (Boundary (S⁰_ s)) (Interior (S⁰_ s)) Source # toInterior :: S⁰_ s -> Maybe (Interior (S⁰_ s)) Source # extendToBoundary :: Interior (S⁰_ s) -> Needle (Interior (S⁰_ s)) -> Maybe (Boundary (S⁰_ s)) Source # smfdWBoundWitness :: SmfdWBoundWitness (S⁰_ s) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (S⁰_ s))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (S⁰_ s)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (S⁰_ s))), Scalar (Needle (Boundary (S⁰_ s))) ~ Scalar (Needle (Interior (S⁰_ s)))) => r) -> r Source #
(Num' k, OpenManifold k) => SemimanifoldWithBoundary (ZeroDim k) Source #
Instance details Defined in Data.Manifold.WithBoundary.Class Associated Types type Interior (ZeroDim k) Source # type Boundary (ZeroDim k) Source # type HalfNeedle (ZeroDim k) Source # Methods (.+^\|) :: ZeroDim k -> Needle (Interior (ZeroDim k)) -> Either (Boundary (ZeroDim k), Scalar (Needle (Interior (ZeroDim k)))) (Interior (ZeroDim k)) Source # fromInterior :: Interior (ZeroDim k) -> ZeroDim k Source # fromBoundary :: Boundary (ZeroDim k) -> ZeroDim k Source # (\|+^) :: Boundary (ZeroDim k) -> HalfNeedle (ZeroDim k) -> ZeroDim k Source # separateInterior :: ZeroDim k -> Either (Boundary (ZeroDim k)) (Interior (ZeroDim k)) Source # toInterior :: ZeroDim k -> Maybe (Interior (ZeroDim k)) Source # extendToBoundary :: Interior (ZeroDim k) -> Needle (Interior (ZeroDim k)) -> Maybe (Boundary (ZeroDim k)) Source # smfdWBoundWitness :: SmfdWBoundWitness (ZeroDim k) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (ZeroDim k))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (ZeroDim k)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (ZeroDim k))), Scalar (Needle (Boundary (ZeroDim k))) ~ Scalar (Needle (Interior (ZeroDim k)))) => r) -> r Source #
(Num' n, OpenManifold n, LinearManifold (a n), Scalar (a n) ~ n, Needle (a n) ~ a n) => SemimanifoldWithBoundary (Point a n) Source #
Instance details Defined in Data.Manifold.WithBoundary Associated Types type Interior (Point a n) Source # type Boundary (Point a n) Source # type HalfNeedle (Point a n) Source # Methods (.+^\|) :: Point a n -> Needle (Interior (Point a n)) -> Either (Boundary (Point a n), Scalar (Needle (Interior (Point a n)))) (Interior (Point a n)) Source # fromInterior :: Interior (Point a n) -> Point a n Source # fromBoundary :: Boundary (Point a n) -> Point a n Source # (\|+^) :: Boundary (Point a n) -> HalfNeedle (Point a n) -> Point a n Source # separateInterior :: Point a n -> Either (Boundary (Point a n)) (Interior (Point a n)) Source # toInterior :: Point a n -> Maybe (Interior (Point a n)) Source # extendToBoundary :: Interior (Point a n) -> Needle (Interior (Point a n)) -> Maybe (Boundary (Point a n)) Source # smfdWBoundWitness :: SmfdWBoundWitness (Point a n) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (Point a n))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (Point a n)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (Point a n))), Scalar (Needle (Boundary (Point a n))) ~ Scalar (Needle (Interior (Point a n)))) => r) -> r Source #
(ProjectableBoundary a, ProjectableBoundary b, SameScalar LinearSpace '[Needle (Interior a), Needle (Interior b)], RealFrac'' (Scalar (Needle (Interior a))), ProjectableBoundary (Interior a), ProjectableBoundary (Interior b)) => SemimanifoldWithBoundary (a, b) Source #
Instance details Defined in Data.Manifold.WithBoundary Associated Types type Interior (a, b) Source # type Boundary (a, b) Source # type HalfNeedle (a, b) Source # Methods (.+^\|) :: (a, b) -> Needle (Interior (a, b)) -> Either (Boundary (a, b), Scalar (Needle (Interior (a, b)))) (Interior (a, b)) Source # fromInterior :: Interior (a, b) -> (a, b) Source # fromBoundary :: Boundary (a, b) -> (a, b) Source # (\|+^) :: Boundary (a, b) -> HalfNeedle (a, b) -> (a, b) Source # separateInterior :: (a, b) -> Either (Boundary (a, b)) (Interior (a, b)) Source # toInterior :: (a, b) -> Maybe (Interior (a, b)) Source # extendToBoundary :: Interior (a, b) -> Needle (Interior (a, b)) -> Maybe (Boundary (a, b)) Source # smfdWBoundWitness :: SmfdWBoundWitness (a, b) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (a, b))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (a, b)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (a, b))), Scalar (Needle (Boundary (a, b))) ~ Scalar (Needle (Interior (a, b)))) => r) -> r Source #
(LinearSpace v, LinearSpace w, s ~ Scalar v, s ~ Scalar w, Num' s, OpenManifold s) => SemimanifoldWithBoundary (LinearFunction s v w) Source #
Instance details Defined in Data.Manifold.WithBoundary Associated Types type Interior (LinearFunction s v w) Source # type Boundary (LinearFunction s v w) Source # type HalfNeedle (LinearFunction s v w) Source # Methods (.+^\|) :: LinearFunction s v w -> Needle (Interior (LinearFunction s v w)) -> Either (Boundary (LinearFunction s v w), Scalar (Needle (Interior (LinearFunction s v w)))) (Interior (LinearFunction s v w)) Source # fromInterior :: Interior (LinearFunction s v w) -> LinearFunction s v w Source # fromBoundary :: Boundary (LinearFunction s v w) -> LinearFunction s v w Source # (\|+^) :: Boundary (LinearFunction s v w) -> HalfNeedle (LinearFunction s v w) -> LinearFunction s v w Source # separateInterior :: LinearFunction s v w -> Either (Boundary (LinearFunction s v w)) (Interior (LinearFunction s v w)) Source # toInterior :: LinearFunction s v w -> Maybe (Interior (LinearFunction s v w)) Source # extendToBoundary :: Interior (LinearFunction s v w) -> Needle (Interior (LinearFunction s v w)) -> Maybe (Boundary (LinearFunction s v w)) Source # smfdWBoundWitness :: SmfdWBoundWitness (LinearFunction s v w) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (LinearFunction s v w))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (LinearFunction s v w)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (LinearFunction s v w))), Scalar (Needle (Boundary (LinearFunction s v w))) ~ Scalar (Needle (Interior (LinearFunction s v w)))) => r) -> r Source #
(LinearSpace v, LinearSpace w, s ~ Scalar v, s ~ Scalar w, Num' s, OpenManifold s) => SemimanifoldWithBoundary (LinearMap s v w) Source #
Instance details Defined in Data.Manifold.WithBoundary Associated Types type Interior (LinearMap s v w) Source # type Boundary (LinearMap s v w) Source # type HalfNeedle (LinearMap s v w) Source # Methods (.+^\|) :: LinearMap s v w -> Needle (Interior (LinearMap s v w)) -> Either (Boundary (LinearMap s v w), Scalar (Needle (Interior (LinearMap s v w)))) (Interior (LinearMap s v w)) Source # fromInterior :: Interior (LinearMap s v w) -> LinearMap s v w Source # fromBoundary :: Boundary (LinearMap s v w) -> LinearMap s v w Source # (\|+^) :: Boundary (LinearMap s v w) -> HalfNeedle (LinearMap s v w) -> LinearMap s v w Source # separateInterior :: LinearMap s v w -> Either (Boundary (LinearMap s v w)) (Interior (LinearMap s v w)) Source # toInterior :: LinearMap s v w -> Maybe (Interior (LinearMap s v w)) Source # extendToBoundary :: Interior (LinearMap s v w) -> Needle (Interior (LinearMap s v w)) -> Maybe (Boundary (LinearMap s v w)) Source # smfdWBoundWitness :: SmfdWBoundWitness (LinearMap s v w) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (LinearMap s v w))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (LinearMap s v w)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (LinearMap s v w))), Scalar (Needle (Boundary (LinearMap s v w))) ~ Scalar (Needle (Interior (LinearMap s v w)))) => r) -> r Source #
(LinearSpace v, LinearSpace w, s ~ Scalar v, s ~ Scalar w, Num' s, OpenManifold s) => SemimanifoldWithBoundary (Tensor s v w) Source #
Instance details Defined in Data.Manifold.WithBoundary Associated Types type Interior (Tensor s v w) Source # type Boundary (Tensor s v w) Source # type HalfNeedle (Tensor s v w) Source # Methods (.+^\|) :: Tensor s v w -> Needle (Interior (Tensor s v w)) -> Either (Boundary (Tensor s v w), Scalar (Needle (Interior (Tensor s v w)))) (Interior (Tensor s v w)) Source # fromInterior :: Interior (Tensor s v w) -> Tensor s v w Source # fromBoundary :: Boundary (Tensor s v w) -> Tensor s v w Source # (\|+^) :: Boundary (Tensor s v w) -> HalfNeedle (Tensor s v w) -> Tensor s v w Source # separateInterior :: Tensor s v w -> Either (Boundary (Tensor s v w)) (Interior (Tensor s v w)) Source # toInterior :: Tensor s v w -> Maybe (Interior (Tensor s v w)) Source # extendToBoundary :: Interior (Tensor s v w) -> Needle (Interior (Tensor s v w)) -> Maybe (Boundary (Tensor s v w)) Source # smfdWBoundWitness :: SmfdWBoundWitness (Tensor s v w) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (Tensor s v w))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (Tensor s v w)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (Tensor s v w))), Scalar (Needle (Boundary (Tensor s v w))) ~ Scalar (Needle (Interior (Tensor s v w)))) => r) -> r Source #

class (SemimanifoldWithBoundary m, PseudoAffine (Interior m), PseudoAffine (Boundary m)) => PseudoAffineWithBoundary m where Source #

Minimal complete definition

(.--!), (!-|)

Methods

(.--!) :: m -> m -> Needle (Interior m) Source #

Inverse of .+^|, provided the space is connected. For p :: Interior m, q :: m and v = fromInterior p.--!q,

  q .+^| v ≡ Right p

(up to floating-point). Similary, for b :: Boundary m and w = fromBoundary m.--!q,

  q .+^| w ≡ Left (b, 0)

(.-|) :: m -> Boundary m -> Maybe (HalfNeedle m) Source #

(!-|) :: m -> Boundary m -> HalfNeedle m Source #

(.--.) :: m -> m -> Maybe (Needle (Interior m)) Source #

Instances

Instances details

(Num' ℝ, Eq ℝ, OpenManifold ℝ, ProjectableBoundary ℝ) => PseudoAffineWithBoundary ℝ Source #
Instance details Defined in Data.Manifold.WithBoundary Methods (.--!) :: ℝ -> ℝ -> Needle (Interior ℝ) Source # (.-\|) :: ℝ -> Boundary ℝ -> Maybe (HalfNeedle ℝ) Source # (!-\|) :: ℝ -> Boundary ℝ -> HalfNeedle ℝ Source # (.--.) :: ℝ -> ℝ -> Maybe (Needle (Interior ℝ)) Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => PseudoAffineWithBoundary (V0 s) Source #
Instance details Defined in Data.Manifold.WithBoundary Methods (.--!) :: V0 s -> V0 s -> Needle (Interior (V0 s)) Source # (.-\|) :: V0 s -> Boundary (V0 s) -> Maybe (HalfNeedle (V0 s)) Source # (!-\|) :: V0 s -> Boundary (V0 s) -> HalfNeedle (V0 s) Source # (.--.) :: V0 s -> V0 s -> Maybe (Needle (Interior (V0 s))) Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => PseudoAffineWithBoundary (V1 s) Source #
Instance details Defined in Data.Manifold.WithBoundary Methods (.--!) :: V1 s -> V1 s -> Needle (Interior (V1 s)) Source # (.-\|) :: V1 s -> Boundary (V1 s) -> Maybe (HalfNeedle (V1 s)) Source # (!-\|) :: V1 s -> Boundary (V1 s) -> HalfNeedle (V1 s) Source # (.--.) :: V1 s -> V1 s -> Maybe (Needle (Interior (V1 s))) Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => PseudoAffineWithBoundary (V2 s) Source #
Instance details Defined in Data.Manifold.WithBoundary Methods (.--!) :: V2 s -> V2 s -> Needle (Interior (V2 s)) Source # (.-\|) :: V2 s -> Boundary (V2 s) -> Maybe (HalfNeedle (V2 s)) Source # (!-\|) :: V2 s -> Boundary (V2 s) -> HalfNeedle (V2 s) Source # (.--.) :: V2 s -> V2 s -> Maybe (Needle (Interior (V2 s))) Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => PseudoAffineWithBoundary (V3 s) Source #
Instance details Defined in Data.Manifold.WithBoundary Methods (.--!) :: V3 s -> V3 s -> Needle (Interior (V3 s)) Source # (.-\|) :: V3 s -> Boundary (V3 s) -> Maybe (HalfNeedle (V3 s)) Source # (!-\|) :: V3 s -> Boundary (V3 s) -> HalfNeedle (V3 s) Source # (.--.) :: V3 s -> V3 s -> Maybe (Needle (Interior (V3 s))) Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => PseudoAffineWithBoundary (V4 s) Source #
Instance details Defined in Data.Manifold.WithBoundary Methods (.--!) :: V4 s -> V4 s -> Needle (Interior (V4 s)) Source # (.-\|) :: V4 s -> Boundary (V4 s) -> Maybe (HalfNeedle (V4 s)) Source # (!-\|) :: V4 s -> Boundary (V4 s) -> HalfNeedle (V4 s) Source # (.--.) :: V4 s -> V4 s -> Maybe (Needle (Interior (V4 s))) Source #
(Semimanifold a, Semimanifold (VRep a), Needle a ~ GenericNeedle a, OpenManifold (Scalar (Needle (Rep a Void))), LinearSpace (Needle (Rep a Void)), Num' (Scalar (Needle (Rep a Void)))) => PseudoAffineWithBoundary (GenericNeedle a) Source #
Instance details Defined in Data.Manifold.WithBoundary Methods (.--!) :: GenericNeedle a -> GenericNeedle a -> Needle (Interior (GenericNeedle a)) Source # (.-\|) :: GenericNeedle a -> Boundary (GenericNeedle a) -> Maybe (HalfNeedle (GenericNeedle a)) Source # (!-\|) :: GenericNeedle a -> Boundary (GenericNeedle a) -> HalfNeedle (GenericNeedle a) Source # (.--.) :: GenericNeedle a -> GenericNeedle a -> Maybe (Needle (Interior (GenericNeedle a))) Source #
RealFloat'' s => PseudoAffineWithBoundary (S²_ s) Source #
Instance details Defined in Data.Manifold.WithBoundary Methods (.--!) :: S²_ s -> S²_ s -> Needle (Interior (S²_ s)) Source # (.-\|) :: S²_ s -> Boundary (S²_ s) -> Maybe (HalfNeedle (S²_ s)) Source # (!-\|) :: S²_ s -> Boundary (S²_ s) -> HalfNeedle (S²_ s) Source # (.--.) :: S²_ s -> S²_ s -> Maybe (Needle (Interior (S²_ s))) Source #
RealFloat'' s => PseudoAffineWithBoundary (S¹_ s) Source #
Instance details Defined in Data.Manifold.WithBoundary Methods (.--!) :: S¹_ s -> S¹_ s -> Needle (Interior (S¹_ s)) Source # (.-\|) :: S¹_ s -> Boundary (S¹_ s) -> Maybe (HalfNeedle (S¹_ s)) Source # (!-\|) :: S¹_ s -> Boundary (S¹_ s) -> HalfNeedle (S¹_ s) Source # (.--.) :: S¹_ s -> S¹_ s -> Maybe (Needle (Interior (S¹_ s))) Source #
(Num' k, OpenManifold k) => PseudoAffineWithBoundary (ZeroDim k) Source #
Instance details Defined in Data.Manifold.WithBoundary.Class Methods (.--!) :: ZeroDim k -> ZeroDim k -> Needle (Interior (ZeroDim k)) Source # (.-\|) :: ZeroDim k -> Boundary (ZeroDim k) -> Maybe (HalfNeedle (ZeroDim k)) Source # (!-\|) :: ZeroDim k -> Boundary (ZeroDim k) -> HalfNeedle (ZeroDim k) Source # (.--.) :: ZeroDim k -> ZeroDim k -> Maybe (Needle (Interior (ZeroDim k))) Source #
(Num' n, OpenManifold n, LinearManifold (a n), Scalar (a n) ~ n, Needle (a n) ~ a n) => PseudoAffineWithBoundary (Point a n) Source #
Instance details Defined in Data.Manifold.WithBoundary Methods (.--!) :: Point a n -> Point a n -> Needle (Interior (Point a n)) Source # (.-\|) :: Point a n -> Boundary (Point a n) -> Maybe (HalfNeedle (Point a n)) Source # (!-\|) :: Point a n -> Boundary (Point a n) -> HalfNeedle (Point a n) Source # (.--.) :: Point a n -> Point a n -> Maybe (Needle (Interior (Point a n))) Source #
(ProjectableBoundary a, ProjectableBoundary b, SameScalar LinearSpace '[Needle (Interior a), Needle (Interior b), Needle (Boundary a), Needle (Boundary b)], ProjectableBoundary (Interior a), ProjectableBoundary (Interior b), RealFrac'' (Scalar (Needle (Interior a)))) => PseudoAffineWithBoundary (a, b) Source #
Instance details Defined in Data.Manifold.WithBoundary Methods (.--!) :: (a, b) -> (a, b) -> Needle (Interior (a, b)) Source # (.-\|) :: (a, b) -> Boundary (a, b) -> Maybe (HalfNeedle (a, b)) Source # (!-\|) :: (a, b) -> Boundary (a, b) -> HalfNeedle (a, b) Source # (.--.) :: (a, b) -> (a, b) -> Maybe (Needle (Interior (a, b))) Source #
(LinearSpace v, LinearSpace w, s ~ Scalar v, s ~ Scalar w, Num' s, OpenManifold s) => PseudoAffineWithBoundary (LinearFunction s v w) Source #
Instance details Defined in Data.Manifold.WithBoundary Methods (.--!) :: LinearFunction s v w -> LinearFunction s v w -> Needle (Interior (LinearFunction s v w)) Source # (.-\|) :: LinearFunction s v w -> Boundary (LinearFunction s v w) -> Maybe (HalfNeedle (LinearFunction s v w)) Source # (!-\|) :: LinearFunction s v w -> Boundary (LinearFunction s v w) -> HalfNeedle (LinearFunction s v w) Source # (.--.) :: LinearFunction s v w -> LinearFunction s v w -> Maybe (Needle (Interior (LinearFunction s v w))) Source #
(LinearSpace v, LinearSpace w, s ~ Scalar v, s ~ Scalar w, Num' s, OpenManifold s) => PseudoAffineWithBoundary (LinearMap s v w) Source #
Instance details Defined in Data.Manifold.WithBoundary Methods (.--!) :: LinearMap s v w -> LinearMap s v w -> Needle (Interior (LinearMap s v w)) Source # (.-\|) :: LinearMap s v w -> Boundary (LinearMap s v w) -> Maybe (HalfNeedle (LinearMap s v w)) Source # (!-\|) :: LinearMap s v w -> Boundary (LinearMap s v w) -> HalfNeedle (LinearMap s v w) Source # (.--.) :: LinearMap s v w -> LinearMap s v w -> Maybe (Needle (Interior (LinearMap s v w))) Source #
(LinearSpace v, LinearSpace w, s ~ Scalar v, s ~ Scalar w, Num' s, OpenManifold s) => PseudoAffineWithBoundary (Tensor s v w) Source #
Instance details Defined in Data.Manifold.WithBoundary Methods (.--!) :: Tensor s v w -> Tensor s v w -> Needle (Interior (Tensor s v w)) Source # (.-\|) :: Tensor s v w -> Boundary (Tensor s v w) -> Maybe (HalfNeedle (Tensor s v w)) Source # (!-\|) :: Tensor s v w -> Boundary (Tensor s v w) -> HalfNeedle (Tensor s v w) Source # (.--.) :: Tensor s v w -> Tensor s v w -> Maybe (Needle (Interior (Tensor s v w))) Source #

class PseudoAffineWithBoundary m => ProjectableBoundary m where Source #

Minimal complete definition

projectToBoundary, marginFromBoundary

Methods

projectToBoundary Source #

Arguments

:: m	Point `p` to project
-> Boundary m	Intended “course region” representative `r` on boundary – we seek a point that is reachable from there.
-> Maybe (Needle (Boundary m), Scalar (Needle (Interior m)))	Needle `δr` connecting `r` to projection of the `p`, and a measure `d` of normal-distance such that `marginFromBoundary (r.+~^δr) d == p`.

marginFromBoundary :: Boundary m -> Scalar (Needle (Interior m)) -> m Source #

needleBoundaryIsTriviallyProjectible :: forall r. (ProjectableBoundary (Needle (Interior m)) => r) -> r Source #

default needleBoundaryIsTriviallyProjectible :: ProjectableBoundary (Needle (Interior m)) => (ProjectableBoundary (Needle (Interior m)) => r) -> r Source #

scalarBoundaryIsTriviallyProjectible :: forall r. (ProjectableBoundary (Scalar (Needle (Interior m))) => r) -> r Source #

default scalarBoundaryIsTriviallyProjectible :: ProjectableBoundary (Scalar (Needle (Interior m))) => (ProjectableBoundary (Scalar (Needle (Interior m))) => r) -> r Source #

Instances

Instances details

(Num' ℝ, Eq ℝ, OpenManifold ℝ, ProjectableBoundary ℝ) => ProjectableBoundary ℝ Source #
Instance details Defined in Data.Manifold.WithBoundary Methods projectToBoundary :: ℝ -> Boundary ℝ -> Maybe (Needle (Boundary ℝ), Scalar (Needle (Interior ℝ))) Source # marginFromBoundary :: Boundary ℝ -> Scalar (Needle (Interior ℝ)) -> ℝ Source # needleBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Needle (Interior ℝ)) => r) -> r Source # scalarBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Scalar (Needle (Interior ℝ))) => r) -> r Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => ProjectableBoundary (V0 s) Source #
Instance details Defined in Data.Manifold.WithBoundary Methods projectToBoundary :: V0 s -> Boundary (V0 s) -> Maybe (Needle (Boundary (V0 s)), Scalar (Needle (Interior (V0 s)))) Source # marginFromBoundary :: Boundary (V0 s) -> Scalar (Needle (Interior (V0 s))) -> V0 s Source # needleBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Needle (Interior (V0 s))) => r) -> r Source # scalarBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Scalar (Needle (Interior (V0 s)))) => r) -> r Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => ProjectableBoundary (V1 s) Source #
Instance details Defined in Data.Manifold.WithBoundary Methods projectToBoundary :: V1 s -> Boundary (V1 s) -> Maybe (Needle (Boundary (V1 s)), Scalar (Needle (Interior (V1 s)))) Source # marginFromBoundary :: Boundary (V1 s) -> Scalar (Needle (Interior (V1 s))) -> V1 s Source # needleBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Needle (Interior (V1 s))) => r) -> r Source # scalarBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Scalar (Needle (Interior (V1 s)))) => r) -> r Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => ProjectableBoundary (V2 s) Source #
Instance details Defined in Data.Manifold.WithBoundary Methods projectToBoundary :: V2 s -> Boundary (V2 s) -> Maybe (Needle (Boundary (V2 s)), Scalar (Needle (Interior (V2 s)))) Source # marginFromBoundary :: Boundary (V2 s) -> Scalar (Needle (Interior (V2 s))) -> V2 s Source # needleBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Needle (Interior (V2 s))) => r) -> r Source # scalarBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Scalar (Needle (Interior (V2 s)))) => r) -> r Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => ProjectableBoundary (V3 s) Source #
Instance details Defined in Data.Manifold.WithBoundary Methods projectToBoundary :: V3 s -> Boundary (V3 s) -> Maybe (Needle (Boundary (V3 s)), Scalar (Needle (Interior (V3 s)))) Source # marginFromBoundary :: Boundary (V3 s) -> Scalar (Needle (Interior (V3 s))) -> V3 s Source # needleBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Needle (Interior (V3 s))) => r) -> r Source # scalarBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Scalar (Needle (Interior (V3 s)))) => r) -> r Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => ProjectableBoundary (V4 s) Source #
Instance details Defined in Data.Manifold.WithBoundary Methods projectToBoundary :: V4 s -> Boundary (V4 s) -> Maybe (Needle (Boundary (V4 s)), Scalar (Needle (Interior (V4 s)))) Source # marginFromBoundary :: Boundary (V4 s) -> Scalar (Needle (Interior (V4 s))) -> V4 s Source # needleBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Needle (Interior (V4 s))) => r) -> r Source # scalarBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Scalar (Needle (Interior (V4 s)))) => r) -> r Source #
RealFloat'' s => ProjectableBoundary (S²_ s) Source #
Instance details Defined in Data.Manifold.WithBoundary Methods projectToBoundary :: S²_ s -> Boundary (S²_ s) -> Maybe (Needle (Boundary (S²_ s)), Scalar (Needle (Interior (S²_ s)))) Source # marginFromBoundary :: Boundary (S²_ s) -> Scalar (Needle (Interior (S²_ s))) -> S²_ s Source # needleBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Needle (Interior (S²_ s))) => r) -> r Source # scalarBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Scalar (Needle (Interior (S²_ s)))) => r) -> r Source #
RealFloat'' s => ProjectableBoundary (S¹_ s) Source #
Instance details Defined in Data.Manifold.WithBoundary Methods projectToBoundary :: S¹_ s -> Boundary (S¹_ s) -> Maybe (Needle (Boundary (S¹_ s)), Scalar (Needle (Interior (S¹_ s)))) Source # marginFromBoundary :: Boundary (S¹_ s) -> Scalar (Needle (Interior (S¹_ s))) -> S¹_ s Source # needleBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Needle (Interior (S¹_ s))) => r) -> r Source # scalarBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Scalar (Needle (Interior (S¹_ s)))) => r) -> r Source #
(Num' k, ProjectableBoundary k, OpenManifold k) => ProjectableBoundary (ZeroDim k) Source #
Instance details Defined in Data.Manifold.WithBoundary.Class Methods projectToBoundary :: ZeroDim k -> Boundary (ZeroDim k) -> Maybe (Needle (Boundary (ZeroDim k)), Scalar (Needle (Interior (ZeroDim k)))) Source # marginFromBoundary :: Boundary (ZeroDim k) -> Scalar (Needle (Interior (ZeroDim k))) -> ZeroDim k Source # needleBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Needle (Interior (ZeroDim k))) => r) -> r Source # scalarBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Scalar (Needle (Interior (ZeroDim k)))) => r) -> r Source #
(Num' n, OpenManifold n, LinearManifold (a n), ProjectableBoundary n, Scalar (a n) ~ n, Needle (a n) ~ a n) => ProjectableBoundary (Point a n) Source #
Instance details Defined in Data.Manifold.WithBoundary Methods projectToBoundary :: Point a n -> Boundary (Point a n) -> Maybe (Needle (Boundary (Point a n)), Scalar (Needle (Interior (Point a n)))) Source # marginFromBoundary :: Boundary (Point a n) -> Scalar (Needle (Interior (Point a n))) -> Point a n Source # needleBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Needle (Interior (Point a n))) => r) -> r Source # scalarBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Scalar (Needle (Interior (Point a n)))) => r) -> r Source #
(ProjectableBoundary a, ProjectableBoundary b, SameScalar LinearSpace '[Needle (Interior a), Needle (Interior b), Needle (Boundary a), Needle (Boundary b)], ProjectableBoundary (Interior a), ProjectableBoundary (Interior b), RealFrac'' (Scalar (Needle (Interior a)))) => ProjectableBoundary (a, b) Source #
Instance details Defined in Data.Manifold.WithBoundary Methods projectToBoundary :: (a, b) -> Boundary (a, b) -> Maybe (Needle (Boundary (a, b)), Scalar (Needle (Interior (a, b)))) Source # marginFromBoundary :: Boundary (a, b) -> Scalar (Needle (Interior (a, b))) -> (a, b) Source # needleBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Needle (Interior (a, b))) => r) -> r Source # scalarBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Scalar (Needle (Interior (a, b)))) => r) -> r Source #
(LinearSpace v, LinearSpace w, s ~ Scalar v, s ~ Scalar w, Num' s, OpenManifold s, ProjectableBoundary s) => ProjectableBoundary (LinearMap s v w) Source #
Instance details Defined in Data.Manifold.WithBoundary Methods projectToBoundary :: LinearMap s v w -> Boundary (LinearMap s v w) -> Maybe (Needle (Boundary (LinearMap s v w)), Scalar (Needle (Interior (LinearMap s v w)))) Source # marginFromBoundary :: Boundary (LinearMap s v w) -> Scalar (Needle (Interior (LinearMap s v w))) -> LinearMap s v w Source # needleBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Needle (Interior (LinearMap s v w))) => r) -> r Source # scalarBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Scalar (Needle (Interior (LinearMap s v w)))) => r) -> r Source #

data SmfdWBoundWitness m where Source #

Constructors

OpenManifoldWitness :: forall m. OpenManifold m => SmfdWBoundWitness m
SmfdWBoundWitness :: forall m. (OpenManifold (Interior m), OpenManifold (Boundary m), FullSubspace (HalfNeedle m) ~ Needle (Boundary m)) => SmfdWBoundWitness m

class AdditiveMonoid h where #

Minimal complete definition

Nothing

Methods

zeroHV :: h #

addHVs :: h -> h -> h #

Instances

Instances details

AdditiveMonoid Int16
Instance details Defined in Data.Monoid.Additive Methods zeroHV :: Int16 # addHVs :: Int16 -> Int16 -> Int16 #
AdditiveMonoid Int32
Instance details Defined in Data.Monoid.Additive Methods zeroHV :: Int32 # addHVs :: Int32 -> Int32 -> Int32 #
AdditiveMonoid Int64
Instance details Defined in Data.Monoid.Additive Methods zeroHV :: Int64 # addHVs :: Int64 -> Int64 -> Int64 #
AdditiveMonoid Int8
Instance details Defined in Data.Monoid.Additive Methods zeroHV :: Int8 # addHVs :: Int8 -> Int8 -> Int8 #
AdditiveMonoid Word16
Instance details Defined in Data.Monoid.Additive Methods zeroHV :: Word16 # addHVs :: Word16 -> Word16 -> Word16 #
AdditiveMonoid Word32
Instance details Defined in Data.Monoid.Additive Methods zeroHV :: Word32 # addHVs :: Word32 -> Word32 -> Word32 #
AdditiveMonoid Word64
Instance details Defined in Data.Monoid.Additive Methods zeroHV :: Word64 # addHVs :: Word64 -> Word64 -> Word64 #
AdditiveMonoid Word8
Instance details Defined in Data.Monoid.Additive Methods zeroHV :: Word8 # addHVs :: Word8 -> Word8 -> Word8 #
AdditiveMonoid Integer
Instance details Defined in Data.Monoid.Additive Methods zeroHV :: Integer # addHVs :: Integer -> Integer -> Integer #
AdditiveMonoid Double
Instance details Defined in Data.Monoid.Additive Methods zeroHV :: Double # addHVs :: Double -> Double -> Double #
AdditiveMonoid Float
Instance details Defined in Data.Monoid.Additive Methods zeroHV :: Float # addHVs :: Float -> Float -> Float #
AdditiveMonoid Int
Instance details Defined in Data.Monoid.Additive Methods zeroHV :: Int # addHVs :: Int -> Int -> Int #
AdditiveMonoid Word
Instance details Defined in Data.Monoid.Additive Methods zeroHV :: Word # addHVs :: Word -> Word -> Word #
Num k => AdditiveMonoid (Cℝay (ZeroDim k))
Instance details Defined in Data.Monoid.Additive Methods zeroHV :: Cℝay (ZeroDim k) # addHVs :: Cℝay (ZeroDim k) -> Cℝay (ZeroDim k) -> Cℝay (ZeroDim k) #
AdditiveGroup (Needle (Rep a Void)) => AdditiveMonoid (GenericNeedle a)
Instance details Defined in Data.Monoid.Additive Methods zeroHV :: GenericNeedle a # addHVs :: GenericNeedle a -> GenericNeedle a -> GenericNeedle a #
AdditiveMonoid (ZeroDim k)
Instance details Defined in Data.Monoid.Additive Methods zeroHV :: ZeroDim k # addHVs :: ZeroDim k -> ZeroDim k -> ZeroDim k #
(AdditiveMonoid h, AdditiveMonoid i) => AdditiveMonoid (h, i)
Instance details Defined in Data.Monoid.Additive Methods zeroHV :: (h, i) # addHVs :: (h, i) -> (h, i) -> (h, i) #
AdditiveMonoid h => AdditiveMonoid (Rec0 h s)
Instance details Defined in Data.Monoid.Additive Methods zeroHV :: Rec0 h s # addHVs :: Rec0 h s -> Rec0 h s -> Rec0 h s #
(AdditiveMonoid h, AdditiveMonoid i, AdditiveMonoid j) => AdditiveMonoid (h, i, j)
Instance details Defined in Data.Monoid.Additive Methods zeroHV :: (h, i, j) # addHVs :: (h, i, j) -> (h, i, j) -> (h, i, j) #
(AdditiveMonoid (f p), AdditiveMonoid (g p)) => AdditiveMonoid ((f :*: g) p)
Instance details Defined in Data.Monoid.Additive Methods zeroHV :: (f :: g) p # addHVs :: (f :: g) p -> (f :: g) p -> (f :: g) p #
AdditiveMonoid (f p) => AdditiveMonoid (M1 i c f p)
Instance details Defined in Data.Monoid.Additive Methods zeroHV :: M1 i c f p # addHVs :: M1 i c f p -> M1 i c f p -> M1 i c f p #

class AdditiveMonoid h => HalfSpace h where #

Minimal complete definition

Nothing

Associated Types

type FullSubspace h #

type FullSubspace h = GenericFullSubspace h

type Ray h #

type Ray h = Ray (AMRep h)

type MirrorJoin h #

type MirrorJoin h = GenericMirrorJoin h

Methods

scaleNonNeg :: Ray h -> h -> h #

fromFullSubspace :: FullSubspace h -> h #

projectToFullSubspace :: h -> FullSubspace h #

fullSubspaceIsVectorSpace :: ((VectorSpace (FullSubspace h), ScalarSpace (Scalar (FullSubspace h)), Scalar (FullSubspace h) ~ MirrorJoin (Ray h)) => r) -> r #

rayIsHalfSpace :: (HalfSpace (Ray h) => r) -> r #

mirrorJoinIsVectorSpace :: ((VectorSpace (MirrorJoin h), Scalar (MirrorJoin h) ~ MirrorJoin (Ray h)) => r) -> r #

fromPositiveHalf :: h -> MirrorJoin h #

fromNegativeHalf :: h -> MirrorJoin h #

Instances

Instances details

(Num k, VectorSpace k, Scalar k ~ k) => HalfSpace (Cℝay (ZeroDim k))
Instance details Defined in Data.Monoid.Additive Associated Types type FullSubspace (Cℝay (ZeroDim k)) # type Ray (Cℝay (ZeroDim k)) # type MirrorJoin (Cℝay (ZeroDim k)) # Methods scaleNonNeg :: Ray (Cℝay (ZeroDim k)) -> Cℝay (ZeroDim k) -> Cℝay (ZeroDim k) # fromFullSubspace :: FullSubspace (Cℝay (ZeroDim k)) -> Cℝay (ZeroDim k) # projectToFullSubspace :: Cℝay (ZeroDim k) -> FullSubspace (Cℝay (ZeroDim k)) # fullSubspaceIsVectorSpace :: ((VectorSpace (FullSubspace (Cℝay (ZeroDim k))), ScalarSpace (Scalar (FullSubspace (Cℝay (ZeroDim k)))), Scalar (FullSubspace (Cℝay (ZeroDim k))) ~ MirrorJoin (Ray (Cℝay (ZeroDim k)))) => r) -> r # rayIsHalfSpace :: (HalfSpace (Ray (Cℝay (ZeroDim k))) => r) -> r # mirrorJoinIsVectorSpace :: ((VectorSpace (MirrorJoin (Cℝay (ZeroDim k))), Scalar (MirrorJoin (Cℝay (ZeroDim k))) ~ MirrorJoin (Ray (Cℝay (ZeroDim k)))) => r) -> r # fromPositiveHalf :: Cℝay (ZeroDim k) -> MirrorJoin (Cℝay (ZeroDim k)) # fromNegativeHalf :: Cℝay (ZeroDim k) -> MirrorJoin (Cℝay (ZeroDim k)) #
ScalarSpace k => HalfSpace (ZeroDim k)
Instance details Defined in Data.Monoid.Additive Associated Types type FullSubspace (ZeroDim k) # type Ray (ZeroDim k) # type MirrorJoin (ZeroDim k) # Methods scaleNonNeg :: Ray (ZeroDim k) -> ZeroDim k -> ZeroDim k # fromFullSubspace :: FullSubspace (ZeroDim k) -> ZeroDim k # projectToFullSubspace :: ZeroDim k -> FullSubspace (ZeroDim k) # fullSubspaceIsVectorSpace :: ((VectorSpace (FullSubspace (ZeroDim k)), ScalarSpace (Scalar (FullSubspace (ZeroDim k))), Scalar (FullSubspace (ZeroDim k)) ~ MirrorJoin (Ray (ZeroDim k))) => r) -> r # rayIsHalfSpace :: (HalfSpace (Ray (ZeroDim k)) => r) -> r # mirrorJoinIsVectorSpace :: ((VectorSpace (MirrorJoin (ZeroDim k)), Scalar (MirrorJoin (ZeroDim k)) ~ MirrorJoin (Ray (ZeroDim k))) => r) -> r # fromPositiveHalf :: ZeroDim k -> MirrorJoin (ZeroDim k) # fromNegativeHalf :: ZeroDim k -> MirrorJoin (ZeroDim k) #
(HalfSpace x, VectorSpace y, AdditiveMonoid y, Ray x ~ Cℝay (ZeroDim (Scalar y))) => HalfSpace (x, y)
Instance details Defined in Data.Monoid.Additive Associated Types type FullSubspace (x, y) # type Ray (x, y) # type MirrorJoin (x, y) # Methods scaleNonNeg :: Ray (x, y) -> (x, y) -> (x, y) # fromFullSubspace :: FullSubspace (x, y) -> (x, y) # projectToFullSubspace :: (x, y) -> FullSubspace (x, y) # fullSubspaceIsVectorSpace :: ((VectorSpace (FullSubspace (x, y)), ScalarSpace (Scalar (FullSubspace (x, y))), Scalar (FullSubspace (x, y)) ~ MirrorJoin (Ray (x, y))) => r) -> r # rayIsHalfSpace :: (HalfSpace (Ray (x, y)) => r) -> r # mirrorJoinIsVectorSpace :: ((VectorSpace (MirrorJoin (x, y)), Scalar (MirrorJoin (x, y)) ~ MirrorJoin (Ray (x, y))) => r) -> r # fromPositiveHalf :: (x, y) -> MirrorJoin (x, y) # fromNegativeHalf :: (x, y) -> MirrorJoin (x, y) #
HalfSpace h => HalfSpace (Rec0 h s)
Instance details Defined in Data.Monoid.Additive Associated Types type FullSubspace (Rec0 h s) # type Ray (Rec0 h s) # type MirrorJoin (Rec0 h s) # Methods scaleNonNeg :: Ray (Rec0 h s) -> Rec0 h s -> Rec0 h s # fromFullSubspace :: FullSubspace (Rec0 h s) -> Rec0 h s # projectToFullSubspace :: Rec0 h s -> FullSubspace (Rec0 h s) # fullSubspaceIsVectorSpace :: ((VectorSpace (FullSubspace (Rec0 h s)), ScalarSpace (Scalar (FullSubspace (Rec0 h s))), Scalar (FullSubspace (Rec0 h s)) ~ MirrorJoin (Ray (Rec0 h s))) => r) -> r # rayIsHalfSpace :: (HalfSpace (Ray (Rec0 h s)) => r) -> r # mirrorJoinIsVectorSpace :: ((VectorSpace (MirrorJoin (Rec0 h s)), Scalar (MirrorJoin (Rec0 h s)) ~ MirrorJoin (Ray (Rec0 h s))) => r) -> r # fromPositiveHalf :: Rec0 h s -> MirrorJoin (Rec0 h s) # fromNegativeHalf :: Rec0 h s -> MirrorJoin (Rec0 h s) #
(HalfSpace (f p), VectorSpace (g p), AdditiveMonoid (g p), Ray (f p) ~ Cℝay (ZeroDim (Scalar (g p)))) => HalfSpace ((f :*: g) p)
Instance details Defined in Data.Monoid.Additive Associated Types type FullSubspace ((f :: g) p) # type Ray ((f :: g) p) # type MirrorJoin ((f :: g) p) # Methods scaleNonNeg :: Ray ((f :: g) p) -> (f :: g) p -> (f :: g) p # fromFullSubspace :: FullSubspace ((f :: g) p) -> (f :: g) p # projectToFullSubspace :: (f :: g) p -> FullSubspace ((f :: g) p) # fullSubspaceIsVectorSpace :: ((VectorSpace (FullSubspace ((f :: g) p)), ScalarSpace (Scalar (FullSubspace ((f :: g) p))), Scalar (FullSubspace ((f :: g) p)) ~ MirrorJoin (Ray ((f :: g) p))) => r) -> r # rayIsHalfSpace :: (HalfSpace (Ray ((f :: g) p)) => r) -> r # mirrorJoinIsVectorSpace :: ((VectorSpace (MirrorJoin ((f :: g) p)), Scalar (MirrorJoin ((f :: g) p)) ~ MirrorJoin (Ray ((f :: g) p))) => r) -> r # fromPositiveHalf :: (f :: g) p -> MirrorJoin ((f :: g) p) # fromNegativeHalf :: (f :: g) p -> MirrorJoin ((f :: g) p) #
HalfSpace (f p) => HalfSpace (M1 i c f p)
Instance details Defined in Data.Monoid.Additive Associated Types type FullSubspace (M1 i c f p) # type Ray (M1 i c f p) # type MirrorJoin (M1 i c f p) # Methods scaleNonNeg :: Ray (M1 i c f p) -> M1 i c f p -> M1 i c f p # fromFullSubspace :: FullSubspace (M1 i c f p) -> M1 i c f p # projectToFullSubspace :: M1 i c f p -> FullSubspace (M1 i c f p) # fullSubspaceIsVectorSpace :: ((VectorSpace (FullSubspace (M1 i c f p)), ScalarSpace (Scalar (FullSubspace (M1 i c f p))), Scalar (FullSubspace (M1 i c f p)) ~ MirrorJoin (Ray (M1 i c f p))) => r) -> r # rayIsHalfSpace :: (HalfSpace (Ray (M1 i c f p)) => r) -> r # mirrorJoinIsVectorSpace :: ((VectorSpace (MirrorJoin (M1 i c f p)), Scalar (MirrorJoin (M1 i c f p)) ~ MirrorJoin (Ray (M1 i c f p))) => r) -> r # fromPositiveHalf :: M1 i c f p -> MirrorJoin (M1 i c f p) # fromNegativeHalf :: M1 i c f p -> MirrorJoin (M1 i c f p) #

Orphan instances

(Num' ℝ, Eq ℝ, OpenManifold ℝ, ProjectableBoundary ℝ) => ProjectableBoundary ℝ Source #
Instance details Methods projectToBoundary :: ℝ -> Boundary ℝ -> Maybe (Needle (Boundary ℝ), Scalar (Needle (Interior ℝ))) Source # marginFromBoundary :: Boundary ℝ -> Scalar (Needle (Interior ℝ)) -> ℝ Source # needleBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Needle (Interior ℝ)) => r) -> r Source # scalarBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Scalar (Needle (Interior ℝ))) => r) -> r Source #
(Num' ℝ, Eq ℝ, OpenManifold ℝ, ProjectableBoundary ℝ) => PseudoAffineWithBoundary ℝ Source #
Instance details Methods (.--!) :: ℝ -> ℝ -> Needle (Interior ℝ) Source # (.-\|) :: ℝ -> Boundary ℝ -> Maybe (HalfNeedle ℝ) Source # (!-\|) :: ℝ -> Boundary ℝ -> HalfNeedle ℝ Source # (.--.) :: ℝ -> ℝ -> Maybe (Needle (Interior ℝ)) Source #
(Num' ℝ, Eq ℝ, OpenManifold ℝ, ProjectableBoundary ℝ) => SemimanifoldWithBoundary ℝ Source #
Instance details Associated Types type Interior ℝ Source # type Boundary ℝ Source # type HalfNeedle ℝ Source # Methods (.+^\|) :: ℝ -> Needle (Interior ℝ) -> Either (Boundary ℝ, Scalar (Needle (Interior ℝ))) (Interior ℝ) Source # fromInterior :: Interior ℝ -> ℝ Source # fromBoundary :: Boundary ℝ -> ℝ Source # (\|+^) :: Boundary ℝ -> HalfNeedle ℝ -> ℝ Source # separateInterior :: ℝ -> Either (Boundary ℝ) (Interior ℝ) Source # toInterior :: ℝ -> Maybe (Interior ℝ) Source # extendToBoundary :: Interior ℝ -> Needle (Interior ℝ) -> Maybe (Boundary ℝ) Source # smfdWBoundWitness :: SmfdWBoundWitness ℝ Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior ℝ)) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior ℝ))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary ℝ)), Scalar (Needle (Boundary ℝ)) ~ Scalar (Needle (Interior ℝ))) => r) -> r Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => ProjectableBoundary (V0 s) Source #
Instance details Methods projectToBoundary :: V0 s -> Boundary (V0 s) -> Maybe (Needle (Boundary (V0 s)), Scalar (Needle (Interior (V0 s)))) Source # marginFromBoundary :: Boundary (V0 s) -> Scalar (Needle (Interior (V0 s))) -> V0 s Source # needleBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Needle (Interior (V0 s))) => r) -> r Source # scalarBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Scalar (Needle (Interior (V0 s)))) => r) -> r Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => ProjectableBoundary (V1 s) Source #
Instance details Methods projectToBoundary :: V1 s -> Boundary (V1 s) -> Maybe (Needle (Boundary (V1 s)), Scalar (Needle (Interior (V1 s)))) Source # marginFromBoundary :: Boundary (V1 s) -> Scalar (Needle (Interior (V1 s))) -> V1 s Source # needleBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Needle (Interior (V1 s))) => r) -> r Source # scalarBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Scalar (Needle (Interior (V1 s)))) => r) -> r Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => ProjectableBoundary (V2 s) Source #
Instance details Methods projectToBoundary :: V2 s -> Boundary (V2 s) -> Maybe (Needle (Boundary (V2 s)), Scalar (Needle (Interior (V2 s)))) Source # marginFromBoundary :: Boundary (V2 s) -> Scalar (Needle (Interior (V2 s))) -> V2 s Source # needleBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Needle (Interior (V2 s))) => r) -> r Source # scalarBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Scalar (Needle (Interior (V2 s)))) => r) -> r Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => ProjectableBoundary (V3 s) Source #
Instance details Methods projectToBoundary :: V3 s -> Boundary (V3 s) -> Maybe (Needle (Boundary (V3 s)), Scalar (Needle (Interior (V3 s)))) Source # marginFromBoundary :: Boundary (V3 s) -> Scalar (Needle (Interior (V3 s))) -> V3 s Source # needleBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Needle (Interior (V3 s))) => r) -> r Source # scalarBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Scalar (Needle (Interior (V3 s)))) => r) -> r Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => ProjectableBoundary (V4 s) Source #
Instance details Methods projectToBoundary :: V4 s -> Boundary (V4 s) -> Maybe (Needle (Boundary (V4 s)), Scalar (Needle (Interior (V4 s)))) Source # marginFromBoundary :: Boundary (V4 s) -> Scalar (Needle (Interior (V4 s))) -> V4 s Source # needleBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Needle (Interior (V4 s))) => r) -> r Source # scalarBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Scalar (Needle (Interior (V4 s)))) => r) -> r Source #
RealFloat'' s => ProjectableBoundary (S²_ s) Source #
Instance details Methods projectToBoundary :: S²_ s -> Boundary (S²_ s) -> Maybe (Needle (Boundary (S²_ s)), Scalar (Needle (Interior (S²_ s)))) Source # marginFromBoundary :: Boundary (S²_ s) -> Scalar (Needle (Interior (S²_ s))) -> S²_ s Source # needleBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Needle (Interior (S²_ s))) => r) -> r Source # scalarBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Scalar (Needle (Interior (S²_ s)))) => r) -> r Source #
RealFloat'' s => ProjectableBoundary (S¹_ s) Source #
Instance details Methods projectToBoundary :: S¹_ s -> Boundary (S¹_ s) -> Maybe (Needle (Boundary (S¹_ s)), Scalar (Needle (Interior (S¹_ s)))) Source # marginFromBoundary :: Boundary (S¹_ s) -> Scalar (Needle (Interior (S¹_ s))) -> S¹_ s Source # needleBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Needle (Interior (S¹_ s))) => r) -> r Source # scalarBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Scalar (Needle (Interior (S¹_ s)))) => r) -> r Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => PseudoAffineWithBoundary (V0 s) Source #
Instance details Methods (.--!) :: V0 s -> V0 s -> Needle (Interior (V0 s)) Source # (.-\|) :: V0 s -> Boundary (V0 s) -> Maybe (HalfNeedle (V0 s)) Source # (!-\|) :: V0 s -> Boundary (V0 s) -> HalfNeedle (V0 s) Source # (.--.) :: V0 s -> V0 s -> Maybe (Needle (Interior (V0 s))) Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => PseudoAffineWithBoundary (V1 s) Source #
Instance details Methods (.--!) :: V1 s -> V1 s -> Needle (Interior (V1 s)) Source # (.-\|) :: V1 s -> Boundary (V1 s) -> Maybe (HalfNeedle (V1 s)) Source # (!-\|) :: V1 s -> Boundary (V1 s) -> HalfNeedle (V1 s) Source # (.--.) :: V1 s -> V1 s -> Maybe (Needle (Interior (V1 s))) Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => PseudoAffineWithBoundary (V2 s) Source #
Instance details Methods (.--!) :: V2 s -> V2 s -> Needle (Interior (V2 s)) Source # (.-\|) :: V2 s -> Boundary (V2 s) -> Maybe (HalfNeedle (V2 s)) Source # (!-\|) :: V2 s -> Boundary (V2 s) -> HalfNeedle (V2 s) Source # (.--.) :: V2 s -> V2 s -> Maybe (Needle (Interior (V2 s))) Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => PseudoAffineWithBoundary (V3 s) Source #
Instance details Methods (.--!) :: V3 s -> V3 s -> Needle (Interior (V3 s)) Source # (.-\|) :: V3 s -> Boundary (V3 s) -> Maybe (HalfNeedle (V3 s)) Source # (!-\|) :: V3 s -> Boundary (V3 s) -> HalfNeedle (V3 s) Source # (.--.) :: V3 s -> V3 s -> Maybe (Needle (Interior (V3 s))) Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => PseudoAffineWithBoundary (V4 s) Source #
Instance details Methods (.--!) :: V4 s -> V4 s -> Needle (Interior (V4 s)) Source # (.-\|) :: V4 s -> Boundary (V4 s) -> Maybe (HalfNeedle (V4 s)) Source # (!-\|) :: V4 s -> Boundary (V4 s) -> HalfNeedle (V4 s) Source # (.--.) :: V4 s -> V4 s -> Maybe (Needle (Interior (V4 s))) Source #
(Semimanifold a, Semimanifold (VRep a), Needle a ~ GenericNeedle a, OpenManifold (Scalar (Needle (Rep a Void))), LinearSpace (Needle (Rep a Void)), Num' (Scalar (Needle (Rep a Void)))) => PseudoAffineWithBoundary (GenericNeedle a) Source #
Instance details Methods (.--!) :: GenericNeedle a -> GenericNeedle a -> Needle (Interior (GenericNeedle a)) Source # (.-\|) :: GenericNeedle a -> Boundary (GenericNeedle a) -> Maybe (HalfNeedle (GenericNeedle a)) Source # (!-\|) :: GenericNeedle a -> Boundary (GenericNeedle a) -> HalfNeedle (GenericNeedle a) Source # (.--.) :: GenericNeedle a -> GenericNeedle a -> Maybe (Needle (Interior (GenericNeedle a))) Source #
RealFloat'' s => PseudoAffineWithBoundary (S²_ s) Source #
Instance details Methods (.--!) :: S²_ s -> S²_ s -> Needle (Interior (S²_ s)) Source # (.-\|) :: S²_ s -> Boundary (S²_ s) -> Maybe (HalfNeedle (S²_ s)) Source # (!-\|) :: S²_ s -> Boundary (S²_ s) -> HalfNeedle (S²_ s) Source # (.--.) :: S²_ s -> S²_ s -> Maybe (Needle (Interior (S²_ s))) Source #
RealFloat'' s => PseudoAffineWithBoundary (S¹_ s) Source #
Instance details Methods (.--!) :: S¹_ s -> S¹_ s -> Needle (Interior (S¹_ s)) Source # (.-\|) :: S¹_ s -> Boundary (S¹_ s) -> Maybe (HalfNeedle (S¹_ s)) Source # (!-\|) :: S¹_ s -> Boundary (S¹_ s) -> HalfNeedle (S¹_ s) Source # (.--.) :: S¹_ s -> S¹_ s -> Maybe (Needle (Interior (S¹_ s))) Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => SemimanifoldWithBoundary (V0 s) Source #
Instance details Associated Types type Interior (V0 s) Source # type Boundary (V0 s) Source # type HalfNeedle (V0 s) Source # Methods (.+^\|) :: V0 s -> Needle (Interior (V0 s)) -> Either (Boundary (V0 s), Scalar (Needle (Interior (V0 s)))) (Interior (V0 s)) Source # fromInterior :: Interior (V0 s) -> V0 s Source # fromBoundary :: Boundary (V0 s) -> V0 s Source # (\|+^) :: Boundary (V0 s) -> HalfNeedle (V0 s) -> V0 s Source # separateInterior :: V0 s -> Either (Boundary (V0 s)) (Interior (V0 s)) Source # toInterior :: V0 s -> Maybe (Interior (V0 s)) Source # extendToBoundary :: Interior (V0 s) -> Needle (Interior (V0 s)) -> Maybe (Boundary (V0 s)) Source # smfdWBoundWitness :: SmfdWBoundWitness (V0 s) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (V0 s))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (V0 s)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (V0 s))), Scalar (Needle (Boundary (V0 s))) ~ Scalar (Needle (Interior (V0 s)))) => r) -> r Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => SemimanifoldWithBoundary (V1 s) Source #
Instance details Associated Types type Interior (V1 s) Source # type Boundary (V1 s) Source # type HalfNeedle (V1 s) Source # Methods (.+^\|) :: V1 s -> Needle (Interior (V1 s)) -> Either (Boundary (V1 s), Scalar (Needle (Interior (V1 s)))) (Interior (V1 s)) Source # fromInterior :: Interior (V1 s) -> V1 s Source # fromBoundary :: Boundary (V1 s) -> V1 s Source # (\|+^) :: Boundary (V1 s) -> HalfNeedle (V1 s) -> V1 s Source # separateInterior :: V1 s -> Either (Boundary (V1 s)) (Interior (V1 s)) Source # toInterior :: V1 s -> Maybe (Interior (V1 s)) Source # extendToBoundary :: Interior (V1 s) -> Needle (Interior (V1 s)) -> Maybe (Boundary (V1 s)) Source # smfdWBoundWitness :: SmfdWBoundWitness (V1 s) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (V1 s))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (V1 s)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (V1 s))), Scalar (Needle (Boundary (V1 s))) ~ Scalar (Needle (Interior (V1 s)))) => r) -> r Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => SemimanifoldWithBoundary (V2 s) Source #
Instance details Associated Types type Interior (V2 s) Source # type Boundary (V2 s) Source # type HalfNeedle (V2 s) Source # Methods (.+^\|) :: V2 s -> Needle (Interior (V2 s)) -> Either (Boundary (V2 s), Scalar (Needle (Interior (V2 s)))) (Interior (V2 s)) Source # fromInterior :: Interior (V2 s) -> V2 s Source # fromBoundary :: Boundary (V2 s) -> V2 s Source # (\|+^) :: Boundary (V2 s) -> HalfNeedle (V2 s) -> V2 s Source # separateInterior :: V2 s -> Either (Boundary (V2 s)) (Interior (V2 s)) Source # toInterior :: V2 s -> Maybe (Interior (V2 s)) Source # extendToBoundary :: Interior (V2 s) -> Needle (Interior (V2 s)) -> Maybe (Boundary (V2 s)) Source # smfdWBoundWitness :: SmfdWBoundWitness (V2 s) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (V2 s))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (V2 s)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (V2 s))), Scalar (Needle (Boundary (V2 s))) ~ Scalar (Needle (Interior (V2 s)))) => r) -> r Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => SemimanifoldWithBoundary (V3 s) Source #
Instance details Associated Types type Interior (V3 s) Source # type Boundary (V3 s) Source # type HalfNeedle (V3 s) Source # Methods (.+^\|) :: V3 s -> Needle (Interior (V3 s)) -> Either (Boundary (V3 s), Scalar (Needle (Interior (V3 s)))) (Interior (V3 s)) Source # fromInterior :: Interior (V3 s) -> V3 s Source # fromBoundary :: Boundary (V3 s) -> V3 s Source # (\|+^) :: Boundary (V3 s) -> HalfNeedle (V3 s) -> V3 s Source # separateInterior :: V3 s -> Either (Boundary (V3 s)) (Interior (V3 s)) Source # toInterior :: V3 s -> Maybe (Interior (V3 s)) Source # extendToBoundary :: Interior (V3 s) -> Needle (Interior (V3 s)) -> Maybe (Boundary (V3 s)) Source # smfdWBoundWitness :: SmfdWBoundWitness (V3 s) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (V3 s))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (V3 s)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (V3 s))), Scalar (Needle (Boundary (V3 s))) ~ Scalar (Needle (Interior (V3 s)))) => r) -> r Source #
(Num' s, Eq s, OpenManifold s, ProjectableBoundary s) => SemimanifoldWithBoundary (V4 s) Source #
Instance details Associated Types type Interior (V4 s) Source # type Boundary (V4 s) Source # type HalfNeedle (V4 s) Source # Methods (.+^\|) :: V4 s -> Needle (Interior (V4 s)) -> Either (Boundary (V4 s), Scalar (Needle (Interior (V4 s)))) (Interior (V4 s)) Source # fromInterior :: Interior (V4 s) -> V4 s Source # fromBoundary :: Boundary (V4 s) -> V4 s Source # (\|+^) :: Boundary (V4 s) -> HalfNeedle (V4 s) -> V4 s Source # separateInterior :: V4 s -> Either (Boundary (V4 s)) (Interior (V4 s)) Source # toInterior :: V4 s -> Maybe (Interior (V4 s)) Source # extendToBoundary :: Interior (V4 s) -> Needle (Interior (V4 s)) -> Maybe (Boundary (V4 s)) Source # smfdWBoundWitness :: SmfdWBoundWitness (V4 s) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (V4 s))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (V4 s)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (V4 s))), Scalar (Needle (Boundary (V4 s))) ~ Scalar (Needle (Interior (V4 s)))) => r) -> r Source #
(Semimanifold a, Semimanifold (VRep a), Needle a ~ GenericNeedle a, OpenManifold (Scalar (Needle (Rep a Void))), LinearSpace (Needle (Rep a Void)), Num' (Scalar (Needle (Rep a Void)))) => SemimanifoldWithBoundary (GenericNeedle a) Source #
Instance details Associated Types type Interior (GenericNeedle a) Source # type Boundary (GenericNeedle a) Source # type HalfNeedle (GenericNeedle a) Source # Methods (.+^\|) :: GenericNeedle a -> Needle (Interior (GenericNeedle a)) -> Either (Boundary (GenericNeedle a), Scalar (Needle (Interior (GenericNeedle a)))) (Interior (GenericNeedle a)) Source # fromInterior :: Interior (GenericNeedle a) -> GenericNeedle a Source # fromBoundary :: Boundary (GenericNeedle a) -> GenericNeedle a Source # (\|+^) :: Boundary (GenericNeedle a) -> HalfNeedle (GenericNeedle a) -> GenericNeedle a Source # separateInterior :: GenericNeedle a -> Either (Boundary (GenericNeedle a)) (Interior (GenericNeedle a)) Source # toInterior :: GenericNeedle a -> Maybe (Interior (GenericNeedle a)) Source # extendToBoundary :: Interior (GenericNeedle a) -> Needle (Interior (GenericNeedle a)) -> Maybe (Boundary (GenericNeedle a)) Source # smfdWBoundWitness :: SmfdWBoundWitness (GenericNeedle a) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (GenericNeedle a))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (GenericNeedle a)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (GenericNeedle a))), Scalar (Needle (Boundary (GenericNeedle a))) ~ Scalar (Needle (Interior (GenericNeedle a)))) => r) -> r Source #
RealFloat'' s => SemimanifoldWithBoundary (D¹_ s) Source #
Instance details Associated Types type Interior (D¹_ s) Source # type Boundary (D¹_ s) Source # type HalfNeedle (D¹_ s) Source # Methods (.+^\|) :: D¹_ s -> Needle (Interior (D¹_ s)) -> Either (Boundary (D¹_ s), Scalar (Needle (Interior (D¹_ s)))) (Interior (D¹_ s)) Source # fromInterior :: Interior (D¹_ s) -> D¹_ s Source # fromBoundary :: Boundary (D¹_ s) -> D¹_ s Source # (\|+^) :: Boundary (D¹_ s) -> HalfNeedle (D¹_ s) -> D¹_ s Source # separateInterior :: D¹_ s -> Either (Boundary (D¹_ s)) (Interior (D¹_ s)) Source # toInterior :: D¹_ s -> Maybe (Interior (D¹_ s)) Source # extendToBoundary :: Interior (D¹_ s) -> Needle (Interior (D¹_ s)) -> Maybe (Boundary (D¹_ s)) Source # smfdWBoundWitness :: SmfdWBoundWitness (D¹_ s) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (D¹_ s))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (D¹_ s)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (D¹_ s))), Scalar (Needle (Boundary (D¹_ s))) ~ Scalar (Needle (Interior (D¹_ s)))) => r) -> r Source #
RealFloat'' s => SemimanifoldWithBoundary (S²_ s) Source #
Instance details Associated Types type Interior (S²_ s) Source # type Boundary (S²_ s) Source # type HalfNeedle (S²_ s) Source # Methods (.+^\|) :: S²_ s -> Needle (Interior (S²_ s)) -> Either (Boundary (S²_ s), Scalar (Needle (Interior (S²_ s)))) (Interior (S²_ s)) Source # fromInterior :: Interior (S²_ s) -> S²_ s Source # fromBoundary :: Boundary (S²_ s) -> S²_ s Source # (\|+^) :: Boundary (S²_ s) -> HalfNeedle (S²_ s) -> S²_ s Source # separateInterior :: S²_ s -> Either (Boundary (S²_ s)) (Interior (S²_ s)) Source # toInterior :: S²_ s -> Maybe (Interior (S²_ s)) Source # extendToBoundary :: Interior (S²_ s) -> Needle (Interior (S²_ s)) -> Maybe (Boundary (S²_ s)) Source # smfdWBoundWitness :: SmfdWBoundWitness (S²_ s) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (S²_ s))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (S²_ s)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (S²_ s))), Scalar (Needle (Boundary (S²_ s))) ~ Scalar (Needle (Interior (S²_ s)))) => r) -> r Source #
RealFloat'' s => SemimanifoldWithBoundary (S¹_ s) Source #
Instance details Associated Types type Interior (S¹_ s) Source # type Boundary (S¹_ s) Source # type HalfNeedle (S¹_ s) Source # Methods (.+^\|) :: S¹_ s -> Needle (Interior (S¹_ s)) -> Either (Boundary (S¹_ s), Scalar (Needle (Interior (S¹_ s)))) (Interior (S¹_ s)) Source # fromInterior :: Interior (S¹_ s) -> S¹_ s Source # fromBoundary :: Boundary (S¹_ s) -> S¹_ s Source # (\|+^) :: Boundary (S¹_ s) -> HalfNeedle (S¹_ s) -> S¹_ s Source # separateInterior :: S¹_ s -> Either (Boundary (S¹_ s)) (Interior (S¹_ s)) Source # toInterior :: S¹_ s -> Maybe (Interior (S¹_ s)) Source # extendToBoundary :: Interior (S¹_ s) -> Needle (Interior (S¹_ s)) -> Maybe (Boundary (S¹_ s)) Source # smfdWBoundWitness :: SmfdWBoundWitness (S¹_ s) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (S¹_ s))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (S¹_ s)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (S¹_ s))), Scalar (Needle (Boundary (S¹_ s))) ~ Scalar (Needle (Interior (S¹_ s)))) => r) -> r Source #
RealFloat'' s => SemimanifoldWithBoundary (S⁰_ s) Source #
Instance details Associated Types type Interior (S⁰_ s) Source # type Boundary (S⁰_ s) Source # type HalfNeedle (S⁰_ s) Source # Methods (.+^\|) :: S⁰_ s -> Needle (Interior (S⁰_ s)) -> Either (Boundary (S⁰_ s), Scalar (Needle (Interior (S⁰_ s)))) (Interior (S⁰_ s)) Source # fromInterior :: Interior (S⁰_ s) -> S⁰_ s Source # fromBoundary :: Boundary (S⁰_ s) -> S⁰_ s Source # (\|+^) :: Boundary (S⁰_ s) -> HalfNeedle (S⁰_ s) -> S⁰_ s Source # separateInterior :: S⁰_ s -> Either (Boundary (S⁰_ s)) (Interior (S⁰_ s)) Source # toInterior :: S⁰_ s -> Maybe (Interior (S⁰_ s)) Source # extendToBoundary :: Interior (S⁰_ s) -> Needle (Interior (S⁰_ s)) -> Maybe (Boundary (S⁰_ s)) Source # smfdWBoundWitness :: SmfdWBoundWitness (S⁰_ s) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (S⁰_ s))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (S⁰_ s)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (S⁰_ s))), Scalar (Needle (Boundary (S⁰_ s))) ~ Scalar (Needle (Interior (S⁰_ s)))) => r) -> r Source #
(Num' n, OpenManifold n, LinearManifold (a n), ProjectableBoundary n, Scalar (a n) ~ n, Needle (a n) ~ a n) => ProjectableBoundary (Point a n) Source #
Instance details Methods projectToBoundary :: Point a n -> Boundary (Point a n) -> Maybe (Needle (Boundary (Point a n)), Scalar (Needle (Interior (Point a n)))) Source # marginFromBoundary :: Boundary (Point a n) -> Scalar (Needle (Interior (Point a n))) -> Point a n Source # needleBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Needle (Interior (Point a n))) => r) -> r Source # scalarBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Scalar (Needle (Interior (Point a n)))) => r) -> r Source #
(ProjectableBoundary a, ProjectableBoundary b, SameScalar LinearSpace '[Needle (Interior a), Needle (Interior b), Needle (Boundary a), Needle (Boundary b)], ProjectableBoundary (Interior a), ProjectableBoundary (Interior b), RealFrac'' (Scalar (Needle (Interior a)))) => ProjectableBoundary (a, b) Source #
Instance details Methods projectToBoundary :: (a, b) -> Boundary (a, b) -> Maybe (Needle (Boundary (a, b)), Scalar (Needle (Interior (a, b)))) Source # marginFromBoundary :: Boundary (a, b) -> Scalar (Needle (Interior (a, b))) -> (a, b) Source # needleBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Needle (Interior (a, b))) => r) -> r Source # scalarBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Scalar (Needle (Interior (a, b)))) => r) -> r Source #
(Num' n, OpenManifold n, LinearManifold (a n), Scalar (a n) ~ n, Needle (a n) ~ a n) => PseudoAffineWithBoundary (Point a n) Source #
Instance details Methods (.--!) :: Point a n -> Point a n -> Needle (Interior (Point a n)) Source # (.-\|) :: Point a n -> Boundary (Point a n) -> Maybe (HalfNeedle (Point a n)) Source # (!-\|) :: Point a n -> Boundary (Point a n) -> HalfNeedle (Point a n) Source # (.--.) :: Point a n -> Point a n -> Maybe (Needle (Interior (Point a n))) Source #
(ProjectableBoundary a, ProjectableBoundary b, SameScalar LinearSpace '[Needle (Interior a), Needle (Interior b), Needle (Boundary a), Needle (Boundary b)], ProjectableBoundary (Interior a), ProjectableBoundary (Interior b), RealFrac'' (Scalar (Needle (Interior a)))) => PseudoAffineWithBoundary (a, b) Source #
Instance details Methods (.--!) :: (a, b) -> (a, b) -> Needle (Interior (a, b)) Source # (.-\|) :: (a, b) -> Boundary (a, b) -> Maybe (HalfNeedle (a, b)) Source # (!-\|) :: (a, b) -> Boundary (a, b) -> HalfNeedle (a, b) Source # (.--.) :: (a, b) -> (a, b) -> Maybe (Needle (Interior (a, b))) Source #
(Num' n, OpenManifold n, LinearManifold (a n), Scalar (a n) ~ n, Needle (a n) ~ a n) => SemimanifoldWithBoundary (Point a n) Source #
Instance details Associated Types type Interior (Point a n) Source # type Boundary (Point a n) Source # type HalfNeedle (Point a n) Source # Methods (.+^\|) :: Point a n -> Needle (Interior (Point a n)) -> Either (Boundary (Point a n), Scalar (Needle (Interior (Point a n)))) (Interior (Point a n)) Source # fromInterior :: Interior (Point a n) -> Point a n Source # fromBoundary :: Boundary (Point a n) -> Point a n Source # (\|+^) :: Boundary (Point a n) -> HalfNeedle (Point a n) -> Point a n Source # separateInterior :: Point a n -> Either (Boundary (Point a n)) (Interior (Point a n)) Source # toInterior :: Point a n -> Maybe (Interior (Point a n)) Source # extendToBoundary :: Interior (Point a n) -> Needle (Interior (Point a n)) -> Maybe (Boundary (Point a n)) Source # smfdWBoundWitness :: SmfdWBoundWitness (Point a n) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (Point a n))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (Point a n)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (Point a n))), Scalar (Needle (Boundary (Point a n))) ~ Scalar (Needle (Interior (Point a n)))) => r) -> r Source #
(ProjectableBoundary a, ProjectableBoundary b, SameScalar LinearSpace '[Needle (Interior a), Needle (Interior b)], RealFrac'' (Scalar (Needle (Interior a))), ProjectableBoundary (Interior a), ProjectableBoundary (Interior b)) => SemimanifoldWithBoundary (a, b) Source #
Instance details Associated Types type Interior (a, b) Source # type Boundary (a, b) Source # type HalfNeedle (a, b) Source # Methods (.+^\|) :: (a, b) -> Needle (Interior (a, b)) -> Either (Boundary (a, b), Scalar (Needle (Interior (a, b)))) (Interior (a, b)) Source # fromInterior :: Interior (a, b) -> (a, b) Source # fromBoundary :: Boundary (a, b) -> (a, b) Source # (\|+^) :: Boundary (a, b) -> HalfNeedle (a, b) -> (a, b) Source # separateInterior :: (a, b) -> Either (Boundary (a, b)) (Interior (a, b)) Source # toInterior :: (a, b) -> Maybe (Interior (a, b)) Source # extendToBoundary :: Interior (a, b) -> Needle (Interior (a, b)) -> Maybe (Boundary (a, b)) Source # smfdWBoundWitness :: SmfdWBoundWitness (a, b) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (a, b))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (a, b)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (a, b))), Scalar (Needle (Boundary (a, b))) ~ Scalar (Needle (Interior (a, b)))) => r) -> r Source #
(LinearSpace v, LinearSpace w, s ~ Scalar v, s ~ Scalar w, Num' s, OpenManifold s, ProjectableBoundary s) => ProjectableBoundary (LinearMap s v w) Source #
Instance details Methods projectToBoundary :: LinearMap s v w -> Boundary (LinearMap s v w) -> Maybe (Needle (Boundary (LinearMap s v w)), Scalar (Needle (Interior (LinearMap s v w)))) Source # marginFromBoundary :: Boundary (LinearMap s v w) -> Scalar (Needle (Interior (LinearMap s v w))) -> LinearMap s v w Source # needleBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Needle (Interior (LinearMap s v w))) => r) -> r Source # scalarBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Scalar (Needle (Interior (LinearMap s v w)))) => r) -> r Source #
(LinearSpace v, LinearSpace w, s ~ Scalar v, s ~ Scalar w, Num' s, OpenManifold s) => PseudoAffineWithBoundary (LinearFunction s v w) Source #
Instance details Methods (.--!) :: LinearFunction s v w -> LinearFunction s v w -> Needle (Interior (LinearFunction s v w)) Source # (.-\|) :: LinearFunction s v w -> Boundary (LinearFunction s v w) -> Maybe (HalfNeedle (LinearFunction s v w)) Source # (!-\|) :: LinearFunction s v w -> Boundary (LinearFunction s v w) -> HalfNeedle (LinearFunction s v w) Source # (.--.) :: LinearFunction s v w -> LinearFunction s v w -> Maybe (Needle (Interior (LinearFunction s v w))) Source #
(LinearSpace v, LinearSpace w, s ~ Scalar v, s ~ Scalar w, Num' s, OpenManifold s) => PseudoAffineWithBoundary (LinearMap s v w) Source #
Instance details Methods (.--!) :: LinearMap s v w -> LinearMap s v w -> Needle (Interior (LinearMap s v w)) Source # (.-\|) :: LinearMap s v w -> Boundary (LinearMap s v w) -> Maybe (HalfNeedle (LinearMap s v w)) Source # (!-\|) :: LinearMap s v w -> Boundary (LinearMap s v w) -> HalfNeedle (LinearMap s v w) Source # (.--.) :: LinearMap s v w -> LinearMap s v w -> Maybe (Needle (Interior (LinearMap s v w))) Source #
(LinearSpace v, LinearSpace w, s ~ Scalar v, s ~ Scalar w, Num' s, OpenManifold s) => PseudoAffineWithBoundary (Tensor s v w) Source #
Instance details Methods (.--!) :: Tensor s v w -> Tensor s v w -> Needle (Interior (Tensor s v w)) Source # (.-\|) :: Tensor s v w -> Boundary (Tensor s v w) -> Maybe (HalfNeedle (Tensor s v w)) Source # (!-\|) :: Tensor s v w -> Boundary (Tensor s v w) -> HalfNeedle (Tensor s v w) Source # (.--.) :: Tensor s v w -> Tensor s v w -> Maybe (Needle (Interior (Tensor s v w))) Source #
(LinearSpace v, LinearSpace w, s ~ Scalar v, s ~ Scalar w, Num' s, OpenManifold s) => SemimanifoldWithBoundary (LinearFunction s v w) Source #
Instance details Associated Types type Interior (LinearFunction s v w) Source # type Boundary (LinearFunction s v w) Source # type HalfNeedle (LinearFunction s v w) Source # Methods (.+^\|) :: LinearFunction s v w -> Needle (Interior (LinearFunction s v w)) -> Either (Boundary (LinearFunction s v w), Scalar (Needle (Interior (LinearFunction s v w)))) (Interior (LinearFunction s v w)) Source # fromInterior :: Interior (LinearFunction s v w) -> LinearFunction s v w Source # fromBoundary :: Boundary (LinearFunction s v w) -> LinearFunction s v w Source # (\|+^) :: Boundary (LinearFunction s v w) -> HalfNeedle (LinearFunction s v w) -> LinearFunction s v w Source # separateInterior :: LinearFunction s v w -> Either (Boundary (LinearFunction s v w)) (Interior (LinearFunction s v w)) Source # toInterior :: LinearFunction s v w -> Maybe (Interior (LinearFunction s v w)) Source # extendToBoundary :: Interior (LinearFunction s v w) -> Needle (Interior (LinearFunction s v w)) -> Maybe (Boundary (LinearFunction s v w)) Source # smfdWBoundWitness :: SmfdWBoundWitness (LinearFunction s v w) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (LinearFunction s v w))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (LinearFunction s v w)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (LinearFunction s v w))), Scalar (Needle (Boundary (LinearFunction s v w))) ~ Scalar (Needle (Interior (LinearFunction s v w)))) => r) -> r Source #
(LinearSpace v, LinearSpace w, s ~ Scalar v, s ~ Scalar w, Num' s, OpenManifold s) => SemimanifoldWithBoundary (LinearMap s v w) Source #
Instance details Associated Types type Interior (LinearMap s v w) Source # type Boundary (LinearMap s v w) Source # type HalfNeedle (LinearMap s v w) Source # Methods (.+^\|) :: LinearMap s v w -> Needle (Interior (LinearMap s v w)) -> Either (Boundary (LinearMap s v w), Scalar (Needle (Interior (LinearMap s v w)))) (Interior (LinearMap s v w)) Source # fromInterior :: Interior (LinearMap s v w) -> LinearMap s v w Source # fromBoundary :: Boundary (LinearMap s v w) -> LinearMap s v w Source # (\|+^) :: Boundary (LinearMap s v w) -> HalfNeedle (LinearMap s v w) -> LinearMap s v w Source # separateInterior :: LinearMap s v w -> Either (Boundary (LinearMap s v w)) (Interior (LinearMap s v w)) Source # toInterior :: LinearMap s v w -> Maybe (Interior (LinearMap s v w)) Source # extendToBoundary :: Interior (LinearMap s v w) -> Needle (Interior (LinearMap s v w)) -> Maybe (Boundary (LinearMap s v w)) Source # smfdWBoundWitness :: SmfdWBoundWitness (LinearMap s v w) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (LinearMap s v w))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (LinearMap s v w)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (LinearMap s v w))), Scalar (Needle (Boundary (LinearMap s v w))) ~ Scalar (Needle (Interior (LinearMap s v w)))) => r) -> r Source #
(LinearSpace v, LinearSpace w, s ~ Scalar v, s ~ Scalar w, Num' s, OpenManifold s) => SemimanifoldWithBoundary (Tensor s v w) Source #
Instance details Associated Types type Interior (Tensor s v w) Source # type Boundary (Tensor s v w) Source # type HalfNeedle (Tensor s v w) Source # Methods (.+^\|) :: Tensor s v w -> Needle (Interior (Tensor s v w)) -> Either (Boundary (Tensor s v w), Scalar (Needle (Interior (Tensor s v w)))) (Interior (Tensor s v w)) Source # fromInterior :: Interior (Tensor s v w) -> Tensor s v w Source # fromBoundary :: Boundary (Tensor s v w) -> Tensor s v w Source # (\|+^) :: Boundary (Tensor s v w) -> HalfNeedle (Tensor s v w) -> Tensor s v w Source # separateInterior :: Tensor s v w -> Either (Boundary (Tensor s v w)) (Interior (Tensor s v w)) Source # toInterior :: Tensor s v w -> Maybe (Interior (Tensor s v w)) Source # extendToBoundary :: Interior (Tensor s v w) -> Needle (Interior (Tensor s v w)) -> Maybe (Boundary (Tensor s v w)) Source # smfdWBoundWitness :: SmfdWBoundWitness (Tensor s v w) Source # needleIsOpenMfd :: (OpenManifold (Needle (Interior (Tensor s v w))) => r) -> r Source # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (Tensor s v w)))) => r) -> r Source # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (Tensor s v w))), Scalar (Needle (Boundary (Tensor s v w))) ~ Scalar (Needle (Interior (Tensor s v w)))) => r) -> r Source #