Copyright | (c) Justus Sagemüller 2018 |
---|---|
License | GPL v3 |
Maintainer | (@) jsag $ hvl.no |
Stability | experimental |
Portability | portable |
Safe Haskell | None |
Language | Haskell2010 |
Synopsis
- pattern TangentBundle :: m -> Needle m -> FibreBundle m (Needle m)
- pattern (:@.) :: f -> m -> FibreBundle m f
- tangentAt :: (AdditiveGroup (Needle m), m ~ Interior m) => m -> TangentBundle m
- data TransportOnNeedleWitness k m f where
- TransportOnNeedle :: ParallelTransporting (LinearFunction (Scalar (Needle m))) (Needle m) (Needle f) => TransportOnNeedleWitness k m f
- data ForgetTransportProperties k m f where
- ForgetTransportProperties :: ParallelTransporting (->) m f => ForgetTransportProperties k m f
- class (PseudoAffine m, m ~ Interior m, Category k, Object k f) => ParallelTransporting k m f where
- transportOnNeedleWitness :: TransportOnNeedleWitness k m f
- forgetTransportProperties :: ForgetTransportProperties k m f
- parallelTransport :: m -> Needle m -> k f f
- translateAndInvblyParTransport :: m -> Needle m -> (m, (k f f, k f f))
- transformEmbeddedTangents :: forall x f v. (NaturallyEmbedded (FibreBundle x f) (FibreBundle v v), v ~ Interior v) => (v -> v) -> FibreBundle x f -> FibreBundle x f
Documentation
pattern TangentBundle :: m -> Needle m -> FibreBundle m (Needle m) Source #
pattern (:@.) :: f -> m -> FibreBundle m f infixr 5 Source #
Provided for convenience. Flipped synonym of FibreBundle
, restricted to manifolds
without boundary (so the type of the whole can be inferred from its interior).
tangentAt :: (AdditiveGroup (Needle m), m ~ Interior m) => m -> TangentBundle m Source #
A zero vector in the fibre bundle at the given position. Intended to be used
with tangent-modifying lenses such as delta
.
data TransportOnNeedleWitness k m f where Source #
TransportOnNeedle :: ParallelTransporting (LinearFunction (Scalar (Needle m))) (Needle m) (Needle f) => TransportOnNeedleWitness k m f |
data ForgetTransportProperties k m f where Source #
ForgetTransportProperties :: ParallelTransporting (->) m f => ForgetTransportProperties k m f |
class (PseudoAffine m, m ~ Interior m, Category k, Object k f) => ParallelTransporting k m f where Source #
transportOnNeedleWitness :: TransportOnNeedleWitness k m f Source #
transportOnNeedleWitness :: ParallelTransporting (LinearFunction (Scalar (Needle m))) (Needle m) (Needle f) => TransportOnNeedleWitness k m f Source #
forgetTransportProperties :: ForgetTransportProperties k m f Source #
forgetTransportProperties :: ParallelTransporting (->) m f => ForgetTransportProperties k m f Source #
parallelTransport :: m -> Needle m -> k f f Source #
translateAndInvblyParTransport :: m -> Needle m -> (m, (k f f, k f f)) Source #
Instances
transformEmbeddedTangents :: forall x f v. (NaturallyEmbedded (FibreBundle x f) (FibreBundle v v), v ~ Interior v) => (v -> v) -> FibreBundle x f -> FibreBundle x f Source #
ex -> ey
, ey -> ez
, ez -> ex