Utilities

Ease of notation

The following terms introduce a nicer notation for some operations, for example using the ∈ operator, $p ∈ \mathcal M$ to determine whether $p$ is a point on the AbstractManifold $\mathcal M$.

Base.inFunction
Base.in(p, M::AbstractManifold; kwargs...)
p ∈ M

Check, whether a point p is a valid point (i.e. in) a AbstractManifold M. This method employs is_point deactivating the error throwing option.

source
Base.in(p, TpM::TangentSpace; kwargs...)
X ∈ TangentSpace(M, p)

Check whether X is a tangent vector from (in) the tangent space $T_p\mathcal M$, i.e. the TangentSpace at p on the AbstractManifold M. This method uses is_vector deactivating the error throw option.

source

Fallback for the exponential map: Solving the corresponding ODE

When additionally loading NLSolve.jl the following fallback for the exponential map is available.

Public documentation

Specific exception types

For some manifolds it is useful to keep an extra index, at which point on the manifold, the error occurred as well as to collect all errors that occurred on a manifold. This page contains the manifold-specific error messages this package introduces.