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Maybe fix interlinks?
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mateuszbaran committed Dec 4, 2024
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Expand Up @@ -32,9 +32,9 @@ Specifically they are requirements that $\mathcal{M}$ is a second-countable Haus

JuliaManifolds has a few functions for working at this level.
First, [`manifold_dimension`](@ref) returns the number `n` for a given manifold.
Next, [`get_chart_index`](@extref) points to one of the charts such that $p$ is in its domain.
The value of chart on a point can be calculated using [`get_parameters`](@extref) and its inverse using [`get_point`](@extref).
When we have two charts $\phi_i, \phi_j$, the composition $\phi_j \circ \phi_i^{-1}$ is called the transition map from $\phi_i$ to $\phi_j$, see [`transition_map`](@extref).
Next, [`get_chart_index`](@extref `Manifolds.get_chart_index`) points to one of the charts such that $p$ is in its domain.
The value of chart on a point can be calculated using [`get_parameters`](@extref `Manifolds.get_parameters`) and its inverse using [`get_point`](@extref `Manifolds.get_point`).
When we have two charts $\phi_i, \phi_j$, the composition $\phi_j \circ \phi_i^{-1}$ is called the transition map from $\phi_i$ to $\phi_j$, see [`transition_map`](@extref `Manifolds.transition_map`).
More details are discussed in [this page](https://juliamanifolds.github.io/Manifolds.jl/stable/features/atlases/) and [this tutorial](https://juliamanifolds.github.io/Manifolds.jl/stable/tutorials/working-in-charts/) demonstrates a use case.
Often additional restrictions are imposed, for example only atlases with only [differentiable](https://en.wikipedia.org/wiki/Differentiable_manifold), smooth or [analytic](https://en.wikipedia.org/wiki/Analytic_manifold) transition maps are considered.

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