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Finishing touches
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GeorgeR227 committed Sep 4, 2024
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# Harmonics of the Sphere

This page shows how to use Decapodes tooling to explore the harmonics of a discrete manifold. This isn't using any decapode specific code, but it
is emblematic of a more advanced analysis you might want to do on your decapode.
This page shows how to use Decapodes tooling to explore the harmonics of a discrete manifold. This isn't using any Decapodes specific code, but it
is emblematic of a more advanced analysis you might want to do on your Decapode.

In this case we are trying to visualize the roots of the Laplacian on a discrete manifold.

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subdivide_duals!(sd, Barycenter());
```

Compute the laplacian eigenvectors using [LinearAlgebra.eigen](https://docs.julialang.org/en/v1/stdlib/LinearAlgebra/#LinearAlgebra.eigen). This requires making the sparse Laplacian matrix dense with `collect`. Alternatively, use [Arpack.jl](https://arpack.julialinearalgebra.org/stable/).

```@example Harmonics
Δ0 = -Δ(0,sd)
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