# Is there any interest in creating a FEM Julia organization?

**URL:** <https://discourse.julialang.org/t/is-there-any-interest-in-creating-a-fem-julia-organization/7035>\
**Category:** Community\
**Tags:** diffeq\
**Created:** [November 13, 2017, 5:27am UTC](https://discourse.julialang.org/t/is-there-any-interest-in-creating-a-fem-julia-organization/7035 "2017-11-13T05:27:15Z")\
**Posts on this page:** 1\
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**Author:** ![chakravala](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chakravala/32/6832_2.png) [@chakravala](https://discourse.julialang.org/u/chakravala)\
**Post date:** [September 22, 2019, 9:49am UTC](https://discourse.julialang.org/t/is-there-any-interest-in-creating-a-fem-julia-organization/7035/48 "2019-09-22T09:49:13Z")

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That’s a good question, I will investigate some more on that. There is a general cellular homology theory

> **[Cellular homology](https://en.m.wikipedia.org/wiki/Cellular_homology)**
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> In mathematics, cellular homology in algebraic topology is a homology theory for the category of CW-complexes. It agrees with singular homology, and can provide an effective means of computing homology modules.
> If 
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> X
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> {\\displaystyle X}
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> is a CW-complex with n-skeleton 
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> X
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> n
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> {\\displaystyle X\_{n}}
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> , the cellular-homology modules are defined as the homology groups ...

> **[n-skeleton](https://en.m.wikipedia.org/wiki/N-skeleton)**
>
> In mathematics, particularly in algebraic topology, the n-skeleton of a topological space X presented as a simplicial complex (resp. CW complex) refers to the subspace Xn that is the union of the simplices of X (resp. cells of X) of dimensions m ≤ n. In other words, given an inductive definition of a complex, the n-skeleton is obtained by stopping at the n-th step.
> These subspaces increase with n. The 0-skeleton is a discrete space, and the 1-skeleton a topological graph. The skeletons of a spac...

> **[Simplicial set](https://en.m.wikipedia.org/wiki/Simplicial_set)**
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> In mathematics, a simplicial set is an object composed of simplices in a specific way. Simplicial sets are higher-dimensional generalizations of directed graphs, partially ordered sets and categories. Formally, a simplicial set may be defined as a contravariant functor from the simplex category to the category of sets. Simplicial sets were introduced in 1950 by Samuel Eilenberg and Joseph A. Zilber.
> Every simplicial set gives rise to a "nice" topological space, known as its geometric realization...

So the answer is yes, it seems that hyper cubes are possible to represent with a simplicial set… it is closely tied together with the CW-complex. Simplicial set is a generalization, taking unions of subspaces.

For example, if we have 4 vertices (to make a square) we might use `v12 - v14 + v23 + v34` to represent the boundary of the square by using 1-simplices. So I’d say you can represent them… you can also get that result by computing (on `master`) the boundary of the 2-cube square `v123 + v134` itself:

```plaintext
julia> using Grassmann, Leibniz; @basis tangent(ℝ^4,2,4); #master branch

julia> ∂(v1234) # boundary of 3-simplex
0 - 1∂₄v₁₂₃ + 1∂₃v₁₂₄ - 1∂₂v₁₃₄ + 1∂₁v₂₃₄

julia> ∂(v123+v134) # boundary of 2-cube
0 + 1∂₃v₁₂ - 1∂₂v₁₃ + 1∂₄v₁₃ - 1∂₃v₁₄ + 1∂₁v₂₃ + 1∂₁v₃₄

```

Note the extra edges `1∂₄v₁₃ - 1∂₂v₁₃` which cancel out if you set `∂ᵢ = ∂ⱼ` for `i≠j` so it works.

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