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feat: implement Simplicial with canonical orientations #13

@FiberedSkies

Description

@FiberedSkies

Description

Implement a Simplicial variant of the current general cell complex implementation using Cell and Skeleton with canonical orientations. Canonical orientation over a simplicial being defined as $[b:a] = (-1)^n$ if you have to remove the $n$-th vertex of $b$ to get back $a$, and $[b:a] = 0$ if $a$ is not a face of $b$.

Details

  • implement Simplicial as a specific Skeleton of $n$ dimensions with 0-cells (vertices), 1-cells (edges), 2-cells (2-simplex/triangles), etc. must function for up to an arbitrary $n$ dimensions.
  • implement a builder pattern for a CellularSheaf with canonical orientations as described above and initialized restrictions from a Simplicial

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    enhancementNew feature or requestmaththis issue requires implementing pure mathspriority: mediumuximproves user experience

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