K Decomposability_of_Simplicial_Complexes

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title: K-Decomposability of Simplicial Complexes permalink: wiki/K-Decomposability_of_Simplicial_Complexes/ layout: wiki

The working file is [trunk/M2/Macaulay2/packages/development/msri2010/SimplicialDecomposability.m2] on the SVN repository.

Goals

• Compute a shelling order of a shellable simplicial complex.
• Compute whether or not a simplicial complex is shellable.
• Compute whether or not a simplicial complex is vertex-decomposable.
• Compute whether or not a pure simplicial complex is k-decomposable.

To Do

• isShelling: actually determine if it is a shelling.
• shellingOrder: actually find a shelling order
• Add tests for isShelling, isSimplex, hVector, isShellable.
• Add the more general k-decomposability routine.
• Add tests for the k-decomposability routines.
• shellingOrder: Add other Strategies beyond "Naive".
• Implement not-necessarily-pure versions of:
  • iskDecomposable
  • isSheddingFace
  • isShellable
  • isShelling
  • isVertexDecomposable
  • shellingOrder
• Thorough testing
• Cache shelling order
• Add fTriangle and hTriangle routines
• Optimise the code -- Always needed!