I began to learn topology with respect to sagemath. I am confused by product function.
sage: S = SimplicialComplex([[0,1],[1,2]])
sage: W = SimplicialComplex([[0,1]])
sage: T = S.product(W)
T
Simplicial complex with 6 vertices and 4 facets
why this has 4 facets.Can give me detailed calculation process？
S consists of two 1-simplices: two edges. W is a single edge. Their product, therefore, consists of two squares: [0,1] x [0,1] and [1,2] x [0,1]. If you triangulate the squares by drawing diagonals on each one, you get four triangles. Those are the four facets in S.product(W).
If you run T.facets?, you will get documentation, the first line of which is "The maximal faces (a.k.a. facets) of this simplicial complex.". The facets are the maximal simplices.
Asked: 2024-06-22 19:28:49 +0100
Seen: 173 times
Last updated: Jun 22
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