Documentation Clarification

[jackychen08]

Hi, I am confused by the documentation/definition of the incidence_matrix function in cell_complex.py. It's not clear to me whether the function calculates an up-incidence matrix of rank r, a down-incidence matrix of rank r, or if there is a way to use the function to calculate a (r,k)-incidence matrix.

For instance, if I had a cell complex with cells of rank 1,2,3 corresponding to nodes, edges and faces respectively, what would be the best way to calculate the (2,3) incidence matrix to see which edges are incident to faces?

[mhajij]

cell complexes do not support ranks beyond 2. The incidence matrix in a cell complex takes a single parameter, as it is supposed to be the linear rep of the boundary map in algebraic topology.

For instance CC.incidence_matrix(1) of a cell complex CC computes the incidence between 0 and 1 rank cells (nodes and edges). incidence_matrix(2) computes between edges and faces (rank 2 cells).

If you want to go for node and face incidence then you are looking for set-based incidence which is supported in combinatorial complex or colored hypergraph. In that case when you need to compute the incidence between rank i and rank j you pass use : incidence_matrix(i,j). Hope that helps.

[jackychen08]

Thank you for the clarification!