Issues upon beta testing

[ninamiolane]

Simplicial complex notebook

The definition of an abstract simplicial complex is given: what makes it abstract? can be remove the "abstract" adjective, since the non-abstract version is not defined and the python class does not have Abstract in the name

"The degree of an incidence matrix references the degree of the classes we are comparing. An incidence matrix of degree 1 compares which vertices are incident with which edges, of degree 2 compares which vertices are incident with which faces"
--> corrected: degree 2 compares edges with faces?
--> corrected: use rank instead of degree, since the API uses rank.

"The entry in row x and column y is 1 if x and y are related (called incident in this context) and 0 if they are not [2]"
--> Does not take into account the -1 presented in the notebook.

"if the i 𝑡ℎ
vertex is not incident to j 𝑡ℎ
vertex via an edge incident to i 𝑡ℎ
vertex, ≠
0 if it is incident."
--> slightly unclear, rephrase?

"The up-Laplacian function up_laplacian_matrix returns a matrix where row 1 will return the up-Laplacian of edge 1, row 2 will return the up-Laplacian of edge 2 and so on." --> unclear, rephrase?

The python code uses 0-indexing but the text tends to use 1-indexing, "the first, the second" which makes it confusing.

"# setting what data we want to attach to which faces. order here is important." -> how is order important?