Extend betti_numbers for SimplicialComplex to allow computing Betti numbers over a field instead of the integers

[antonydellavecchia]

Extend betti_numbers function to accept optional parameter for the Field

[HechtiDerLachs]

Maybe it would be worthwhile to add
betti_numbers(R::Ring, S::SimplicialComplex) = betti_numbers(characteristic(R), S) ?
And betti_number([p::Int], S::SimplicialComplex, i::Int) to return only a single Betti number?

Another question I had: The function returns a list of integers. Is it clear that the first entry always stands for the 0-th Betti number, the second for the first, etc.? If yes, everything is fine. But otherwise, one could think of returning a dictionary?

Sorry for the delayed review, btw. The request slipped me through. Feel free to ping me through other channels if this happens again.

[fingolfin]

@antonydellavecchia what's the status of this? Should it be re-reviewed?

[fingolfin]

@HechtiDerLachs will talk to @antonydellavecchia about this, they wanted to meet later today anyway.

[antonydellavecchia]

@antonydellavecchia what's the status of this? Should it be re-reviewed?

I'll implement what @HechtiDerLachs suggested above at some point today or this week

[HechtiDerLachs]

Looks good to me. Kept simple.

Edit: Wait! Sorry. Now the signature is for Rings. But can we assume that the rank command works then on the matrices? Do we want to assume that?