The failing tests suggest that I did something which was not mathematically legitimate. Maybe this can still be helpful for people who know the matroid realization space code? Otherwise, feel free to close this!

Hi, thanks for looking into it! The output that you sent to me on Slack looks reasonable. The printing of the number of variables appearing in the base ring is not ideal though, since the realization space is 0 dimensional. So there should be no variable x1 and no avoidance loci.

CC @LukasKuehne

Tests look better now. Looks like this PR can be taken more serious, then?

So there should be no variable x1 and no avoidance loci.

This might be an issue. I think we do not allow for creation of polynomial rings with zero variables. But the people working on the realization spaces might have another catch for that, I don't know...

So there should be no variable x1 and no avoidance loci.

This might be an issue. I think we do not allow for creation of polynomial rings with zero variables. But the people working on the realization spaces might have another catch for that, I don't know...

You can create polynomial rings with zero variables (for example, polynomial_ring(QQ, 0, :x) works).

So there should be no variable x1 and no avoidance loci.

This might be an issue. I think we do not allow for creation of polynomial rings with zero variables. But the people working on the realization spaces might have another catch for that, I don't know...

Hi,
Can you briefly copy the issue you're trying to solve here (I didn't see the original post on slack)?
So far I think we returned different rings, either a polynomial ring or just a field/ZZ if there are no variables. Is it that you're trying to fix?

The issue is the following error:

julia> r = matroid_from_bases([[3,5],[3,4],[2,5],[2,4]],5)
Matroid of rank 2 on 5 elements

julia> realization_space(r,char=0)
ERROR: ArgumentError: reducing over an empty collection is not allowed; consider supplying `init` to the reducer
[...]