Does magma know the singularity type of a point in a scheme? I've seen some functions but they all seem to be about curves.
This is my context: I have a surface in $P^2\times P^1$ with zero dimensional singular locus. For each point in this locus I would like to know whether it is a node or not (node=ordinary double point=formal completion looks like a polynomial ring modded out by non-degenerate quadric + higher terms).
If so, is there a way to write down a function which goes through all the singular points and returns whether they are all nodes?