isNormal for non-equidimensional rings

Nobody has claimed this yet.

Currently regular but non-equidimensional rings seem to return false via the isNormal function.

For instance if
R = QQ[x,y,z]/(x_(x+1), y_(x+1))
then isNormal(R) == false

Presumably the issue is that when S2 is checked for, it checks various Exts to see if they are nonzero (and with appropriate dimensional support). Non-equidimensional rings will have Exts in funny dimensions. I suppose one could run this on each connected component separately and then it would be fine.

I guess one should also be careful with the R1 check, if you had X a singular curve disjoint union with a smooth surface, then the singular locus has dimension 0 and the scheme has dimension 2, but I wouldn't say that X is R1.

Best wishes,

Karl

Start with the isNormal function and reproduce the reported QQ[x,y,z]/(x_(x+1), y_(x+1)) example. Read how its S2 and R1 checks handle Exts, connected components, and non-equidimensional dimensions. Done means the regular non-equidimensional case is accepted while the stated R1 edge case remains correctly classified; no files or tests are named.

Written by the indexing model from the issue text.