#10529: dimension() and is_smooth() for algebraic subschemes of toric varieties
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Reporter: vbraun | Owner: AlexGhitza
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.7
Component: algebraic geometry | Keywords:
Author: Volker Braun | Upstream: N/A
Reviewer: Andrey Novoseltsev | Merged:
Work_issues: |
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Comment(by novoselt):
1. If you don't really care, I'd go with `Jacobian_ideal` since it is more
clear.
2. But in the affine case the defining equations are not implied and I
gave examples where they are not included. I agree with your points about
adding them. In fact, I was very confused and frustrated when I was
computing Milnor numbers for a certain example and results didn't match
with expectations precisely because of "extra critical points". However, I
don't want to go against usual definitions and conventions. Could you
please give a reference to the definition of a Jacobian ideal in the sense
that you have implemented?
3-4. I was thinking about a particular point, not testing smoothness of
the whole scheme ;-) I am OK to leave it for the future.
6-9. If these issues are addressed in #10540, I propose either moving the
main patch of this ticket to #10540 or putting it in front of #10540 in
the queue and making sure that they are merged together. The second option
probably makes more sense, but it will add 2 more tickets as prerequisites
for this one.
7. The suggested optimization will work for any definition of "best", it
is just a more efficient way of determining whether a certain patch is
acceptable at all or not.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10529#comment:24>
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