Opened 10 years ago
Closed 10 years ago
#6920 closed defect (fixed)
irreducible components function is stupid in case of projective space
Reported by: | was | Owned by: | was |
---|---|---|---|
Priority: | major | Milestone: | sage-4.3.2 |
Component: | algebraic geometry | Keywords: | |
Cc: | Merged in: | sage-4.3.2.alpha0 | |
Authors: | William Stein | Reviewers: | Alex Ghitza |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
I just ran the following on sagenb.org (so the latest release): PP.<x,y,z,w> = ProjectiveSpace(3,QQ) f = x^3 + y^3 + z^3 + w^3 R = f.parent() I = [f] + [f.derivative(zz) for zz in PP.gens()] V = PP.subscheme(I) V.irreducible_components() The output is: [ Closed subscheme of Projective Space of dimension 3 over Rational Field defined by: w z y x ] [ Closed subscheme of Projective Space of dimension 3 over Rational Field defined by: w z y x ] I think that the problem is that normally Proj(R) is defined to be all prime ideals that do not contain sum_{d > 0} S_d where R is a graded ring graded by non-negative integers, and S_d is the ideal generated by homogeneous elements of degree d. I glanced at irreducible_components and it just returns all of the prime ideals coming from the primary decomposition. In the case that the ambient scheme is projective, it should exclude some. Victor Miller
P.S. I wrote this code, so I think it's OK for me to call this stupid. -- William
Attachments (1)
Change History (4)
Changed 10 years ago by
comment:1 Changed 10 years ago by
- Report Upstream set to N/A
- Status changed from new to needs_review
comment:2 Changed 10 years ago by
- Reviewers set to Alex Ghitza
- Status changed from needs_review to positive_review
comment:3 Changed 10 years ago by
- Merged in set to sage-4.3.2.alpha0
- Resolution set to fixed
- Status changed from positive_review to closed
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Looks good.