#6920: irreducible components function is stupid in case of projective space
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Reporter: was | Owner: was
Type: defect | Status: new
Priority: major | Milestone: sage-4.1.2
Component: algebraic geometry | Keywords:
Reviewer: | Author:
Merged: |
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{{{
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
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6920>
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