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
On Sep 8, 7:56 pm, Kwankyu <[email protected]> wrote:
> Hi,
>
> What was f? What is the version of your Sage and what is the platform?
>
> Kwankyu
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