This is simpler
sage: psi = C.hom(liftedbasis, P2)
sage: psi.image()
Closed subscheme of Projective Space of dimension 2 over Rational Field
defined by:
x^2 + x*y + 2*y*z
On Monday, October 30, 2023 at 5:45:27 AM UTC+9 Nils Bruin wrote:
On Monday, 30 October 2023 at 00:19:47 UTC+13 Kwankyu
On Monday, 30 October 2023 at 00:26:55 UTC+13 G. M.-S. wrote:
If I understand you correctly, SageMath is a bit loose at the moment about
its categories.
That's not what I meant also not what is indicated by what I noticed: by
the looks of it, sage does know about euclidean domains and has
On Monday, 30 October 2023 at 00:19:47 UTC+13 Kwankyu wrote:
What is your code?
P2. = ProjectiveSpace(QQ, 2)
f = 2*x^5 - 4*x^3*y*z + x^2*y*z^2 + 2*x*y^3*z + 2*x*y^2*z^2+ y^5
C = Curve(f)
kC = C.function_field()
D = kC(kC.base_field().gen(0)).differential().divisor()
L,m,s =
Does anyone have any tips for how to compute the kernel of a map between
polynomial algebras, or for checking whether the map is injective? I have
families of such maps involving algebras with many generators. I'm working
over GF(2), if that matters. In one example I defined the map phi: R -> S
The most pressing problem in sage at the moment seems to be that presently
there only seem to be morphisms between schemes. You need rational maps for
this (especially from a singular model, the map to a canonical model might
only be a rational map).
"SchemeMorphism" in Sage is a map
Nils,
Thank you again for your explanations and insights, with which I agree.
As confirmed by the intersection methods you mention, I was thinking
about consistency.
I try to make my students grasp the concepts of integral domains, GCD
domains, UFDs, PIDs, Euclidean domains and fields.
One tool
