Now with (draft) PR
https://github.com/sagemath/sage/pull/36592
the ask.sagemath problem is solved by
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()
K = kC.gen().differential().divisor() # canonical divisor
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 00:19:47 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 =
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
On Saturday, 28 October 2023 at 18:50:12 UTC-7 Nils Bruin wrote:
On Saturday, 28 October 2023 at 15:26:35 UTC-7 Kwankyu wrote:
f1, f2, f3 are univariate polynomials (say in y) over rational function
field (say in x). Then x and y are not always the variables X and Y of the
coordinate ring of
On Saturday, 28 October 2023 at 15:26:35 UTC-7 Kwankyu wrote:
f1, f2, f3 are univariate polynomials (say in y) over rational function
field (say in x). Then x and y are not always the variables X and Y of the
coordinate ring of the affine plane. Things are more complicated if the
curve is in
That's actually trivially simple: if [f1,f2,f3] is the basis of your
Riemann-Roch space, you just consider the map defined by [f1:f2:f3]. So you
lift f1,f2,f3 to rational functions on the affine space that contains your
curve: you just take the rational function representation and forget the
Nils, thanks to you, too, for your responses.
On Saturday, October 28, 2023 at 11:16:39 AM UTC-7 Nils Bruin wrote:
> On Saturday, 28 October 2023 at 05:39:26 UTC-7 Kwankyu wrote:
>
> I looked the Magma code in ask.sagemath. There's no problem in computing a
> canonical divisor for the curve
On Saturday, 28 October 2023 at 05:39:26 UTC-7 Kwankyu wrote:
I looked the Magma code in ask.sagemath. There's no problem in computing a
canonical divisor for the curve (through the attached function field).
Computing a basis of the Riemann-Roch space is no problem as well. Actually
the hard
Thanks for all of your posts, Kwankyu. Helpful and informative.
John
On Saturday, October 28, 2023 at 6:19:48 AM UTC-7 Kwankyu wrote:
> To answer John's question:
>
> sage: P2. = ProjectiveSpace(QQ, 2)
> sage: 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
> sage: C =
To answer John's question:
sage: P2. = ProjectiveSpace(QQ, 2)
sage: 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
sage: C = P2.curve(f)
sage: F = C.function_field()
sage: z, = F.gens()
sage: K = z.differential().divisor() # canonical divisor
sage: (-K).dimension()
3
sage: f1,
Let me mention also the related PR
https://github.com/sagemath/sage/pull/35467
which implements Jacobian groups of curves (again via function field),
referencing Nils' old code. The PR is long sleeping in draft state. If
anyone finds it useful, I may wake it up.
On Saturday, October 28,
Hi,
I replied to Dima's comment in
https://github.com/sagemath/sage/commit/977ace651af9b99689f7b6507f91f8b4e2588ae9#r131138149.
Note that the "divisor" method of a curve had existed long before I added
function field machinery and attached function fields to curves. Hence
actually there are
On Sat, Oct 28, 2023 at 1:02 AM John H Palmieri wrote:
> Yes, I noticed that, too. It also fails to provide any information about what
> ``v`` should be (beyond saying that it should be a "valid object"): there is
> no INPUT block.
I've left a comment here:
Hi Dima,
Yes, I noticed that, too. It also fails to provide any information about
what ``v`` should be (beyond saying that it should be a "valid object"):
there is no INPUT block.
On Friday, October 27, 2023 at 3:51:10 PM UTC-7 Dima Pasechnik wrote:
> By the way, the docstring of divisor()
By the way, the docstring of divisor() misses an example, it's
def divisor(self, v, base_ring=None, check=True, reduce=True):
r"""
Return the divisor specified by ``v``.
.. WARNING::
The coefficients of the divisor must be in the base ring
and
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