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 =
Thanks, Nils.
My question was motivated by using SageMath in my teachings.
Do you think it would be difficult/worthwhile taking care of this?
I mean, ideals in euclidean rings (or at least in ZZ).
Guillermo
On Sat, 28 Oct 2023 at 18:44, Nils Bruin wrote:
> I'm sure its omission is just an
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 10:22:15 UTC-7 G. M.-S. wrote:
Thanks, Nils.
My question was motivated by using SageMath in my teachings.
Do you think it would be difficult/worthwhile taking care of this?
I mean, ideals in euclidean rings (or at least in ZZ).
Mathematically or
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
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
I'm sure its omission is just an oversight. For fractional ideals in number
fields it is defined:
sage: K.=QuadraticField(7)
sage: I=K.fractional_ideal(5)
sage: J=K.fractional_ideal(3)
sage: I.intersection(J)
Fractional ideal (15)
I doubt that just knowing a ring is a PID makes computing
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
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
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,
I wonder why SageMath cannot compute the intersection of 2 ideals in ZZ.
Is this due to the fact that ZZ would "only" be a PID?
Guillermo
┌┐
│ SageMath version 10.1, Release Date: 2023-08-20│
│ Using
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
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,
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