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, 2023 at 9:39:26 PM UTC+9 Kwankyu wrote: > 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 two systems of "divisors" of curves in Sage. > > The old system was implemented by William Stein, David Kohel, and Volker > Braun. In the old system, a divisor is a formal sum of rational points with > multiplicities. It is mainly implemented in > `src/sage/schemes/generic/divisor.py`. Overall it is very rudimentary. Dima > and John is attempting to use this system. > > The new system was implemented by me. Here a divisor is a formal sum of > places of a function field with multiplicities. This system is available > via the function field attached to a curve. This is much more powerful than > the old system. You can compute the Riemann-Roch space of a divisor. Nils > is using this system. > > I never attempted to combine the two systems, being afraid of breaking the > old system (or just being lazy :-) There are similarly two systems in Magma > too. But in Magma, the two systems are integrated tightly and seamlessly. I > did some integration in Sage too but far from complete compared with Magma. > > 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 part is to construct the morphism from C to P2 from the basis. > Magma does this seamlessly. But Sage lacks this functionality (perhaps > because I did not implement it). I think, the gist of the matter is to > convert an element of the function field to a rational function of the > coordinate ring of P2. I have no idea how to do this now... Once you > construct the morphism, Sage can also compute the image of the morphism > (perhaps I implemented this). Hence unfortunately the Magma code cannot be > line by line converted to Sage code at present. > > On Saturday, October 28, 2023 at 8:27:07 AM UTC+9 Dima Pasechnik wrote: > >> On Sat, Oct 28, 2023 at 1:02 AM John H Palmieri <jhpalm...@gmail.com> >> 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: >> >> https://github.com/sagemath/sage/commit/977ace651af9b99689f7b6507f91f8b4e2588ae9#r131117132 >> >> >> fortunately, the author, @kwankyu is active >> >> I can't locate the ticket, but it was merged in 9.0.beta9 >> >> >> > >> > >> > On Friday, October 27, 2023 at 3:51:10 PM UTC-7 Dima Pasechnik wrote: >> >> >> >> 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 the terms must be reduced. If you set ``check=False`` >> >> and/or ``reduce=False`` it is your responsibility to pass >> >> a valid object ``v``. >> >> >> >> EXAMPLES:: >> >> >> >> sage: x,y,z = PolynomialRing(QQ, 3, names='x,y,z').gens() >> >> sage: C = Curve(y^2*z - x^3 - 17*x*z^2 + y*z^2) >> >> >> >> """ >> >> >> >> Is there an issue for this? >> >> >> >> On Sat, Oct 28, 2023 at 12:42 AM Nils Bruin <nbr...@sfu.ca> wrote: >> >> > >> >> > A canonical divisor is the divisor of any differential on C so the >> following does the trick: >> >> > >> >> > sage: kC=C.function_field() >> >> > sage: kC(kC.base_field().gen(0)).differential().divisor() >> >> > >> >> > It doesn't look like we quite have computation of Riemann-Roch >> spaces natively in sage yet, so finding effective representatives requires >> a little more work. In the RiemannSurface code this is done using >> singular's adjoint ideal code (or by Baker's theorem in cases where it >> applies). For this curve the canonical class is of degree -2, so there are >> no effective representatives in this case. >> >> > >> >> > On Friday, 27 October 2023 at 15:14:00 UTC-7 John H Palmieri wrote: >> >> >> >> >> >> If anyone here knows anything about canonical divisors and their >> implementation in Sage, please see >> https://ask.sagemath.org/question/74034/converting-algebraic-geometry-magmas-code-to-sage/. >> >> The setup: >> >> >> >> >> >> sage: P2.<x,y,z> = 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) >> >> >> >> >> >> How do you get the canonical divisor for C? >> >> >> >> >> >> (I encourage you to post answers directly to ask.sagemath.org, if >> you're willing.) >> >> >> >> >> >> -- >> >> >> John >> >> >> >> >> > -- >> >> > You received this message because you are subscribed to the Google >> Groups "sage-support" group. >> >> > To unsubscribe from this group and stop receiving emails from it, >> send an email to sage-support...@googlegroups.com. >> >> > To view this discussion on the web visit >> https://groups.google.com/d/msgid/sage-support/91b14570-b83e-4dbf-8bca-0a2eff538a50n%40googlegroups.com. >> >> >> > >> > -- >> > You received this message because you are subscribed to the Google >> Groups "sage-support" group. >> > To unsubscribe from this group and stop receiving emails from it, send >> an email to sage-support...@googlegroups.com. >> > To view this discussion on the web visit >> https://groups.google.com/d/msgid/sage-support/391d8ee7-0329-4a15-bc88-4b84973389abn%40googlegroups.com. >> >> >> > -- You received this message because you are subscribed to the Google Groups "sage-support" group. 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