As a small update, the repository now contains code to - perform arithmetic for - the imaginary model (ramified, one point at infinity) for all cases - the real model (split, two points at infinity) for all cases - the real model (inert, zero points at infinity) for even genus Which allows us to do "as much" as Magma does for Jacobians of hyperellipticc curves from the perspective of arithmetic.
My current "test" for the arithmetic is that D - D = 0 for all cases, that jacobian_order * D = zero and that order_from_multiple(D) works. If people have other ideas for tests, please let me know. Of course at the moment these tests are over finite fields but you can reasonable use other fields (as Sabrina's message shows) but I am less sure about how to do randomised testing here. - We also have a function which can randomly (but not uniformly) sample elements of the Jacobian for all the cases. - We can compute the order of the Jacobian from the frob. polynomial and using the arithmetic and in-build `order_from_multiple` then find the order of divisors I think the next thing to do is to look at isomorphisms and maybe even isogenies (Richelot only for genus two perhaps?) If you are interested in this area and want to contribute, then I think fleshing out the code in this repo will be easier during these early stages and once it feels complete we can look at replacing the current code in sagemath with this newer version. On Thursday, March 7, 2024 at 9:40:58 PM UTC Sabrina Kunzweiler wrote: > Thanks for mentioning the related discussion. We checked that in the new > implementation in Giacomo's repository, this issue is solved. > > In the example that was given in the chat, we obtain the following output: > ``` > sage: R.<x> = QQ[] > sage: f = 144*x^6 - 240*x^5 + 148*x^4 + 16*x^3 - 16*x^2 - 4*x + 1 > sage: H = HyperellipticCurveNew(f) > sage: J = Jacobian(H) > sage: P = J(H([0,1]))-J(H([0,-1])) > sage: (5*P).is_zero() > False > sage: 5*P > (1, 0 : 2) > ``` > Here, this means $$ 5 P = (1:12:0) - (1:-12:0) $$ which coincides with the > result from magma. > > > Kwankyu Lee schrieb am Donnerstag, 7. März 2024 um 05:44:33 UTC+1: > >> It's still here: https://github.com/sagemath/sage/issues/32024 > > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/16695996-c9bc-4a08-a1a4-37179e7a8956n%40googlegroups.com.
