Calculate places of rational field over large finite field GF(2^128) using SageMath

asked 2024-11-24 17:21:14 +0100

anonymous user

Anonymous

updated 2024-12-08 22:17:27 +0100

Is there a better way than just trying to manually enumerate them?

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What are "rational places"? It'd help, if you provide a Sage code illustrating your question.

Max Alekseyev gravatar imageMax Alekseyev ( 2024-11-26 13:44:31 +0100 )edit

This is the code:

sage: R.<x,y,z> = PolynomialRing(GF(2^128), 3)
sage: f = y^2*z - x^3 - 2*x*z^2 - z^3
sage: C = Curve(f)
sage: F = C.function_field()
sage: F.places()

When I run this Sage stalls for a long time and then crashes. I was wondering if it was because the function field is too big.

sknc gravatar imagesknc ( 2024-11-26 18:52:25 +0100 )edit

My Sage 10.5.beta9 crashes right away for already for GF(2^2) and GF(3^2), and so it does not seem to be related to large fields but rather to non-prime fields.

Please report the issue at https://github.com/sagemath/sage/issues

Max Alekseyev gravatar imageMax Alekseyev ( 2024-11-26 21:29:59 +0100 )edit

I have Sage 10.4, and both GF(2^2) and GF(3^2) work fine for me.

sknc gravatar imagesknc ( 2024-11-27 00:03:28 +0100 )edit

I've checked 10.5rc0 - it also works fine on GF(2^2) and GF(3^2).

Max Alekseyev gravatar imageMax Alekseyev ( 2024-11-27 06:20:34 +0100 )edit
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