Drawing curves in Oscar.jl

This repository contains examples on how to draw curves in Oscar.jl [1]. It contains three scripts.

Note that currently you need to use the branch

lk/experimental/drawing_curves

to run these examples.

Run the scripts from the root of this directory:

julia scripts/SCRIPT.jl

scripts/apple.jl

Draw the "apple" example from the paper.

scripts/apple_solving.jl

Script that runs different solvers available in Oscar.jl on the apple example. The goal is to highlight the differences.

scripts/gudkov.jl

Run a computation to construct the curves $C_5$ and $C_1$ from Gudkov's paper [2]. In Julia you can just call

include("scripts/gudkov.jl")

This also draws the intermediate stages.

If you are only interested in the polynomials for $C_5$ and $C_1$, they are stored in the data folder in the mrdi file format [3]. You can load them in the following way

julia> (C5, C1) = load("data/C5_C1.mrdi")

References

[1] Oscar.jl - OSCAR -- Open Source Computer Algebra Research system

[2] D. A. Gudkov. “Construction of a new series of M-curves”. English. In: Sov. Math., Dokl. 12 (1971), pp. 1559–1563. zbmath

[3] A. Della Vecchia, M. Joswig, B. Lorenz: A FAIR file format for mathematical software. Buzzard, Kevin (ed.) et al., Mathematical software – ICMS 2024. 8th international conference, Durham, UK, July 22–25, 2024. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 14749, 234-244 (2024).