This repository contains Magma code for reconstructing plane quartic curves from their Dixmier--Ohno invariants.
Please try using JRSijsling/quartic
instead whenever possible: This packages supersedes the current one.
You need to have Magma installed on your machine to use this code. These algorithms use the Magma algorithm MinimizeReducePlaneQuartic
, due to Elsenhans and Stoll, to simplify any output over the rationals. In order for this to work properly, one needs a bug fix of a function at the end of the file magma/package/Geometry/SrfDP/mindred.m
, which can be found in BugFix.m
. Alternatively, it is possible to attach this new file separately.
You can enable the functionality of this package in Magma by attaching the quartic_reconstruction/magma/spec
file with AttachSpec
. To make this independent of the directory in which you find yourself, and to active this on startup by default, you may want to indicate the relative path in your ~/.magmarc
file, by adding the line
AttachSpec("~/Programs/quartic_reconstruction/magma/spec");
An example that tests the routines in this package can be found in Example.m
.
Verbose comments are enabled by
SetVerbose("Reconstruction", n);
where n
is either 1
or 2
. A higher value gives more comments.
The papers described the algorithms for minimization and reduction algorithms that are mentioned above and that play a crucial role when using these algorithms over the rationals are:
Andreas-Stephan Elsenhans
Good models for cubic surfaces
Preprint at https://math.uni-paderborn.de/fileadmin/mathematik/AG-Computeralgebra/Preprints-elsenhans/red_5.pdf
Michael Stoll
Reduction theory of point clusters in projective space
Groups Geom. Dyn. 5 (2011), no. 2, 553-565
Preprint at arXiv:0909.2808
Please cite the following preprint if this code has been helpful in your research:
Reynald Lercier, Christophe Ritzenthaler, and Jeroen Sijsling
Reconstructing plane quartic from their invariants
Preprint at arXiv:1606.05594