This repository contains Magma code for reconstructing plane quartic curves from their Dixmier--Ohno invariants.
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 the file
magma/package/Geometry/SrfDP/, 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
An example that tests the routines in this package can be found in
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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:
Good models for cubic surfaces
Preprint at https://math.uni-paderborn.de/fileadmin/mathematik/AG-Computeralgebra/Preprints-elsenhans/red_5.pdf
Reduction theory of point clusters in projective space
Groups Geom. Dyn. 5 (2011), no. 2, 553-565
Preprint at arXiv:0909.2808
Citing this code
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