compcox.lib -
a Singular package for
Cox ring computations

Ulrich Derenthal, Armand Heim, Jürgen Hausen,
Simon Keicher, Antonio Laface
Current version: May 2015


This is the accompanying software package of the paper "Cox rings of cubic surfaces and smooth Fano threefolds". It implements the algorithms developed in "Computing Cox rings" to compute Cox rings of modifications.

This is a package for the computer algebra system Singular.


Given a modification \(X_2 \to X_1\) of projective varieties, e.g., a series of blow ups, where one of the Cox rings \(\mathcal{R}(X_i)\) is known, this package provides procedures to obtain the other Cox ring. This includes algorithms to

  • verify finite generation of \(\mathcal{R}(X_i)\),
  • verify a guess of generators for \(\mathcal{R}(X_i)\),
  • produce a guess of generators for \(\mathcal{R}(X_2)\),
  • present the new Cox ring by generators and relations.