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Software

gfanlib.so - a Singular interface to Gfanlib and more

"gfanlib.so" is a binary library for Singular that enables basic features of convex geometry through an interface to Gfanlib.

It contains cones, polytopes and fans as well as basic functions thereon. Moreover, it contains algorithms for computing Gröbner fans, Gröbner complexes and tropical varieties. For example, given a cone by inequalities and equations, compute its rays and its lineality space, or, given an ideal over the rational numbers, compute its tropical variety with respect to the trivial or the p-adic valuation.

This library is part of the official Singular distribution.

polymake.so - a Singular interface to polymake

"polymake.so" is a binary library for Singular that enables selected features of polymake through an interface to it. Example include, hilbertBasis of cones, interior points and minkowski sums of polytopes, provided the local Polymake installation is capable of computing them (some features of Polymake depend on other third party software).

This library is part of the official Singular distribution.

gitfan.lib - a Singular library for computing GIT fans

"gitfan.lib" is a Singular library for computing the GIT-fan of an affine variety, which describes the variation of possible GIT quotients with respect to torus actions depending on the choice of the line bundle. One of the focuses hereby is to exploit potential symmetries in the ideal, which translate to transformation matrices under which the fan is invariant.

Geometric invariant theory was developed by Mumford, the GIT fan was introduced through the works of Thaddeus and Dolgachev, Hu, and the special case of the torus action was treated by Berchthold, Hausen and Keicher.

This library is part of the official Singular distribution, though the symmetry features are not made public yet, it is joint work with Janko Boehm and Simon Keicher.

graal.lib - a Singular library for computing in localizations at prime ideals

"graal.lib" is a Singular library for a computational treatment of localizations at prime ideals and their associated graded rings based on a work of Mora. Not only does it construct a ring isomorphic to the localization of an affine coordinate ring at a prime ideal, the algorithms in this library aim to exploit the topology in the localization by computing first and foremost in the associated graded ring and lifting the result to the localization afterwards. Features include a check for regularity and the resolution of ideals.

This library is part of the official Singular distribution. It is joint work with Magdaleen Marais.

divisors.lib - a Singular library for divisors and polyhedral divisors

"divisors.lib" is a Singular library which encapsules a custom class for divisors on algebraic varieties, including methods for computing with them. This includes the group structure, the computation of global sections and a test for linear equivalence.

Additionally, we provide a custom class for polyhedral divisors as introduced in the work of Altmann, Hausen on polyhedral divisors and algebraic torus actions. They are a natural generalization of the construction of affine toric varieties and can be used to shave off an effective torus action on an affine variety to a polyhedral structure.

This library is part of the official distribution of Singular, it is joint work with Janko Boehm, Lars Kastner, Benjamin Lorenz and Hans Schönemann.

Singular online

Singular online is an online plattform for Singular. In addition, it hosts various interactive tutorials. It is based on the Interactive Shell framework by Franziska Hinkelmann, Lars Kastner and Mike Stillman.

Singular online is joint work with Franziska Hinkelmann, Lars Kastner and Mike Stillman.