8th polymake conference and developer meeting

Richard Sieg: What's new in Normaliz?

Normaliz is an open-source software for computations in rational cones and affine monoids. Normaliz offers a rich variety of input types for cones and lattices. It can be accessed from several computer algebra systems, and provides a C++ class library for use in other software, in particular polymake.

We will introduce the two main computational goals, namely the Hilbert basis and series, and give an overview of the algorithmic ideas behind the computations. We will then present some new features in Normaliz: the subdivision of large simplicial cones for significant faster computations and the Python interface PyNormaliz, which can be used as an interface to other software packages and as an interactive shell for computations.

Lars Kastner, Kristin Shaw, Anna-Lena Winz: Cellular sheaf cohomology in Polymake

This talk will be an introduction to the topics of cellular sheaves, cosheaves and their (co)homologies, together with a live presentation of their new implementation within Polymake. In particular, we will explain how cellular sheaves on discrete objects such as polytopes, fans and tropical varieties can be used to recover geometric invariants of complex algebraic varieties. These phenomenon will be illustrated with polymake examples.