SINGULAR: A new level of abstraction and performance

Singular is a well-established computer algebra system for polynomial computations, with applications to algebra, algebraic geometry, and singularity theory. The first goal of our project is to rewrite the interpreter of the Singular user language in order to achieve a new level of expressiveness and to allow for just-in-time compilation. This will also facilitate the integration of Singular as a cornerstone of the unified computer algebra system created within the TRR 195. Our second goal is to advance massively parallel methods in computational algebraic geometry, with particular focus on syzygies, Feynman integrals, and resolutions of singularities.