arXiv subjects
Publications and source records attributed to Antony Della Vecchia.
We discuss implementation details of OSCAR's serialization framework, highlighting the design decisions that allow the fine tuning of serialization methods for specific use cases. In particular, we show how the mrdi file format can be used for distributed computing.
We introduce the AlgebraicStatistics section of the OSCAR computer algebra system. We give an overview of its extensible design and highlight its features including serialization of data types for sharing results and creating databases, and state-of-the-art implicitization algorithms.
Improved algorithms for computing (partial and full) exterior algebraic shifts of hypergraphs and simplicial complexes are presented. The main benefit is in positive characteristic. Experiments with an implementation in OSCAR with various inputs such as bipartite graphs and triangulations of two and three dimensional manifolds show that the method considerably extends for which simplicial complexes exterior algebraic shifts can be computed in practice.
We describe a generic JSON based file format which is suitable for computations in computer algebra. This is implemented in the computer algebra system OSCAR, but we also indicate how it can be used in a different context.
We study algebraic shifting of uniform hypergraphs and finite simplicial complexes in the exterior algebra with respect to matrices which are not necessarily generic. Several questions raised by Kalai (2002) are addressed. For instance, it turns out that the combinatorial shifting of Erdős$\unicode{x2013}$Ko$\unicode{x2013}$Rado (1961) arises as a special case. Moreover, we identify a sufficient condition for partial shifting to preserve the Betti numbers of a simplicial complex; examples show that this condition is sharp.