The Hydra-k partial fields

TL;DR

This paper presents computational results related to Hydra-k partial fields, which are used to study quinary matroids with inequivalent representations, by implementing extensive Mathematica calculations.

Contribution

It provides the necessary computational proofs for properties of Hydra-k partial fields, advancing the understanding of quinary matroids.

Findings

Computational proofs of properties of Hydra-k partial fields

Implementation of extensive Mathematica calculations

Enhanced understanding of inequivalent representations of quinary matroids

Abstract

In the paper "Confinement of matroid representations to subsets of partial fields" (arXiv:0806.4487) we introduced the Hydra-k partial fields to study quinary matroids with inequivalent representations. The proofs of some results on these partial fields require extensive computations. This paper contains these computations, implemented in Mathematica.