Automating the Calculation of Hilbert-Kunz Multiplicities and F-Signatures

TL;DR

This paper introduces software that automates the calculation of Hilbert-Kunz multiplicities and F-signatures for intersection algebras over polynomial rings, aiding researchers in algebraic geometry.

Contribution

It provides the first automation tool for computing these invariants specifically for intersection algebras over polynomial rings.

Findings

Successful implementation of the software for specific algebra classes

Demonstrated efficiency and accuracy of the automated calculations

Facilitated further research in algebraic invariants

Abstract

The Hilbert-Kunz multiplicity and $F$-signature are important invariants for researchers in commutative algebra and algebraic geometry. We provide software, and describe the automation of a calculation, for the two invariants in the case of intersection algebras over polynomial rings.