Elimination Templates in Macaulay2

TL;DR

The paper presents a Macaulay2 package called EliminationTemplates for constructing automatic solvers for parameter-dependent zero-dimensional radical ideals, with applications in computer vision.

Contribution

It introduces a new Macaulay2 package that automates the construction of elimination templates for parameterized polynomial systems, with detailed construction and specialization methods.

Findings

Provides a self-contained description of elimination template construction.

Demonstrates package usage on computer vision examples.

Facilitates solving parameter-dependent polynomial systems automatically.

Abstract

We introduce the package \texttt{EliminationTemplates} for the Macaulay2 computer algebra system, which provides tools for constructing automatic solvers for families of zero-dimensional radical ideals depending on algebraically independent parameters. This article provides a self-contained description of how elimination templates are constructed for such families and their specialization properties. Additionally, we describe the main functionality and datatypes provided by our package, and illustrate its usage on several examples, including applications from computer vision from which elimination templates originated.