# Elimination Templates in Macaulay2

arXiv: https://arxiv.org/abs/2605.00278 · HTML: https://mlsanity.com/paper/2605.00278/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 19 references that are in the map.
- First posted on arXiv 30 Apr 2026.

## Builds on (most cited first, 5 of 5)

- [Galois/monodromy groups for decomposing minimal problems in 3D reconstruction](https://mlsanity.com/paper/2105.04460/) (2021)
- [Distortion Varieties](https://mlsanity.com/paper/1610.01860/) (2016)
- [Optimizing Elimination Templates by Greedy Parameter Search](https://mlsanity.com/paper/2203.14901/) (2022)
- [GAPS: Generator for Automatic Polynomial Solvers](https://mlsanity.com/paper/2004.11765/) (2020)
- [Automatic Solver Generator for Systems of Laurent Polynomial Equations](https://mlsanity.com/paper/2307.00320/) (2023)

## Abstract (arXiv)

We introduce the package textttEliminationTemplates 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.