# GAPS: Generator for Automatic Polynomial Solvers

arXiv: https://arxiv.org/abs/2004.11765 · HTML: https://mlsanity.com/paper/2004.11765/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Apr 2020.

## Built on by (most cited first, 7 of 7)

- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [Snapshot of Algebraic Vision](https://mlsanity.com/paper/2210.11443/) (2022)
- [GPU-Based Homotopy Continuation for Minimal Problems in Computer Vision](https://mlsanity.com/paper/2112.03444/) (2021)
- [Handbook on Leveraging Lines for Two-View Relative Pose Estimation](https://mlsanity.com/paper/2309.16040/) (2023)
- [Trifocal Tensor and Relative Pose Estimation with Known Vertical Direction](https://mlsanity.com/paper/2512.19110/) (2025)
- [Elimination Templates in Macaulay2](https://mlsanity.com/paper/2605.00278/) (2026)
- [Solving Minimal Problems Without Matrix Inversion Using FFT-Based Interpolation](https://mlsanity.com/paper/2605.06572/) (2026)

## Abstract (arXiv)

Minimal problems in computer vision raise the demand of generating efficient automatic solvers for polynomial equation systems. Given a polynomial system repeated with different coefficient instances, the traditional Gr"obner basis or normal form based solution is very inefficient. Fortunately the Gr"obner basis of a same polynomial system with different coefficients is found to share consistent inner structure. By precomputing such structures offline, Gr"obner basis as well as the polynomial system solutions can be solved automatically and efficiently online. In the past decade, several tools have been released to generate automatic solvers for a general minimal problems. The most recent tool autogen from Larsson et al. is a representative of these tools with state-of-the-art performance in solver efficiency. GAPS wraps and improves autogen with more user-friendly interface, more functionality and better stability. We demonstrate in this report the main approach and enhancement features of GAPS. A short tutorial of the software is also included.