The ideal of the trifocal variety

TL;DR

This paper uses advanced mathematical techniques to identify the fundamental algebraic equations defining the trifocal variety and provides a practical test for recognizing trifocal tensors.

Contribution

It introduces the minimal generators of the trifocal variety's ideal and offers an effective method to test if a tensor is trifocal, advancing algebraic geometry applications.

Findings

Derived the minimal generators of the trifocal variety's ideal

Developed an effective test for trifocal tensor identification

Applied representation theory and computational algebra techniques

Abstract

Techniques from representation theory, symbolic computational algebra, and numerical algebraic geometry are used to find the minimal generators of the ideal of the trifocal variety. An effective test for determining whether a given tensor is a trifocal tensor is also given.