Netherlands\
- |
     Department of Mathematics and Computer Science\
    Technische Universiteit Eindhoven\
    P.O. Box 513, 5600 MB Eindhoven, The Netherlands\
    and Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands
author:
- 'Andries E. Brouwer'
- Jan Draisma
title: 'Equivariant Gröbner bases and the Gaussian two-factor model'
---

[^1]

Introduction and results
========================

Equivariant Gröbner bases {#equivariant-gröbner-bases .unnumbered}
-------------------------

Algebraic varieties arising from applications often have many symmetries. When analysing such varieties with tools from computational algebra, it is desirable to do so in an [*equivariant*]{} manner, that is, while keeping track of those symmetries, and if possible exploiting them. The notion of [*Gröbner basis*]{}, which lies at the heart of computational algebra, depends heavily on choices of [*coordinates*]{} and of a [*term order*]{}, which is a well-order on monomials in the coordinates. It is therefore natural, at least from a computational point of view, to study symmetries of ideals that preserve both the coordinates and the term order. Now the term [*symmetry*]{} is usually reserved for certain invertible maps, but it is easy to see that an invertible map cannot preserve a well-order; see Remark \[re:WhyMonoid\]. Hence we are led to relax the condition that symmetries be invertible. On the 