## EquivariantGB Macaulay2 Package

Christopher Hillar, Robert Krone, Anton Leykin

A package for computing equivaraint Gröbner bases.

A polynomial ring over a countably infinite number of variables presents some obstacles to computation because it's not Noetherian. However often the ideals of interest in this setting are endowed with certain symmetry. If *G* is an action on the set of variables of the ring, an ideal is *G*-equivariant if it is closed under the action of *G*. For certain actions, *G*-equivariant ideals are finitely generated up to *G* action, and moreover there exist equivariant Gröbner bases for such ideals.

*EquivariantGB* computes equivariant Gröbner bases for the cases when *G* is the infinite symmetric group, or the semigroup of strictly increasing functions, where the semigroup acts diagonally on variables indexed by a tuple of natural numbers. The ring can also have several blocks of variables each with this structure.

### Code:

EquivariantGB.m2

egbexamples.m2

### MEGA 2013 resources:

Extended Abstract

Slides