# A lattice formulation of the F4 completion procedure

## TL;DR

This paper introduces a lattice-based method for constructing noncommutative Groebner bases using reduction operators, connecting it to the F4 algorithm through Gaussian elimination, and provides an implementation example.

## Contribution

It presents a novel lattice formulation for noncommutative Groebner basis computation, linking it to the F4 algorithm and demonstrating its practical implementation.

## Key findings

- Lattice construction enables simultaneous reduction of S-polynomials.
- Reduction operators facilitate efficient normal form computation.
- The method relates to the F4 algorithm via Gaussian elimination.

## Abstract

We write a procedure for constructing noncommutative Groebner bases. Reductions are done by particular linear projectors, called reduction operators. The operators enable us to use a lattice construction to reduce simultaneously each S-polynomial into a unique normal form. We write an implementation as well as an example to illustrate our procedure. Moreover, the lattice construction is done by Gaussian elimination, which relates our procedure to the F4 algorithm for constructing commutative Groebner bases.