# Criteria for Finite Difference Groebner Bases of Normal Binomial Difference Ideals

## TL;DR

This paper establishes decision criteria and an algorithm for finite difference Groebner bases of normal binomial difference ideals, simplifying complex properties to elementary polynomial conditions.

## Contribution

It introduces novel criteria and an algorithm for finite difference Groebner bases of normal binomial difference ideals, reducing complex properties to elementary polynomial checks.

## Key findings

- Criteria for finite difference Groebner bases are established.
- An algorithm for computing these bases is provided.
- Complex properties are reduced to elementary polynomial conditions.

## Abstract

In this paper, we give decision criteria for normal binomial difference polynomial ideals in the univariate difference polynomial ring F{y} to have finite difference Groebner bases and an algorithm to compute the finite difference Groebner bases if these criteria are satisfied. The novelty of these criteria lies in the fact that complicated properties about difference polynomial ideals are reduced to elementary properties of univariate polynomials in Z[x].