A test for monomial containment

TL;DR

This paper introduces an algorithm to determine monomial containment in polynomial ideals efficiently, avoiding traditional computational methods like Gr"obner bases or factorization.

Contribution

The paper proposes a novel algorithm for monomial containment that bypasses the need for Gr"obner bases, factorization, and sub-resultant computations.

Findings

Algorithm successfully determines monomial containment in polynomial ideals.

Avoids computationally intensive methods like Gr"obner bases.

Offers a potentially more efficient approach for algebraic computations.

Abstract

We present an algorithm to decide whether a given ideal in the polynomial ring contains a monomial without using Gr\"obner bases, factorization or sub-resultant computations.