Polynomial division and Gröbner bases

Samira Zeada

Division in the ring of multivariate polynomials is usually not a part of the standard university math curriculum. However, the algorithm is elementary and it has very important consequences for algebraic computations. In this paper, the algorithm is explained and illustrated with some examples, and the importance of the choice of monomial ordering is stressed. The notion of Gröbner basis is introduced and explained on examples. The paper can be used by math students and teachers as a brief description of this very important topic and introduction for reading more detailed textbooks.