Introduction

Most functions discussed in this chapter rely on Gröbner basis techniques. They either execute corresponding Singular functionality, or are written as pieces of OSCAR code which rely on Singular for Gröbner basis computations. The functions are implemented for multivariate polynomial rings over fields (exact fields supported by OSCAR) and, if not indicated otherwise, for multivariate polynomial rings over the integers.

OSCAR provides functionality for equipping multivariate polynomial rings with gradings. These gradings descend to quotients of multivariate polynomial rings modulo homogeneous ideals. A large majority of the functions discussed in what follows apply to both the ungraded and graded case. For simplicity of the presentation in this documentation, however, such functions are often only illustrated by examples with focus on the former case, but work similarly for homogeneous ideals and graded modules in the latter case.