DiffAlg: a Differential Algebra Package

Abstract

In this article we present DiffAlg.m2, a differential algebra package for Macaulay2. It can perform the following operations: wedge products and exterior differentials of differential forms, contraction and Lie derivatives of differential forms with respect to a vector field and Lie brackets between vector fields. Given a homogeneous differential operator of degree one D, the lack of an algebraic module structure attached to the kernel or image of D hinders the study of D. The main purpose of DiffAlg.m2 is to handle these spaces degree-wise.