An algorithm to compute a presentation of pushforward modules

We describe an algorithm to compute a presentation of the pushforward module $f_*{\mathcal O}_{\mathcal{X}}$ for a finite map germ $f\colon \mathcal{X}\to ({\mathbb{C}}^{n+1},0)$, where $\mathcal{X}$ is Cohen-Macaulay of dimension $n$. The algorithm is an improvement of a method by Mond and Pellikaan. We give applications to problems in singularity theory, computed by means of an implementation in the software Singular.