An algorithm to compute a presentation of pushforward modules

We describe an algorithm to compute a presentation of the pushforward module $f_{\ast }{\mathcal{O}}_{\mathcal{X}}$ for a finite map germ $f\colon $\mathcal{X}$\to ({$\mathbb{C}$}^{n+1},0)$,where$$\mathcal{X}$$isCohen-Macaulayofdimension$n$. 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.