An algorithm to compute a presentation of pushforward modules

We describe an algorithm to compute a presentation of the pushforward module f⁎OX for a finite map germ f:X→(Cn+1,0), where 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.