STRATEGIES FOR COMPUTING MINIMAL FREE RESOLUTIONS

In the present paper we study algorithms based on the theory of Grobne r bases for computing free resolutions of modules over polynomial ring s. We propose a technique which consists in the application of special selection strategies to the Schreyer algorithm. The resulting algorit hm is efficient and, in the graded case, allows a straightforward mini malization algorithm. These techniques generalize to factor rings, ske w commutative rings, and some non-commutative rings. Finally, the prop osed approach is compared with other algorithms by means of an impleme ntation developed in the new system Macaulay2. (C) 1998 Academic Press .