A Koszul Decomposition for the Computation of Linear Syzygies

Abstract.

In the present paper some algorithms are proposed for computing Linear Strands and Betti Numbers of graded modules over polynomial rings. These algorithms are based on a block-decomposition, induced by the Koszul syzygies, of the linear systems involved with the Hilbert's method for computing syzygies. Some further optimizations are suggested and applied by the authors to an implementation they have developed of the algorithms.