Syzygy Computation

Computation of syzygies means finding generators of the module of relations among a given set of module or ideal generators; concretely, for generators g1,…,gn of an ideal I one computes all tuples (a1,…,an) with sum ai gi = 0, i.e., a presentation of the syzygy module and typically part of a free resolution.

The computation of syzygies is the process of finding relations (linear or module relations) among generators of a module or an ideal; concretely it produces generators for the syzygy module, often as part of a free resolution or via Gröbner bases.