On constructing resolutions over the polynomial

摘要

Let $k$ be a field, and $A$ be a polynomial algebra over $k$. Let $Isubseteq A$ be an ideal. We present a novel method for computing resolutions of $A/I$ over $A$. The method is a synthesis of Gr?bner basis techniques and homological perturbation theory. The examples in this paper were computed using computer algebra.