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On Constructing Resolutions Over the Polynomial Algebra

Leif Johansson, Larry Lambe and Emil Sköldberg

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

Homology, Homotopy and Applications, Vol. 4(2), 2002, pp. 315-336

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