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Recursive Computation of Free Resolutions and a Generalized Koszul Complex

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Abstract.

This article describes a new algorithm to compute a free resolution of an ideal of (or module over) a commutative ring R combining the Koszul complex with Groebner basis methods. The algorithm computes the resolution of an ideal I via the resolutions of a sequence of subideals \({{(0)=I_0 \subset\ldots\subset I_r = I}}\) differing by one generator each time. The article discusses special orderings and criteria applicable to this algorithm and gives some timings based on an implementation within the computer algebra system Singular.

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  1. Parkstrasse 12, 15344, Strausberg, Germany

    Thomas Siebert

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  1. Thomas Siebert
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Correspondence to Thomas Siebert.

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Keywords: Free resolution, Koszul complex, Syzygies, Groebner basis algorithm.

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Siebert, T. Recursive Computation of Free Resolutions and a Generalized Koszul Complex. AAECC 14, 133–149 (2003). https://doi.org/10.1007/s00200-003-0120-x

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  • DOI: https://doi.org/10.1007/s00200-003-0120-x

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