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On an implementation of standard bases and syzygies in SINGULAR

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

We describe an implementation of a general standard basis algorithm, valid for any monomial ordering compatible with the natural semigroup structure. We concentrate on new strategies which have proved useful, in particular in the non-wellordering case. Moreover, we describe the first implementation of Schreyer's method to compute syzygies and compare it with other, more classical methods. Comparisons of the computing time of several examples in the system SINGULAR give hints as to which strategies should be used in different classes of examples.

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Grassmann, H., Greuel, G.M., Martin, B. et al. On an implementation of standard bases and syzygies in SINGULAR. AAECC 7, 235–249 (1996). https://doi.org/10.1007/BF01190332

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  • DOI: https://doi.org/10.1007/BF01190332

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