Computing zero-dimensional schemes

Authors:
J. Abbott;M. Kreuzer;L. Robbiano
Affiliations:
Department of Mathematics, University of Genova, 16146 Genova, Italy;Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany;Department of Mathematics, University of Genova, 16146 Genova, Italy
Venue:
Journal of Symbolic Computation
Year:
2005

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Abstract

This paper is a natural continuation of Abbott et al. [Abbott, J., Bigatti, A., Kreuzer, M., Robbiano, L., 2000. Computing ideals of points. J. Symbolic Comput. 30, 341-356] further generalizing the Buchberger-Moller algorithm to zero-dimensional schemes in both affine and projective spaces. We also introduce a new, general way of viewing the problems which can be solved by the algorithm: an approach which looks to be readily applicable in several areas. Implementation issues are also addressed, especially for computations over Q where a trace-lifting paradigm is employed. We give a complexity analysis of the new algorithm for fat points in affine space over Q. Tables of timings show the new algorithm to be efficient in practice.