Computing zero-dimensional schemes
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. (C) 2004 Elsevier Ltd. All rights reserved.
zero-dimensional schemes fat points grobner basis algorithm