This paper generalizes the Buchberger-M\"oller 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~$\bbb Q$ where a trace-lifting paradigm is employed. We give a complexity analysis of the new algorithm for fat points in affine space over~$\bbb Q$. Tables of timings show the new algorithm to be efficient in practice.

Computing zero-dimensional schemes

ABBOTT, JOHN ANTHONY;ROBBIANO, LORENZO
2005

Abstract

This paper generalizes the Buchberger-M\"oller 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~$\bbb Q$ where a trace-lifting paradigm is employed. We give a complexity analysis of the new algorithm for fat points in affine space over~$\bbb Q$. Tables of timings show the new algorithm to be efficient in practice.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11567/267480
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