On a generalization of Stickelberger’s Theorem

We prove two versions of Stickelberger’s Theorem for positive dimensions and use them to compute the connected and irreducible components of a complex algebraic variety. If the variety is given by polynomials of degree ≤d in n variables, then our algorithms run in parallel (sequential) time (nlogd)O...

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Bibliographic Details
Published in:Journal of symbolic computation 2010-12, Vol.45 (12), p.1459-1470
Main Author: Scheiblechner, Peter
Format: Article
Language:English
Subjects:
Connected components
Effective Nullstellensatz
Irreducible components
Stickelberger’s Theorem
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Summary:We prove two versions of Stickelberger’s Theorem for positive dimensions and use them to compute the connected and irreducible components of a complex algebraic variety. If the variety is given by polynomials of degree ≤d in n variables, then our algorithms run in parallel (sequential) time (nlogd)O(1) (dO(n4)). In the case of a hypersurface, the complexity drops to O(n2log2d) (dO(n)). In the proof of the last result we use the effective Nullstellensatz for two polynomials, which we also prove by very elementary methods.
ISSN:0747-7171
1095-855X
DOI:10.1016/j.jsc.2010.06.020