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TitleOn a generalization of Stickelbergerís Theorem
Author(s) Peter Scheiblechner
TypeArticle in Journal
AbstractWe prove two versions of Stickelbergerís 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 ( n log d )^O ( 1 ) ( d^O ( n^4 ) ). In the case of a hypersurface, the complexity drops to O ( n^2 log^2 d ) ( d O ( n ) ). In the proof of the last result we use the effective Nullstellensatz for two polynomials, which we also prove by very elementary methods.
KeywordsStickelbergerís Theorem, Connected components, Irreducible components, Effective Nullstellensatz
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717110001008
LanguageEnglish
JournalJournal of Symbolic Computation
Volume45
Number12
Pages1459 - 1470
Year2010
NoteMEGAí2009
Edition0
Translation No
Refereed No
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