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TitleOn inverse systems and squarefree decomposition of zero-dimensional polynomial ideals
Author(s) Werner Heiß, Ulrich Oberst, Franz Pauer
TypeArticle in Journal
AbstractLet I be a zero-dimensional ideal in a polynomial ring F[s]:= F[s_1, ,s_n] over an arbitrary field F . We show how to compute an F -basis of the inverse system I^⊥ of I . We describe the F[s] -module I^⊥ by generators and relations and characterise the minimal length of a system of F[s] -generators of I^⊥. If the primary decomposition of I is known, such a system can be computed. Finally we generalise the well-known notion of squarefree decomposition of a univariate polynomial to the case of zero-dimensional ideals in F[s] and present an algorithm to compute this decomposition.
KeywordsDual basis, Inverse system, Squarefree decomposition, Systems of generators of minimal length
URL http://www.sciencedirect.com/science/article/pii/S074771710500132X
JournalJournal of Symbolic Computation
Pages261 - 284
NoteLogic, Mathematics and Computer Science: Interactions in honor of Bruno Buchberger (60th birthday)
Translation No
Refereed No