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TitleDerivations and radicals of polynomial ideals over fields of arbitrary characteristic
Author(s) Elisabetta Fortuna, Patrizia M. Gianni, Barry M. Trager
TypeArticle in Journal
AbstractThe purpose of this paper is to give a complete effective solution to the problem of computing radicals of polynomial ideals over general fields of arbitrary characteristic. We prove that Seidenberg’s "Condition P" is both a necessary and sufficient property of the coefficient field in order to be able to perform this computation. Since Condition P is an expensive additional requirement on the ground field, we use derivations and ideal quotients to recover as much of the radical as possible. If we have a basis for the vector space of derivations on our ground field, then the problem of computing radicals can be reduced to computing p th roots of elements in finite dimensional algebras.
Length17
ISSN0747-7171
CopyrightElsevier Science Ltd.
File
URL dx.doi.org/10.1006/jsco.2002.0525
LanguageEnglish
JournalJournal of Symbolic Computation
Volume33
Number5
Pages609-625
PublisherAcademic Press, Inc.
AddressDuluth, MN, USA
Year2002
MonthMay
Translation No
Refereed No
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