The 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.
|Autori:||FORTUNA E; GIANNI P; TRAGER B|
|Titolo:||Derivations and radicals of polynomial ideals over fields of arbitrary characteristic|
|Anno del prodotto:||2002|
|Digital Object Identifier (DOI):||10.1006/jsco.2002.0525|
|Appare nelle tipologie:||1.1 Articolo in rivista|