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TitleAffine solution sets of sparse polynomial systems
Author(s) María Isabel Herrero, Gabriela Jeronimo, Juan Sabia
TypeArticle in Journal
AbstractThis paper focuses on the equidimensional decomposition of affine varieties defined by sparse polynomial systems. For generic systems with fixed supports, we give combinatorial conditions for the existence of positive dimensional components which characterize the equidimensional decomposition of the associated affine variety. This result is applied to design an equidimensional decomposition algorithm for generic sparse systems. For arbitrary sparse systems of n polynomials in n variables with fixed supports, we obtain an upper bound for the degree of the affine variety defined and we present an algorithm which computes finite sets of points representing its equidimensional components.
KeywordsSparse polynomial systems, Equidimensional decomposition of algebraic varieties, Degree of affine varieties, Algorithms and complexity
URL http://www.sciencedirect.com/science/article/pii/S0747717112001149
JournalJournal of Symbolic Computation
Pages34 - 54
NoteEffective Methods in Algebraic Geometry
Translation No
Refereed No