info:eu-repo/semantics/article
Affine solution sets of sparse polynomial systems
Fecha
2013-04Registro en:
Herrero, Maria Isabel; Jeronimo, Gabriela Tali; Sabia, Juan Vicente Rafael; Affine solution sets of sparse polynomial systems; Academic Press Ltd - Elsevier Science Ltd; Journal Of Symbolic Computation; 51; 4-2013; 34-54
0747-7171
CONICET Digital
CONICET
Autor
Herrero, Maria Isabel
Jeronimo, Gabriela Tali
Sabia, Juan Vicente Rafael
Resumen
This 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.