Affine solution sets of sparse polynomial systems

HERRERO, MARÍA ISABEL; JERONIMO, GABRIELA; SABIA, JUAN

JOURNAL OF SYMBOLIC COMPUTATION

ACADEMIC PRESS LTD-ELSEVIER SCIENCE LTD

Lugar: Oxford; Año: 2013 vol. 51 p. 34 - 54

0747-7171

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 varietydefined and we present an algorithm which computes finite sets of points representing its equidimensional components.