Affine solution sets of sparse polynomial systems

作者：Isabel Herrero Maria; Jeronimo Gabriela; Sabia Juan

来源：Journal of Symbolic Computation, 2013, 51: 34-54.

DOI：10.1016/j.jsc.2012.03.006

• Sparse polynomial systems
• Equidimensional decomposition of algebraic varieties
• Degree of affine varieties
• Algorithms and complexity

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.

• 出版日期2013-4