Affine solution sets of sparse polynomial systems

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...

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Detalles Bibliográficos
Autores: Herrero, Maria Isabel, Jeronimo, Gabriela Tali, Sabia, Juan Vicente Rafael
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2013
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/85174
Acceso en línea:http://hdl.handle.net/11336/85174
Access Level:acceso abierto
Palabra clave:ALGORITHMS AND COMPLEXITY
DEGREE OF AFFINE VARIETIES
EQUIDIMENSIONAL DECOMPOSITION OF ALGEBRAIC VARIETIES
SPARSE POLYNOMIAL SYSTEMS
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario: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.