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...
| Autores: | , , |
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| 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 |
| 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. |
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