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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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_07477171_v51_n_p34_Herrero |
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todo:paper_07477171_v51_n_p34_Herrero2023-10-03T15:38:59Z Affine solution sets of sparse polynomial systems Herrero, M.I. Jeronimo, G. Sabia, J. Algorithms and complexity Degree of affine varieties Equidimensional decomposition of algebraic varieties 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 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. © 2012 Elsevier B.V. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_07477171_v51_n_p34_Herrero |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Algorithms and complexity Degree of affine varieties Equidimensional decomposition of algebraic varieties Sparse polynomial systems |
| spellingShingle |
Algorithms and complexity Degree of affine varieties Equidimensional decomposition of algebraic varieties Sparse polynomial systems Herrero, M.I. Jeronimo, G. Sabia, J. Affine solution sets of sparse polynomial systems |
| topic_facet |
Algorithms and complexity Degree of affine varieties Equidimensional decomposition of algebraic varieties Sparse polynomial systems |
| description |
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. © 2012 Elsevier B.V. |
| format |
JOUR |
| author |
Herrero, M.I. Jeronimo, G. Sabia, J. |
| author_facet |
Herrero, M.I. Jeronimo, G. Sabia, J. |
| author_sort |
Herrero, M.I. |
| title |
Affine solution sets of sparse polynomial systems |
| title_short |
Affine solution sets of sparse polynomial systems |
| title_full |
Affine solution sets of sparse polynomial systems |
| title_fullStr |
Affine solution sets of sparse polynomial systems |
| title_full_unstemmed |
Affine solution sets of sparse polynomial systems |
| title_sort |
affine solution sets of sparse polynomial systems |
| url |
http://hdl.handle.net/20.500.12110/paper_07477171_v51_n_p34_Herrero |
| work_keys_str_mv |
AT herreromi affinesolutionsetsofsparsepolynomialsystems AT jeronimog affinesolutionsetsofsparsepolynomialsystems AT sabiaj affinesolutionsetsofsparsepolynomialsystems |
| _version_ |
1807318897483841536 |