Polynomial equation solving by lifting procedures for ramified fibers
Let be given a parametric polynomial equation system which represents a generically unramified family of zero-dimensional algebraic varieties. We exhibit an efficient algorithm which computes a complete description of the solution set of an arbitrary parameter instance from a complete description of...
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2004
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03043975_v315_n2-3_p335_Bompadre http://hdl.handle.net/20.500.12110/paper_03043975_v315_n2-3_p335_Bompadre |
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paper:paper_03043975_v315_n2-3_p335_Bompadre2023-06-08T15:29:35Z Polynomial equation solving by lifting procedures for ramified fibers Efficient polynomial equation solving Newton-Hensel lifting Puiseux expansions of space curves Ramified fibers of dominant mappings Algebra Algorithms Iterative methods Parameter estimation Problem solving Theorem proving Vectors Efficient polynomial equation solving Newton-Hensel lifting Puiseux expansions of space curves Ramified fibers of dominant mappings Polynomials Let be given a parametric polynomial equation system which represents a generically unramified family of zero-dimensional algebraic varieties. We exhibit an efficient algorithm which computes a complete description of the solution set of an arbitrary parameter instance from a complete description of the infinitesimal structure of a particular ramified parameter instance of our family. This generalizes in the case of space curves previous methods of Heintz et al. and Schost, which require the given parameter instance to be unramified. We illustrate our method solving particular polynomial equation systems by deformation techniques. © 2004 Elsevier B.V. All rights reserved. 2004 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03043975_v315_n2-3_p335_Bompadre http://hdl.handle.net/20.500.12110/paper_03043975_v315_n2-3_p335_Bompadre |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Efficient polynomial equation solving Newton-Hensel lifting Puiseux expansions of space curves Ramified fibers of dominant mappings Algebra Algorithms Iterative methods Parameter estimation Problem solving Theorem proving Vectors Efficient polynomial equation solving Newton-Hensel lifting Puiseux expansions of space curves Ramified fibers of dominant mappings Polynomials |
| spellingShingle |
Efficient polynomial equation solving Newton-Hensel lifting Puiseux expansions of space curves Ramified fibers of dominant mappings Algebra Algorithms Iterative methods Parameter estimation Problem solving Theorem proving Vectors Efficient polynomial equation solving Newton-Hensel lifting Puiseux expansions of space curves Ramified fibers of dominant mappings Polynomials Polynomial equation solving by lifting procedures for ramified fibers |
| topic_facet |
Efficient polynomial equation solving Newton-Hensel lifting Puiseux expansions of space curves Ramified fibers of dominant mappings Algebra Algorithms Iterative methods Parameter estimation Problem solving Theorem proving Vectors Efficient polynomial equation solving Newton-Hensel lifting Puiseux expansions of space curves Ramified fibers of dominant mappings Polynomials |
| description |
Let be given a parametric polynomial equation system which represents a generically unramified family of zero-dimensional algebraic varieties. We exhibit an efficient algorithm which computes a complete description of the solution set of an arbitrary parameter instance from a complete description of the infinitesimal structure of a particular ramified parameter instance of our family. This generalizes in the case of space curves previous methods of Heintz et al. and Schost, which require the given parameter instance to be unramified. We illustrate our method solving particular polynomial equation systems by deformation techniques. © 2004 Elsevier B.V. All rights reserved. |
| title |
Polynomial equation solving by lifting procedures for ramified fibers |
| title_short |
Polynomial equation solving by lifting procedures for ramified fibers |
| title_full |
Polynomial equation solving by lifting procedures for ramified fibers |
| title_fullStr |
Polynomial equation solving by lifting procedures for ramified fibers |
| title_full_unstemmed |
Polynomial equation solving by lifting procedures for ramified fibers |
| title_sort |
polynomial equation solving by lifting procedures for ramified fibers |
| publishDate |
2004 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03043975_v315_n2-3_p335_Bompadre http://hdl.handle.net/20.500.12110/paper_03043975_v315_n2-3_p335_Bompadre |
| _version_ |
1768545647527460864 |