Zero-nonzero and real-nonreal sign determination
We consider first the zero-nonzero determination problem, which consists in determining the list of zero-nonzero conditions realized by a finite list of polynomials on a finite set ZâŠCk with C an algebraic closed field. We describe an algorithm to solve the zero-nonzero determination problem and we...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00243795_v439_n10_p3016_Perrucci https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00243795_v439_n10_p3016_Perrucci_oai |
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I28-R145-paper_00243795_v439_n10_p3016_Perrucci_oai2024-08-16 Perrucci, D. Roy, M.-F. 2013 We consider first the zero-nonzero determination problem, which consists in determining the list of zero-nonzero conditions realized by a finite list of polynomials on a finite set ZâŠCk with C an algebraic closed field. We describe an algorithm to solve the zero-nonzero determination problem and we perform its bit complexity analysis. This algorithm, which is in many ways an adaptation of the methods used to solve the more classical sign determination problem, presents also new ideas which can be used to improve sign determination. Then, we consider the real-nonreal sign determination problem, which deals with both the sign determination and the zero-nonzero determination problem. We describe an algorithm to solve the real-nonreal sign determination problem, we perform its bit complexity analysis and we discuss this problem in a parametric context. © 2013 Elsevier Inc. Fil:Perrucci, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. application/pdf http://hdl.handle.net/20.500.12110/paper_00243795_v439_n10_p3016_Perrucci info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar Linear Algebra Its Appl 2013;439(10):3016-3030 Complexity Polynomial equations and inequations systems Sign determination Bit complexity Complexity Finite set Polynomial equation Sign determination Polynomials Algorithms Zero-nonzero and real-nonreal sign determination info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00243795_v439_n10_p3016_Perrucci_oai |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-145 |
| collection |
Repositorio Digital de la Universidad de Buenos Aires (UBA) |
| topic |
Complexity Polynomial equations and inequations systems Sign determination Bit complexity Complexity Finite set Polynomial equation Sign determination Polynomials Algorithms |
| spellingShingle |
Complexity Polynomial equations and inequations systems Sign determination Bit complexity Complexity Finite set Polynomial equation Sign determination Polynomials Algorithms Perrucci, D. Roy, M.-F. Zero-nonzero and real-nonreal sign determination |
| topic_facet |
Complexity Polynomial equations and inequations systems Sign determination Bit complexity Complexity Finite set Polynomial equation Sign determination Polynomials Algorithms |
| description |
We consider first the zero-nonzero determination problem, which consists in determining the list of zero-nonzero conditions realized by a finite list of polynomials on a finite set ZâŠCk with C an algebraic closed field. We describe an algorithm to solve the zero-nonzero determination problem and we perform its bit complexity analysis. This algorithm, which is in many ways an adaptation of the methods used to solve the more classical sign determination problem, presents also new ideas which can be used to improve sign determination. Then, we consider the real-nonreal sign determination problem, which deals with both the sign determination and the zero-nonzero determination problem. We describe an algorithm to solve the real-nonreal sign determination problem, we perform its bit complexity analysis and we discuss this problem in a parametric context. © 2013 Elsevier Inc. |
| format |
Artículo Artículo publishedVersion |
| author |
Perrucci, D. Roy, M.-F. |
| author_facet |
Perrucci, D. Roy, M.-F. |
| author_sort |
Perrucci, D. |
| title |
Zero-nonzero and real-nonreal sign determination |
| title_short |
Zero-nonzero and real-nonreal sign determination |
| title_full |
Zero-nonzero and real-nonreal sign determination |
| title_fullStr |
Zero-nonzero and real-nonreal sign determination |
| title_full_unstemmed |
Zero-nonzero and real-nonreal sign determination |
| title_sort |
zero-nonzero and real-nonreal sign determination |
| publishDate |
2013 |
| url |
http://hdl.handle.net/20.500.12110/paper_00243795_v439_n10_p3016_Perrucci https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00243795_v439_n10_p3016_Perrucci_oai |
| work_keys_str_mv |
AT perruccid zerononzeroandrealnonrealsigndetermination AT roymf zerononzeroandrealnonrealsigndetermination |
| _version_ |
1809357077341011968 |