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 |
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todo:paper_00243795_v439_n10_p3016_Perrucci2023-10-03T14:34:47Z Zero-nonzero and real-nonreal sign determination Perrucci, D. Roy, M.-F. Complexity Polynomial equations and inequations systems Sign determination Bit complexity Complexity Finite set Polynomial equation Sign determination Polynomials Algorithms 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00243795_v439_n10_p3016_Perrucci |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (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 |
JOUR |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_00243795_v439_n10_p3016_Perrucci |
| work_keys_str_mv |
AT perruccid zerononzeroandrealnonrealsigndetermination AT roymf zerononzeroandrealnonrealsigndetermination |
| _version_ |
1807319294398169088 |