Noether's forms for the study of non-composite rational functions and their spectrum
| Autor: | Laurent Busé, Salah Najib, Guillaume Chèze |
|---|---|
| Přispěvatelé: | Geometry, algebra, algorithms (GALAAD), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Max Planck Institute for Mathematics in the Sciences (MPI-MiS), Max-Planck-Gesellschaft, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2011 |
| Předmět: |
FOS: Computer and information sciences
Computer Science - Symbolic Computation Pure mathematics Reduction (recursion theory) Polynomial ring Modulo [MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC] Rational function Symbolic Computation (cs.SC) Commutative Algebra (math.AC) 01 natural sciences 010305 fluids & plasmas symbols.namesake Integer 0103 physical sciences FOS: Mathematics Number Theory (math.NT) 0101 mathematics Mathematics [INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC] Algebra and Number Theory Mathematics - Number Theory 010102 general mathematics Spectrum (functional analysis) Mathematics - Commutative Algebra [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] symbols Irreducibility Noether's theorem |
| Zdroj: | Acta Arithmetica Acta Arithmetica, Instytut Matematyczny PAN, 2011, 147 (3), pp.217-231. ⟨10.4064/aa147-3-2⟩ Acta Arithmetica, 2011, 147 (3), pp.217-231. ⟨10.4064/aa147-3-2⟩ |
| DOI: | 10.4064/aa147-3-2⟩ |
| Popis: | International audience; In this paper, the spectrum and the decomposability of a multivariate rational function are studied by means of the effective Noether's irreducibility theorem given by Ruppert. With this approach, some new effective results are obtained. In particular, we show that the reduction modulo p of the spectrum of a given integer multivariate rational function r coincides with the spectrum of the reduction of r modulo p for p a prime integer greater or equal to an explicit bound. This bound is given in terms of the degree, the height and the number of variables of r. With the same strategy, we also study the decomposability of r modulo p. Some similar explicit results are also provided for the case of polynomials with coefficients in a polynomial ring. |
| Databáze: | OpenAIRE |
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