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http://hdl.handle.net/11320/14668
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Pole DC | Wartość | Język |
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dc.contributor.author | Pąk, Karol | - |
dc.date.accessioned | 2023-02-15T10:42:33Z | - |
dc.date.available | 2023-02-15T10:42:33Z | - |
dc.date.issued | 2022 | - |
dc.identifier.citation | Formalized Mathematics, Volume 30, Issue 3, Pages 169-198 | pl |
dc.identifier.issn | 1426-2630 | - |
dc.identifier.uri | http://hdl.handle.net/11320/14668 | - |
dc.description.abstract | The main purpose of the article is to construct a sophisticated polynomial proposed by Matiyasevich and Robinson [5] that is often used toreduce the number of unknowns in diophantine representations, using the Mizar[1], [2] formalism. The polynomial Jk(a1,...ak, x) =∏ ( X+ϵ₁ √(a₁) = ϵ₂ √(a₂)W +…+ ϵk √ak W^(k-1)) ϵ₁…. ϵk ϵ {±1} with W=∑_(i=1)^k x(2¦1)has integer coefficients and Jk(a1,...ak, x) = 0 for some a1,...,ak, x ∈ Z if and only if a1,...,ak are all squares. However although it is nontrivial to observe that this expression is a polynomial, i.e., eliminating similarelements in the product of all combinations of signs we obtain an expression where every square root will occur with an even power. This work has been partially presented in [7]. | pl |
dc.language.iso | en | pl |
dc.publisher | DeGruyter Open | pl |
dc.rights | Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) | pl |
dc.rights | CC BY-SA 3.0 license | pl |
dc.rights.uri | https://creativecommons.org/licenses/by-sa/3.0/ | pl |
dc.subject | polynomial reduction | pl |
dc.subject | diophantine equation | pl |
dc.title | Prime Representing Polynomial with 10 Unknowns – Introduction | pl |
dc.type | Article | pl |
dc.rights.holder | © 2022 The Author(s) | pl |
dc.rights.holder | CC BY-SA 3.0 license | pl |
dc.identifier.doi | 10.2478/forma-2022-0013 | - |
dc.description.Affiliation | Karol Pąk - Institute of Computer Science, University of Białystok, Poland | pl |
dc.description.references | Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Vol-ker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615_817. | pl |
dc.description.references | Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32,2018. doi:10.1007/s10817-017-9440-6. | pl |
dc.description.references | Marco B. Caminati. Preliminaries to classical first order model theory. Formalized Mathe-matics, 19(3):155–167, 2011. doi:10.2478/v10037-011-0025-2. | pl |
dc.description.references | Taneli Huuskonen. Polish notation. Formalized Mathematics, 23(3):161–176, 2015.doi:10.1515/forma-2015-0014. | pl |
dc.description.references | Yuri Matiyasevich and Julia Robinson. Reduction of an arbitrary diophantine equation toone in 13 unknowns. Acta Arithmetica, 27:521–553, 1975. | pl |
dc.description.references | Karol Pąk. Stirling numbers of the second kind. Formalized Mathematics, 13(2):337–345,2005. | pl |
dc.description.references | Karol Pąk and Cezary Kaliszyk. Formalizing a diophantine representation of the set of prime numbers. In June Andronick and Leonardo de Moura, editors,13th International Conference on Interactive Theorem Proving, ITP 2022, August 7-10, 2022, Haifa, Israel, volume 237 of LIPIcs, pages 26:1–26:8. Schloss Dagstuhl - Leibniz-Zentrum für Informatik,2022. doi:10.4230/LIPIcs.ITP.2022.26 | pl |
dc.identifier.eissn | 1898-9934 | - |
dc.description.volume | 30 | pl |
dc.description.issue | 3 | pl |
dc.description.firstpage | 169 | pl |
dc.description.lastpage | 198 | pl |
dc.identifier.citation2 | Formalized Mathematics | pl |
Występuje w kolekcji(ach): | Artykuły naukowe (WInf) Formalized Mathematics, 2022, Volume 30, Issue 3 |
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