Diophantine sets. Preliminaries

Pole DC	Wartość	Język
dc.contributor.author	Pąk, Karol	-
dc.date.accessioned	2018-08-20T06:41:53Z	-
dc.date.available	2018-08-20T06:41:53Z	-
dc.date.issued	2018	-
dc.identifier.citation	Formalized Mathematics, Volume 26, Issue 1, Pages 81–90	-
dc.identifier.issn	1426-2630	-
dc.identifier.uri	http://hdl.handle.net/11320/6835	-
dc.description.abstract	In this article, we define Diophantine sets using the Mizar formalism. We focus on selected properties of multivariate polynomials, i.e., functions of several variables to show finally that the class of Diophantine sets is closed with respect to the operations of union and intersection. This article is the next in a series [1], [5] aiming to formalize the proof of Matiyasevich’s negative solution of Hilbert’s tenth problem.	-
dc.language.iso	en	-
dc.publisher	DeGruyter Open	-
dc.subject	Hilbert’s 10th problem	-
dc.subject	Pell’s equation	-
dc.subject	multivariate polynomials	-
dc.title	Diophantine sets. Preliminaries	-
dc.type	Article	-
dc.identifier.doi	10.2478/forma-2018-0007	-
dc.description.Affiliation	Institute of Informatics, University of Białystok, Poland	-
dc.description.references	Marcin Acewicz and Karol Pąk. Pell’s equation. Formalized Mathematics, 25(3):197–204, 2017. doi:10.1515/forma-2017-0019.	-
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dc.description.references	Karol Pąk. The Matiyasevich theorem. Preliminaries. Formalized Mathematics, 25(4): 315–322, 2017. doi:10.1515/forma-2017-0029.	-
dc.description.references	Piotr Rudnicki and Andrzej Trybulec. Multivariate polynomials with arbitrary number of variables. Formalized Mathematics, 9(1):95–110, 2001.	-
dc.description.references	Craig Smorynski. Logical Number Theory I, An Introduction. Universitext. Springer-Verlag Berlin Heidelberg, 1991. ISBN 978-3-642-75462-3.	-
dc.description.references	Tetsuya Tsunetou, Grzegorz Bancerek, and Yatsuka Nakamura. Zero-based finite sequences. Formalized Mathematics, 9(4):825–829, 2001.	-
dc.identifier.eissn	1898-9934	-
dc.description.volume	26	-
dc.description.issue	1	-
dc.description.firstpage	81	-
dc.description.lastpage	90	-
dc.identifier.citation2	Formalized Mathematics	-
Występuje w kolekcji(ach):	Artykuły naukowe (WInf) Formalized Mathematics, 2018, Volume 26, Issue 1

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