Arithmetic Operations on Short Finite Sequences

Pole DC	Wartość	Język
dc.contributor.author	Ziobro, Rafał	-
dc.date.accessioned	2019-03-04T10:34:23Z	-
dc.date.available	2019-03-04T10:34:23Z	-
dc.date.issued	2018/10/01	-
dc.identifier.citation	Formalized Mathematics, Volume 26, Issue 3, Pages 199-208	-
dc.identifier.issn	1426-2630	-
dc.identifier.uri	http://hdl.handle.net/11320/7629	-
dc.description.abstract	In contrast to other proving systems Mizar Mathematical Library, considered as one of the largest formal mathematical libraries [4], is maintained as a single base of theorems, which allows the users to benefit from earlier formalized items [3], [2]. This eventually leads to a development of certain branches of articles using common notation and ideas. Such formalism for finite sequences has been developed since 1989 [1] and further developed despite of the controversy over indexing which excludes zero [6], also for some advanced and new mathematics [5].The article aims to add some new machinery for dealing with finite sequences, especially those of short length.	-
dc.language.iso	en	-
dc.publisher	DeGruyter Open	-
dc.subject	finite sequences	-
dc.subject	functions	-
dc.subject	relations	-
dc.title	Arithmetic Operations on Short Finite Sequences	-
dc.type	Article	-
dc.identifier.doi	10.2478/forma-2018-0018	-
dc.description.Affiliation	Department of Carbohydrate Technology, University of Agriculture, Krakow, Poland	-
dc.description.references	Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics,1(1):107–114, 1990.	-
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 Volker 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:10.1007/978-3-319-20615-8_17.	-
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.	-
dc.description.references	Alexander Elizarov, Alexander Kirillovich, Evgeny Lipachev, and Olga Nevzorova. Digital ecosystem OntoMath: Mathematical knowledge analytics and management. In Leonid Kalinichenko, Sergei O. Kuznetsov, and Yannis Manolopoulos, editors, Data Analytics and Management in Data Intensive Domains, pages 33–46. Springer International Publishing, 2017.	-
dc.description.references	Adam Naumowicz and Artur Korniłowicz. A brief overview of Mizar. In International Conference on Theorem Proving in Higher Order Logics, pages 67–72. Springer, 2009. doi:10.1007/978-3-642-03359-9_5.	-
dc.description.references	Piotr Rudnicki and Andrzej Trybulec. On the integrity of a repository of formalized mathematics. Mathematical Knowledge Management, 2003. doi:10.1007/3-540-36469-2_13.	-
dc.identifier.eissn	1898-9934	-
dc.description.volume	26	-
dc.description.issue	3	-
dc.description.firstpage	199	-
dc.description.lastpage	208	-
dc.identifier.citation2	Formalized Mathematics	-
dc.identifier.orcid	0000-0001-9681-4380	-
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