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  3. Formalized Mathematics
  4. Formalized Mathematics, 2017, Volume 25, Issue 2

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    • Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/6283
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    Pole DCWartośćJęzyk
    dc.contributor.authorFuta, Yuichi-
    dc.contributor.authorShidama, Yasunari-
    dc.date.accessioned2018-02-08T08:10:31Z-
    dc.date.available2018-02-08T08:10:31Z-
    dc.date.issued2017-
    dc.identifier.citationFormalized Mathematics, Volume 25, Issue 2, Pages 157–169-
    dc.identifier.issn1426-2630-
    dc.identifier.urihttp://hdl.handle.net/11320/6283-
    dc.description.abstractSummaryIn this article, we formalize in Mizar [5] the definition of dual lattice and their properties. We formally prove that a set of all dual vectors in a rational lattice has the construction of a lattice. We show that a dual basis can be calculated by elements of an inverse of the Gram Matrix. We also formalize a summation of inner products and their properties. Lattice of ℤ-module is necessary for lattice problems, LLL(Lenstra, Lenstra and Lovász) base reduction algorithm and cryptographic systems with lattice [20], [10] and [19].-
    dc.language.isoen-
    dc.publisherDeGruyter Open-
    dc.subjectℤ-lattice-
    dc.subjectdual lattice of ℤ-lattice-
    dc.subjectdual basis of ℤ-lattice-
    dc.titleDual Lattice of ℤ-module Lattice-
    dc.typeArticle-
    dc.identifier.doi10.1515/forma-2017-0015-
    dc.description.AffiliationFuta Yuichi - Tokyo University of Technology, Tokyo, Japan-
    dc.description.AffiliationShidama Yasunari - Shinshu University, Nagano, Japan-
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    dc.description.referencesYuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. Quotient module of ℤ-module. Formalized Mathematics, 20(3):205–214, 2012. doi: 10.2478/v10037-012-0024-y.-
    dc.description.referencesYuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. Matrix of ℤ-module. Formalized Mathematics, 23(1):29–49, 2015. doi: 10.2478/forma-2015-0003.-
    dc.description.referencesAndrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5): 841–845, 1990.-
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    dc.identifier.eissn1898-9934-
    dc.description.volume25-
    dc.description.issue2-
    dc.description.firstpage157-
    dc.description.lastpage169-
    dc.identifier.citation2Formalized Mathematics-
    Występuje w kolekcji(ach):Formalized Mathematics, 2017, Volume 25, Issue 2

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