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http://hdl.handle.net/11320/4836Pełny rekord metadanych
| Pole DC | Wartość | Język |
|---|---|---|
| dc.contributor.author | Futa, Yuichi | pl |
| dc.contributor.author | Okazaki, Hiroyuki | pl |
| dc.contributor.author | Shidama, Yasunari | pl |
| dc.date.accessioned | 2016-12-06T02:00:00Z | pl |
| dc.date.accessioned | 2016-12-12T10:36:07Z | - |
| dc.date.available | 2016-12-06T02:00:00Z | pl |
| dc.date.available | 2016-12-12T10:36:07Z | - |
| dc.date.issued | 2015 | pl |
| dc.identifier.citation | Formalized Mathematics, Volume 23, Issue 1, Pages 29–49 | pl |
| dc.identifier.issn | 1426-2630 | pl |
| dc.identifier.issn | 1898-9934 | pl |
| dc.identifier.uri | http://hdl.handle.net/11320/4836 | - |
| dc.description.abstract | In this article, we formalize a matrix of ℤ-module and its properties. Specially, we formalize a matrix of a linear transformation of ℤ-module, a bilinear form and a matrix of the bilinear form (Gramian matrix). We formally prove that for a finite-rank free ℤ-module V, determinant of its Gramian matrix is constant regardless of selection of its basis. ℤ-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm and cryptographic systems with lattices [22] and coding theory [14]. Some theorems in this article are described by translating theorems in [24], [26] and [19] into theorems of ℤ-module. | pl |
| dc.language.iso | en | pl |
| dc.publisher | De Gruyter Open | pl |
| dc.subject | matrix of Z-module | pl |
| dc.subject | matrix of linear transformation | pl |
| dc.subject | bilinear form | pl |
| dc.title | Matrix of ℤ-module | pl |
| dc.type | Article | pl |
| dc.identifier.doi | 10.2478/forma-2015-0003 | pl |
| dc.description.Affiliation | Yuichi Futa - Japan Advanced Institute of Science and Technology, Ishikawa, Japan | pl |
| dc.description.Affiliation | Hiroyuki Okazaki - Shinshu University, Nagano, Japan | pl |
| dc.description.Affiliation | Yasunari Shidama - Shinshu University, Nagano, Japan | pl |
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| Występuje w kolekcji(ach): | Formalized Mathematics, 2015, Volume 23, Issue 1 | |
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|---|---|---|---|---|
| forma-2015-0003.pdf | 344,94 kB | Adobe PDF | Otwórz |
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