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| Pole DC | Wartość | Język |
|---|---|---|
| dc.contributor.author | Watase, Yasushige | - |
| dc.date.accessioned | 2024-12-31T07:23:10Z | - |
| dc.date.available | 2024-12-31T07:23:10Z | - |
| dc.date.issued | 2024 | - |
| dc.identifier.citation | Formalized Mathematics, Volume 32, Issue 1, Pages 111–120 | pl |
| dc.identifier.issn | 1426-2630 | - |
| dc.identifier.uri | http://hdl.handle.net/11320/17769 | - |
| dc.description.abstract | In this article, we prove the transcendence of the number e using the Mizar formalism, following Hurwitz’s proof. This article prepares the necessary definitions and lemmas. The main body of the proof will be presented separately. | 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.uri | https://creativecommons.org/licenses/by-sa/3.0/ | pl |
| dc.subject | transcendental number | pl |
| dc.subject | algebraic number | pl |
| dc.subject | ring of polynomials | pl |
| dc.title | Formal Proof of Transcendence of the Number e. Part I | pl |
| dc.type | Article | pl |
| dc.rights.holder | © 2024 The Author(s) | pl |
| dc.rights.holder | CC BY-SA 3.0 license | pl |
| dc.identifier.doi | 10.2478/forma-2024-0008 | - |
| dc.description.Affiliation | Suginami-ku Matsunoki 6, 3-21 Tokyo, Japan | pl |
| dc.description.references | Alan Baker. Transcendental Number Theory. Cambridge University Press, 1990. | pl |
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| dc.description.references | Sophie Bernard, Yves Bertot, Laurence Rideau, and Pierre-Yves Strub. Formal proofs of transcendence for e and π as an application of multivariate and symmetric polynomials. In Jeremy Avigad and Adam Chlipala, editors, Proceedings of the 5th ACM SIGPLAN Conference on Certified Programs and Proofs, pages 76–87. ACM, 2016.doi:10.1145/2854065.2854072. | pl |
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| dc.description.references | Charles Hermite. Sur la fonction exponentielle. Gauthier-Villars, 1874. | pl |
| dc.description.references | Adolf Hurwitz. Beweis der Transcendenz der Zahl e. Mathematische Annalen, 43:220–221,1893. | pl |
| dc.description.references | Artur Korniłowicz. Differentiability of polynomials over reals. Formalized Mathematics, 25(1):31–37, 2017. doi:10.1515/forma-2017-0002. | pl |
| dc.description.references | Artur Korniłowicz and Christoph Schwarzweller. The first isomorphism theorem and other properties of rings. Formalized Mathematics, 22(4):291–301, 2014. doi:10.2478/forma-2014-0029. | pl |
| dc.description.references | Artur Korniłowicz, Adam Naumowicz, and Adam Grabowski. All Liouville numbers are transcendental. Formalized Mathematics, 25(1):49–54, 2017. doi:10.1515/forma-2017-0004. | pl |
| dc.description.references | Serge Lang. Introduction to Transcendental Numbers. Addison-Wesley Pub. Co., 1966. | pl |
| dc.description.references | Norman D. Megill and David A. Wheeler. Metamath: A Computer Language for Mathe matical Proofs. Lulu Press, Morrisville, North Carolina, 2019. | pl |
| dc.description.references | Leonardo de Moura and Sebastian Ullrich. The Lean 4 theorem prover and programming language. In Automated Deduction – CADE 28: 28th International Conference on Automated Deduction, Virtual Event, July 12–15, 2021, Proceedings, pages 625–635, Berlin, Heidelberg, 2021. Springer-Verlag. doi:10.1007/978-3-030-79876-5 37. | pl |
| dc.description.references | Karol Pąk. Eigenvalues of a linear transformation. Formalized Mathematics, 16(4):289–295, 2008. doi:10.2478/v10037-008-0035-x. | pl |
| dc.description.references | Christoph Schwarzweller. Field extensions and Kronecker’s construction. Formalized Mathematics, 27(3):229–235, 2019. doi:10.2478/forma-2019-0022. | pl |
| dc.description.references | Christoph Schwarzweller and Agnieszka Rowińska-Schwarzweller. Simple extensions. For malized Mathematics, 31(1):287–298, 2023. doi:10.2478/forma-2023-0023. | pl |
| dc.description.references | Christoph Schwarzweller, Artur Korniłowicz, and Agnieszka Rowińska-Schwarzweller. Some algebraic properties of polynomial rings. Formalized Mathematics, 24(3):227–237, 2016. doi:10.1515/forma-2016-0019. | pl |
| dc.description.references | Yasushige Watase. Derivation of commutative rings and the Leibniz formula for power of derivation. Formalized Mathematics, 29(1):1–8, 2021. doi:10.2478/forma-2021-0001. | pl |
| dc.description.references | Freek Wiedijk. Formalizing 100 theorems. Available online at http://www.cs.ru.nl/~freek/100/. | pl |
| dc.identifier.eissn | 1898-9934 | - |
| dc.description.volume | 32 | pl |
| dc.description.issue | 1 | pl |
| dc.description.firstpage | 111 | pl |
| dc.description.lastpage | 120 | pl |
| dc.identifier.citation2 | Formalized Mathematics | pl |
| Występuje w kolekcji(ach): | Formalized Mathematics, 2024, Volume 32, Issue 1 | |
Pliki w tej pozycji:
| Plik | Opis | Rozmiar | Format | |
|---|---|---|---|---|
| Formal-Proof-of-Transcendence-of-the-Number-e-Part-I.pdf | 313,02 kB | Adobe PDF | Otwórz |
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