Gaussian Integers

Pole DC	Wartość	Język
dc.contributor.author	Futa, Yuichi	-
dc.contributor.author	Okazaki, Hiroyuki	-
dc.contributor.author	Mizushima, Daichi	-
dc.contributor.author	Shidama, Yasunari	-
dc.date.accessioned	2015-12-09T20:39:34Z	-
dc.date.available	2015-12-09T20:39:34Z	-
dc.date.issued	2013	-
dc.identifier.citation	Formalized Mathematics, Volume 21, Issue 2, 2013, Pages 115-125	-
dc.identifier.issn	1426-2630	-
dc.identifier.issn	1898-9934	-
dc.identifier.uri	http://hdl.handle.net/11320/3680	-
dc.description	This research was presented during the 2012 International Symposium on Information Theory and its Applications (ISITA2012) in Honolulu, USA.	-
dc.description.abstract	Gaussian integer is one of basic algebraic integers. In this article we formalize some definitions about Gaussian integers [27]. We also formalize ring (called Gaussian integer ring), Z-module and Z-algebra generated by Gaussian integer mentioned above. Moreover, we formalize some definitions about Gaussian rational numbers and Gaussian rational number field. Then we prove that the Gaussian rational number field and a quotient field of the Gaussian integer ring are isomorphic.	-
dc.description.sponsorship	This work was supported by JSPS KAKENHI 21240001 and 22300285.	-
dc.language.iso	en	-
dc.publisher	De Gruyter Open	-
dc.subject	formalization of Gaussian integers	-
dc.subject	algebraic integers	-
dc.title	Gaussian Integers	-
dc.type	Article	-
dc.identifier.doi	10.2478/forma-2013-0013	-
dc.description.Affiliation	Futa Yuichi - Japan Advanced Institute of Science and Technology Ishikawa, Japan	-
dc.description.Affiliation	Okazaki Hiroyuki - Shinshu University Nagano, Japan	-
dc.description.Affiliation	Mizushima Daichi - Shinshu University Nagano, Japan	-
dc.description.Affiliation	Shidama Yasunari - Shinshu University Nagano, Japan	-
dc.description.references	Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.	-
dc.description.references	Grzegorz Bancerek. König’s theorem. Formalized Mathematics, 1(3):589-593, 1990.	-
dc.description.references	Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.	-
dc.description.references	Józef Białas. Group and field definitions. Formalized Mathematics, 1(3):433-439, 1990.	-
dc.description.references	Czesław Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.	-
dc.description.references	Czesław Bylinski. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.	-
dc.description.references	Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.	-
dc.description.references	Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.	-
dc.description.references	Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.	-
dc.description.references	Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.	-
dc.description.references	Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.	-
dc.description.references	Yuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. Set of points on elliptic curve in projective coordinates. Formalized Mathematics, 19(3):131-138, 2011. doi:10.2478/v10037-011-0021-6.	-
dc.description.references	Yuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. Z-modules. Formalized Mathematics, 20(1):47-59, 2012. doi:10.2478/v10037-012-0007-z.	-
dc.description.references	Andrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5): 841-845, 1990.	-
dc.description.references	Eugeniusz Kusak, Wojciech Leonczuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.	-
dc.description.references	Rafał Kwiatek and Grzegorz Zwara. The divisibility of integers and integer relatively primes. Formalized Mathematics, 1(5):829-832, 1990.	-
dc.description.references	Michał Muzalewski. Construction of rings and left-, right-, and bi-modules over a ring. Formalized Mathematics, 2(1):3-11, 1991.	-
dc.description.references	Christoph Schwarzweller. The correctness of the generic algorithms of Brown and Henrici concerning addition and multiplication in fraction fields. Formalized Mathematics, 6(3): 381-388, 1997.	-
dc.description.references	Christoph Schwarzweller. The ring of integers, Euclidean rings and modulo integers. Formalized Mathematics, 8(1):29-34, 1999.	-
dc.description.references	Christoph Schwarzweller. The field of quotients over an integral domain. Formalized Mathematics, 7(1):69-79, 1998.	-
dc.description.references	Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4): 341-347, 2003.	-
dc.description.references	Andrzej Trybulec and Czesław Bylinski. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.	-
dc.description.references	Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.	-
dc.description.references	Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.	-
dc.description.references	Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.	-
dc.description.references	Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.	-
dc.description.references	Andr´e Weil. Number Theory for Beginners. Springer-Verlag, 1979.	-
dc.description.references	Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.	-
Występuje w kolekcji(ach):	Formalized Mathematics, 2013, Volume 21, Issue 2

Pliki w tej pozycji:

Plik	Opis	Rozmiar	Format
forma-2013-0013.pdf		227,89 kB	Adobe PDF	Otwórz

Pokaż uproszczony widok rekordu Zobacz statystyki

Pozycja ta dostępna jest na podstawie licencji Licencja Creative Commons CCL