Gaussian Integers

• Autorzy: Yuichi Futa , Hiroyuki Okazaki , Daichi Mizushima , Yasunari Shidama
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

formalization of Gaussian integers; algebraic integers

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2013
• Tom: 21
• Numer: 2
• Strony: 115-125

Daty

wydano

2013-06-01

Twórcy

autor

Yuichi Futa

• Japan Advanced Institute of Science and Technology Ishikawa, Japan

autor

Hiroyuki Okazaki

• Shinshu University Nagano, Japan

autor

Daichi Mizushima

• Shinshu University Nagano, Japan
• This research was presented during the 2012 International Symposium on Information
  Theory and its Applications (ISITA2012) in Honolulu, USA.

autor

Yasunari Shidama

• Shinshu University Nagano, Japan

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Identyfikatory

DOI

10.2478/forma-2013-0013