Have a personal or library account? Click to login
Gaussian Integers Cover

Gaussian Integers

Formalized Mathematics
Volume 21 (2013): Issue 2 (June 2013)
By: Yuichi Futa,  Hiroyuki Okazaki,  Daichi Mizushima and  Yasunari Shidama  
Open Access
|Jun 2013

References

  1. [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
    Search in Google Scholar
  2. [2] Grzegorz Bancerek. Konig’s theorem. Formalized Mathematics, 1(3):589-593, 1990.
    Search in Google Scholar
  3. [3] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
    Search in Google Scholar
  4. [4] Józef Białas. Group and field definitions. Formalized Mathematics, 1(3):433-439, 1990.
    Search in Google Scholar
  5. [5] Czesław Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
    Search in Google Scholar
  6. [6] Czesław Bylinski. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
    Search in Google Scholar
  7. [7] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.
    Search in Google Scholar
  8. [8] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
    Search in Google Scholar
  9. [9] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
    Search in Google Scholar
  10. [10] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
    Search in Google Scholar
  11. [11] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
    Search in Google Scholar
  12. [12] 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/v10037-011-0021-6.10.2478/v10037-011-0021-6
    Search in Google Scholar
  13. [13] Yuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. Z-modules. Formalized Mathematics, 20(1):47-59, 2012. doi:10.2478/v10037-012-0007-z.10.2478/v10037-012-0007-z
    Search in Google Scholar
  14. [14] Andrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5): 841-845, 1990.
    Search in Google Scholar
  15. [15] Eugeniusz Kusak, Wojciech Leonczuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.
    Search in Google Scholar
  16. [16] Rafał Kwiatek and Grzegorz Zwara. The divisibility of integers and integer relatively primes. Formalized Mathematics, 1(5):829-832, 1990.
    Search in Google Scholar
  17. [17] Michał Muzalewski. Construction of rings and left-, right-, and bi-modules over a ring. Formalized Mathematics, 2(1):3-11, 1991.
    Search in Google Scholar
  18. [18] 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.
    Search in Google Scholar
  19. [19] Christoph Schwarzweller. The ring of integers, Euclidean rings and modulo integers. Formalized Mathematics, 8(1):29-34, 1999.
    Search in Google Scholar
  20. [20] Christoph Schwarzweller. The field of quotients over an integral domain. Formalized Mathematics, 7(1):69-79, 1998.
    Search in Google Scholar
  21. [21] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4): 341-347, 2003.
    Search in Google Scholar
  22. [22] Andrzej Trybulec and Czesław Bylinski. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.
    Search in Google Scholar
  23. [23] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
    Search in Google Scholar
  24. [24] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.
    Search in Google Scholar
  25. [25] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
    Search in Google Scholar
  26. [26] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
    Search in Google Scholar
  27. [27] Andr´e Weil. Number Theory for Beginners. Springer-Verlag, 1979.10.1007/978-1-4612-9957-8
    Search in Google Scholar
  28. [28] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.
    Search in Google Scholar
DOI: https://doi.org/10.2478/forma-2013-0013 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
Journal RSS Feed
Language: English
Page range: 115 - 125
Published on: Jun 1, 2013
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Keywords:
formalization of Gaussian integers,
algebraic integers
Related subjects:
Computer sciences,
Computer sciences, other,
Mathematics,
General mathematics

© 2013 Yuichi Futa, Hiroyuki Okazaki, Daichi Mizushima, Yasunari Shidama, published by University of Białystok
This work is licensed under the Creative Commons License.

Volume 21 (2013): Issue 2 (June 2013)