ゼロ除算ができる数、輪を実装してみたので解説
https://qiita.com/lotz/items/60c20189f931dd8e5e9f
が面白かった。
/0と0/0を定義し、演算を閉じる。
参考文献の解読を始める。
Wheels
Wheels
On Division by Zero
Jesper Carlstro ̈m
https://www2.math.su.se/reports/2001/11/2001-11.pdf
References
著作権に留意してURLを調べています。リンク先に誤りがあれば、ご教授ください。
M. F. Atiyah and I. G. MacDonald. Introduction to Commutative Algebra. Addison-Wesley, London, 1969.
http://www.saheleriyaziyat.net/images/k1zut2e5peefixbx6kty.pdf
Birkhoff, 1935. See e.g. [BS81] theorem 11.9, p. 75 or [Gra ̈79] theorem 3, p. 171.
F. Borceux. Handbook of Categorical Algebra, volume 2. Cambridge University Press, Cambridge, 1994.
https://www.amazon.com/dp/0521061199
N. Bourbaki. Elements of Mathematics, Algebra, Part I. Addison- Wesley, Reading, Massachusetts, 1973.
http://www.cmat.edu.uy/~marclan/TM/Algebra%20i%20-%20Bourbaki.pdf
S. Burris and H. P. Sankappanavar. A Course in Universal Algebra. Springer-Verlag, New York, 1981.
http://www.math.hawaii.edu/~ralph/Classes/619/univ-algebra.pdf
A. Edalat and P. J. Potts. A new representation for exact real num- bers. In S. Brookes and M. Mislove, editors, Electronic Notes in Theoretical Computer Science, volume 6. Elsevier Science Publishers, 2000.
J. S. Golan. Semirings and their Applications. Kluwer Academic Publishers, Dordrecht, 1999.
https://www.springer.com/gp/book/9780792357865
G. Gra ̈tzer. Universal Algebra. Springer-Verlag, New York, second edition, 1979.
R. Hartshorne. Algebraic Geometry. Springer-Verlag, New York, 1977.
https://www.springer.com/jp/book/9780387902449
A. Heyting. Intuitionism: An Introduction. North-Holland, Amsterdam, 1956.
https://philpapers.org/rec/HEYIAI-2
P. Martin-Lo ̈f. Intuitionistic Type Theory. Bibliopolis, Naples, 1984.
https://archive-pml.github.io/martin-lof/pdfs/Bibliopolis-Book-retypeset-1984.pdf
R. Mines, F. Richman, and W. Ruitenburg. A Course in Constructive Algebra. Springer-Verlag, New York, 1988.
https://www.springer.com/gp/book/9780387966403
M.O ̈berg.Algebraiskaochtopologiskahjul.Examensarbeteimatematik, Stockholm University, 2000.
P. J. Potts. Exact Real Arithmetic using M ̈obius Transformations. PhD thesis, University of London, 1998. Currently available at
http://www.purplefinder.com/~potts/.
A. Setzer. Wheels (draft). Currently available at
http://www-compsci.swan.ac.uk/~csetzer/, 1997.
文書履歴(document history)
ver. 0.01 初稿 20190220
ver. 0.02 はてなブックマーク 追記 20190225
