The properties of negation and zero in ringoids as defined by Kulisch

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Abstract

In [1,2] Kulisch defines (ordered) ringoids and vectoids to provide a theoretical basis for computer arithmetic and interval arithmetic. One interesting aspect of his treatment is the search for necessary and sufficient conditions for a meaningful notion of negation and zero. In this paper we consider this both from the point of view of functions on the underlying set and from a category theoretical standpoint. It turns out that the conditions provided by Kulisch can be restated in other forms, but that the original form is probably both necessary and sufficient for the intended purpose.
Original languageEnglish
Pages142-142
Publication statusPublished - 2016
Event17th International Symposium on Scientific Computing, Computer Arithmetic and Verified Numerics, 2016 - Uppsala University, Uppsala, Sweden
Duration: 26 Sep 201629 Sep 2016
Conference number: 17
http://www.math.uu.se/digitalAssets/499/c_499852-l_1-k_scan2016-book-of-abstracts3.pdf

Conference

Conference17th International Symposium on Scientific Computing, Computer Arithmetic and Verified Numerics, 2016
Abbreviated titleSCAN 2016
CountrySweden
CityUppsala
Period26/09/1629/09/16
Internet address

Keywords

  • ringoid
  • computer arithmetic
  • algebra

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