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

Ronald van Nooijen; Alla Kolechkina

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 language	English
Pages	142-142
Publication status	Published - 2016
Event	17th International Symposium on Scientific Computing, Computer Arithmetic and Verified Numerics, 2016 - Uppsala University, Uppsala, Sweden Duration: 26 Sept 2016 → 29 Sept 2016 Conference number: 17 http://www.math.uu.se/digitalAssets/499/c_499852-l_1-k_scan2016-book-of-abstracts3.pdf

Conference

Conference	17th International Symposium on Scientific Computing, Computer Arithmetic and Verified Numerics, 2016
Abbreviated title	SCAN 2016
Country/Territory	Sweden
City	Uppsala
Period	26/09/16 → 29/09/16
Internet address	http://www.math.uu.se/digitalAssets/499/c_499852-l_1-k_scan2016-book-of-abstracts3.pdf

Keywords

ringoid
computer arithmetic
algebra

Access to Document

scan2016-rvnFinal published version, 60.7 KB

Cite this

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