JUCS - Journal of Universal Computer Science 4(1): 34-47, doi: 10.3217/jucs-004-01-0034
On the Algebra of Intervals and Convex Bodies
expand article infoSvetoslav M. Markov‡
‡ Bulgarian Academy of Sciences, Bulgaria

Corresponding author: Svetoslav Markov ( smarkov@iph.bio.acad.bg )

© Svetoslav Markov.
This article is freely available under the J.UCS Open Content License.
Citation: Markov SM (1998) On the Algebra of Intervals and Convex Bodies. JUCS - Journal of Universal Computer Science 4(1): 34-47. https://doi.org/10.3217/jucs-004-01-0034
Open Access
Abstract
We introduce and study abstract algebraic systems generalizing the arithmetic systems of intervals and convex bodies involving Minkowski operations such as quasimodules and quasilinear systems. Embedding theorems are proved and computational rules for algebraic transformations are given.
Keywords
Interval arithmetic, convex bodies, Minkowski operations, commutative semigroups, isomorphic embedding, quasilinear space.