In this paper we present a new class of semigroups called convex body semigroups which are generated by convex bodies of ℝ k . They generalize to arbitrary dimension the concept of proportionally modular numerical semigroups of Rosales et al. (J. Number Theory 103, 281–294, 2003). Several properties of these semigroups are proven. Affine convex body semigroups obtained from circles and polygons of ℝ2 are characterized. The algorithms for computing minimal system of generators of these semigroups are given. We provide the implementation of some of them.
KeywordsAffine semigroup Circle semigroup Convex body monoid Convex body semigroup Polygonal semigroup
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