Computing the Minkowski Sum of Prisms

AbstractWithin this paper we study the Minkowski sum of prisms (“Cephoids”) in a finite dimensional vector space. For a vector $$a \in \mathbb{R}^n$$ with positive components we write $${\bar{a}} = ({1\over \bar{a}_1}, \cdots , {1\over \bar{a}_n})$$ and denote by $$\prod = \prod^{\bar{a}} = \{x \in \mathbb{R}^n | \langle \bar{a}, {\bf x} \rangle \leqslant 1, {\bf x} \geqslant 0 \}$$ the associated prism. We provide a representation of a finite sum of prisms in terms of inequalities.