Computing Convex Hulls in the Aﬃne Building of SLd
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Submission date: 23. Nov. 2018
MSC-Numbers: 52, 05
Keywords and phrases: tropical geometry, convex hulls, buildings
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We describe an algorithm for computing the convex hull of a ﬁnite collection of points in the aﬃne building of SLd(K), for K a ﬁeld with discrete valuation. These convex hulls describe the relations among a ﬁnite collection of invertible matrices over K. As a consequence, we bound the dimension of the tropical projective space needed to realize the convex hull as a tropical polytope.