Computing Convex Hulls in the Affine Building of SLd
Abstract
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.
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