Computing the Volume of Polytropes

2025/05/14 by Killian Hong-Minh, Paul Sheehan, Hong-Minh, Killian +2
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Computational Geometry and Mesh Generation #Polynomial and algebraic computation #math.CO

paper · pdf · doi:10.48550/arxiv.2505.10587

openalex publication_date 2025/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We apply an algorithm for measuring the volume of polytopes described by Jim Lawrence to polytropes. By using a tropical form of Cramer's rule, we found an efficient way to find all pseudovertices which are necessary for computing the volume. Due to the limited possibilities for hyperplanes of polytropes, this led to a simplification of the algorithm, decreasing the time complexity significantly.

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