Solid angles of polyhedral cones via decompositions and power series

Abstract: This work concerns the normalized solid angle measure of a polyhedral cone. This is well understood in dimensions two and three. For higher dimensions, the measure can be computed via a multivariable hypergeometric series. This series serves as a powerful tool, allowing one to compute the solid angle measure of a simplicial cone of interest, so long as it satisfies a certain condition relating to positive-definiteness. We present two decomposition methods of full-dimensional simplicial cones into finite families of cones satisfying the positive-definite criterion. We present the SageMath implementation of the proposed solid angle computations. This is a joint work with Allison Fitisone.

mathematical softwaresymbolic computationMathematics

Audience: advanced learners

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