Computation of Principal A-determinants through Dimer Dynamics
Jan Stienstra
TL;DR
This paper translates Gulotta's inverse algorithm into matrix operations for computational efficiency and combines it with previous results to provide a fast method for computing principal A-determinants of hypergeometric systems in two variables.
Contribution
It introduces a matrix-based implementation of Gulotta's algorithm and applies it to efficiently compute principal A-determinants for specific hypergeometric systems.
Findings
Developed a matrix-based implementation of Gulotta's algorithm
Provided a fast computational method for principal A-determinants in two variables
Enhanced the practical computation of hypergeometric system invariants
Abstract
In this note we translate the pictorial description of Gulotta's efficient inverse algorithm (arXiv:0807.3012) into matrix operations, so that it can be implemented on a computer. As an application we point out that this in combination with results from our paper arXiv:0803.3908 provides a fast algorithm for computing the principal A-determinant of Gelfand, Kapranov and Zelevinsky for hypergeometric systems in two variables.
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Taxonomy
TopicsMolecular spectroscopy and chirality · Polynomial and algebraic computation · Tensor decomposition and applications