A Polynomial Time Algorithm for Calculating Fourier-Dedekind Sums

We solve an open problem proposed in the book "Computing the continuous discretely" written by Matthias Beck and Sinai Robins. That is, we provide a practical polynomial time algorithm for calculating Fourier-Dedekind sums. The algorithm is simple modular Barvinok's simplicial cone de...

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Vydáno v:Experimental mathematics Ročník 34; číslo 3; s. 342 - 349
Hlavní autoři: Xin, Guoce, Xu, Xinyu
Médium: Journal Article
Jazyk:angličtina
Vydáno: Taylor & Francis 03.07.2025
Témata:
Barvinok's algorithm
constant terms
Dedekind sum
Fourier-Dedekind sum
Primary: 11F20
Secondary: 11Y16
ISSN:1058-6458, 1944-950X
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Shrnutí:We solve an open problem proposed in the book "Computing the continuous discretely" written by Matthias Beck and Sinai Robins. That is, we provide a practical polynomial time algorithm for calculating Fourier-Dedekind sums. The algorithm is simple modular Barvinok's simplicial cone decomposition. It can be easily adapted into De Leora et al.'s LattE package, which gives a nice implementation of Barvinok's polynomial time algorithm.
ISSN:1058-6458
1944-950X
DOI:10.1080/10586458.2024.2364264