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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Abstract 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.
AbstractList 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.
Author Xin, Guoce
Xu, Xinyu
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SubjectTerms Barvinok's algorithm
constant terms
Dedekind sum
Fourier-Dedekind sum
Primary: 11F20
Secondary: 11Y16
Title A Polynomial Time Algorithm for Calculating Fourier-Dedekind Sums
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