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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Veröffentlicht in:Experimental mathematics Jg. 34; H. 3; S. 342 - 349
Hauptverfasser: Xin, Guoce, Xu, Xinyu
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Taylor & Francis 03.07.2025
Schlagworte:
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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References Beck M. (e_1_3_1_6_1) 2001; 109
Knuth D. E. (e_1_3_1_11_1) 1997
e_1_3_1_10_1
Beck M. (e_1_3_1_7_1) 2007
e_1_3_1_9_1
e_1_3_1_14_1
e_1_3_1_8_1
e_1_3_1_13_1
e_1_3_1_12_1
e_1_3_1_5_1
e_1_3_1_18_1
e_1_3_1_17_1
e_1_3_1_16_1
e_1_3_1_15_1
e_1_3_1_3_1
Barvinok E. (e_1_3_1_4_1) 1999; 38
e_1_3_1_2_1
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  year: 2007
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  doi: 10.4064/aa109-2-1
– volume: 109
  start-page: 25
  issue: 2
  year: 2001
  ident: e_1_3_1_6_1
  article-title: Dedekind sums: a combinatorial-geometric viewpoint
  publication-title: Unusual Appl. Number Theory
– ident: e_1_3_1_15_1
  doi: 10.37236/1811
– ident: e_1_3_1_10_1
  doi: 10.1215/S0012-7094-03-11822-0
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  doi: 10.1287/moor.19.4.769
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  doi: 10.5948/UPO9781614440161
– ident: e_1_3_1_8_1
  doi: 10.1016/j.jsc.2003.04.003
– volume-title: The Art of Computer Programming
  year: 1997
  ident: e_1_3_1_11_1
– volume: 38
  start-page: 91
  year: 1999
  ident: e_1_3_1_4_1
  article-title: An algorithmic theory of lattice points in polyhedra
  publication-title: Louis J. Billera
– ident: e_1_3_1_9_1
  doi: 10.2307/2951842
– ident: e_1_3_1_12_1
  doi: 10.1137/060664768
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StartPage 342
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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