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Bulletin of the Polish Academy of Sciences Technical Sciences

The Journal of Polish Academy of Sciences

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Volume 65, Issue 1 (Feb 2017)

Issues

Symbolic integration with respect to the Haar measure on the unitary groups

Z. Puchała
  • Corresponding author
  • Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, 5 Bałtycka Str., 44-100 Gliwice, Poland
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ J.A. Miszczak
  • Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, 5 Bałtycka Str., 44-100 Gliwice, Poland
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2017-02-17 | DOI: https://doi.org/10.1515/bpasts-2017-0003

Abstract

We present IntU package for Mathematica computer algebra system. The presented package performs a symbolic integration of polynomial functions over the unitary group with respect to unique normalized Haar measure. We describe a number of special cases which can be used to optimize the calculation speed for some classes of integrals. We also provide some examples of usage of the presented package.

Keywords: unitary group; Haar measure; circular unitary ensemble; symbolic integration

References

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  • [4] Z. Puchała and J. A. Miszczak, “IntU package for Mathematica” (2011). Software available at http://zksi.iitis.pl/wiki/projects:intu.Google Scholar

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  • [13] C. F. Dunkl, P. Gawron, J. A. Holbrook, Z. Puchała, and K. Życzkowski, “Numerical shadows: measures and densities on the numerical range”, Linear Algebra Appl. 434, 2042-2080 (2011).Google Scholar

  • [14] C. F. Dunkl, P. Gawron, J. A. Holbrook, J. A. Miszczak, Z. Puchała, and K. Życzkowski, “Numerical shadow and geometry of quantum states”, J. Phys. A: Math. Theor. 44 (33), 335301 (2011).Google Scholar

  • [15] M. Enríquez, Z. Puchała, and K. Życzkowski, “Minimal Rényi- -Ingarden-Urbanik entropy of multipartite quantum states”, Entropy 17 (7), 5063 (2015). CrossrefGoogle Scholar

About the article

Published Online: 2017-02-17

Published in Print: 2017-02-01


Citation Information: Bulletin of the Polish Academy of Sciences Technical Sciences, ISSN (Online) 2300-1917, DOI: https://doi.org/10.1515/bpasts-2017-0003.

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