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Mathematica package for calculating polynomial integrals over the unitary group

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IntU is a package for Mathematica computer algebra system, which allows to calculate polynomial integrals over the unitary group with respect to the Haar measure.


The package can be installed by placing IntU.m file in Applications subdirectory of .Mathematica directory.


Help messages for the implemented functions are document in IntU_functions.nb notebook. The are also available in the PDF format in IntU_functions.pdf.


Z. Puchała, J.A. Miszczak, IITiS PAN Gliwice, Poland

Usage and citing

Usage examples are provided in IntU_examples.nb notebook. The package was described in

Z.Puchała, J.A. Miszczak, Symbolic integration with respect to the Haar measure on the unitary group, Bull. Pol. Acad. Sci.-Tech. Sci., Vol 65, No. 1 (2017), DOI:10.1515/bpasts-2017-0003, arXiv:1109.4244

In case of citing our work, please use the following BibTeX data:

  author        = {Pucha{\l}a, Zbigniew and Miszczak, Jaros{\l}aw Adam},
  title         = {Symbolic integration with respect to the {Haar} measure on the unitary group},
  journal       = {Bull. Pol. Acad. Sci.-Tech. Sci.},
  volume        = {65},
  issue         = {1},   
  year          = {2017},
  doi           = {10.1515/bpasts-2017-0003},
  eprint        = {arXiv:1109.4244},
  url           = {}