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

Bulletin of the Polish Academy of Sciences. Technical Sciences

J.A. MiszczakInstitute of Theoretical and Applied Informatics, Polish Academy of Sciences, 5 Ba?tycka Str., 44-100 Gliwice, PolandOther articles by this author:De Gruyter OnlineGoogle Scholar¹  Z. Pucha?aCorresponding authorInstitute of Theoretical and Applied Informatics, Polish Academy of Sciences, 5 Ba?tycka Str., 44-100 Gliwice, PolandEmailOther articles by this author:De Gruyter OnlineGoogle Scholar¹ 

[1] Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, 5 Ba?tycka Str., 44-100 Gliwice, Poland

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

DOI  :  10.1515/bpasts-2017-0003

学科分类：工程和技术（综合）

来源: Polska Akademia Nauk * Centrum Upowszechniania Nauki / Polish Academy of Sciences, Center for the Advancement of Science

【 摘 要 】

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.

【 授权许可】

Unknown