Computing Popov Forms of Matrices Over PBW Extensions

  • Mark GiesbrechtEmail author
  • George LabahnEmail author
  • Yang ZhangEmail author
Conference paper


In this paper we define the Popov and weak Popov forms of matrices over Poincaré–Birkhoff–Witt (PBW) extensions, and exhibit effective algorithms to find them. As applications we give general methods to calculate the ranks of such matrices, and a method to transfer a system of differential equations into a first order equation.



All the authors would like to thank NSERC Canada for their support of this research.


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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Cheriton School of Computer ScienceUniversity of WaterlooWaterloo ONCanada
  2. 2.Department of MathematicsUniversity of ManitobaWinnipeg MBCanada

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