Computing Popov Forms of Matrices Over PBW Extensions

Mark Giesbrecht (), George Labahn () and Yang Zhang ()
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Mark Giesbrecht: University of Waterloo, Cheriton School of Computer Science
George Labahn: University of Waterloo, Cheriton School of Computer Science
Yang Zhang: University of Manitoba, Department of Mathematics

A chapter in Computer Mathematics, 2014, pp 61-65 from Springer

Abstract: Abstract 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.

Keywords: Popov Form; Poincare Birkhoff-Witt (PBW); Skew Polynomial Ring; Admissible Term Order; Weyl Algebra (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-43799-5_6

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DOI: 10.1007/978-3-662-43799-5_6

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