Fraction-free row reduction of matrices of Ore polynomials

Authors:
Bernhard Beckermann;Howard Cheng;George Labahn
Affiliations:
Laboratoire Painlevé UMR 8524 (ANO-EDP), UFR MathématiquesM3, UST Lille, F-59655 Villeneuve dAscq CEDEX, France;Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, Alberta, Canada T1K 3M4;School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Venue:
Journal of Symbolic Computation
Year:
2006

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Abstract

In this paper we give formulas for performing row reduction of a matrix of Ore polynomials in a fraction-free way. The reductions can be used for finding the rank and left nullspace of such matrices. When specialized to matrices of skew polynomials our reduction can be used for computing a weak Popov form of such matrices and for computing a GCRD and an LCLM of skew polynomials or matrices of skew polynomials. The algorithm is suitable for computation in exact arithmetic domains where the growth of coefficients in intermediate computations is a concern. This coefficient growth is controlled by using fraction-free methods. The known factor can be predicted and removed efficiently.