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TitleFraction-free row reduction of matrices of Ore polynomials
Author(s) Bernhard Beckermann, Howard Cheng, George Labahn
TypeArticle in Journal
AbstractIn 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.
KeywordsOre polynomials, Exact arithmetic, Matrix normal forms
URL http://www.sciencedirect.com/science/article/pii/S0747717105001513
JournalJournal of Symbolic Computation
Pages513 - 543
Translation No
Refereed No