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Rational Functions Factorization Algorithm: a symbolic computation for the scalar and matrix cases

Ana C. Conceição
Viktor G. Kravchenko
José C. Pereira
Journal / Anthology

Proceedings of the 1st National Conference on Symbolic Computation in Education and Research (CD-ROM), Instituto Superior Técnico, Lisboa, April 2-3, 2012
Year: 2012

A factorization method for the class of rational matrix functions was proposed by F. D. Gahov, in 1952. At present time, this is the class for which the factorization problem is further developed, having already been found a complete and explicit factorization algorithm. A contemporary description of this well known and widely used algorithm can be found, for instance, in (Mikhlin, Prossdorf, 1986). Due to these facts, and in accordance with our previous work ((Conceic~ao, Kravchenko, Pereira, 2010) and (Conceic~ao, Kravchenko, Pereira, 2011)), it seemed natural for us to attempt the implementation on a computer of such important algorithm. The main goal of this paper is to present the implementation of the rational functions factorization algorithms, for the scalar ([ARFact-Scalar]) and matrix ([ARFact-Matrix]) cases. The [ARFact-Scalar] and [ARFact-Matrix] are analytical algorithms that give explicit factorizations. Several nontrivial examples, both canonical and non-canonical, are presented. Both the algorithms were implemented using the computer algebra system Mathematica, and will be made available to the general public with the publication of the present paper.


Explicit factorization, rational matrix function, rational scalar function, index, left(right) partial indices, algorithm, symbolic computation, Wolfram Mathematica