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A method to determine whether two polynomials are relatively prime

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2 Author(s)
Vogt, W. ; University of Pittsburgh, Pittsburgh, PA, USA ; Bose, N.

In this paper, it is established that a necessary and sufficient condition for two monic polynomialsf(lambda)andg(lambda)to have a common root is thatdet [f(B)] = 0ordet [g(A)] = 0, whereAandBare, respectively, the companion matrices associated withf(lambda)andg(lambda). The simplicity of this method is illustrated by examples.

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Automatic Control, IEEE Transactions on  (Volume:15 ,  Issue: 3 )