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Variation on variation on Euclid's algorithm
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DOI：10.1109/LSP.2004.824053.png)
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Abstract
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In a paper entitled Variation on Euclid's Algorithm for Plynomials, Calvez et al. has shown that the extended Euclid's algorithm can be partially obtained by the nonextended one; in fact, it can obtain only two of the three unknowns of the Bezout's theorem. This letter goes further and shows that all polynomials given by the extended Euclid's algorithm and all the intermediate values can be obtained directly by the nonextended Euclid's algorithm. Consequently, only remainder computations are used. Avoiding multiplications and divisions of polynomials decreases the computational complexity. This variation of Calvez et al. justifies the title of the present letter.
Keywords:
Bezout's theorem
Euclid's algorithm
polynomials
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