A note on the automatic pretreatment of polynomials

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Abstract
A machine computation of the greatest common divisor of two polynomials is a ticklish affair, due to a possibly severe propagation of rounding errors in the successive divisions. Usually a remainder will be put equal to zero if its coefficients are smaller than a certain quantity, which one has generally no idea of how to choose conveniently. It is shown that this vague criterion for neglecting coefficients can be made more precise and depending on each remainder.

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