In the earlier work, Knuth present an algorithm to decrease the coefficient growth in the Euclidean algorithm of polynomials called subresultant algorithm. However, the output polynomials may have a small factor which can be removed. Then later, Brown of Bell Telephone Laboratories showed the subresultant in another way by adding a variant called τ and gave a way to compute the variant. Nevertheless, the way failed to determine every τ correctly.
In this paper, we will give a probabilistic algorithm to determine the variant τ correctly in most cases by adding a few steps instead of computing t(x) when given f(x) and g(x)∈Z[x], where t(x) satisfies that s(x)f(x)+t(x)g(x)=r(x), here t(x),s(x)∈Z[x].

User Name : Yang_Zhang

Posted 30-08-2022 on 12:35:02 AEDT

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