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Subresultant pseudo-remainder sequence is way of computing remainder sequence of two polynomials in $\mathbb{Z}$ and keeping the size of coefficients relatively small, but the signs of the remainders differ from the signs of proper remainders calculated by GCD in $\mathbb{Q}$.

It is possible to modify the pseudo-remainder sequence so that the signs coincide with those of Sturm sequnce.

The above article mentions that it is possible to modify the subresultant pseudo-remainder sequence similarly but does not explain how:

For input polynomials with integers coefficients, this allows retrieval of Sturm sequences consisting of polynomials with integer coefficients. The subresultant pseudo-remainder sequence may be modified similarly, in which case the signs of the remainders coincide with those computed over the rationals.

Please, does anyone know how to modify the subresultant pseudo-remainder sequence so that "the signs of the remainders coincide with those computed over the rationals"? Or perhaps someone is having a link to relevant literature?

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