How to find (compute) a separant

Let $f$ be an arbitrary (unitary) polynomial over a valued field $\mathbb F=\langle F,R\rangle$. In [Algebra i Logika, 53, No. 6, 704–709 (2014)], a separant $\sigma_f$ of such a polynomial was defined to be an element of a value group $\Gamma_{R_0}$ for any algebraically closed extension $\mathbb F_0=\langle F_0,R_0\rangle\ge\mathbb F$. Specifically, the separant was used to obtain a generalization of Hensel's lemma. We show a more algebraic way (compared to the previous) for finding a separant.