How to Find (Compute) a Separant

Let f be an arbitrary (unitary) polynomial over a valued field $\mathbb{F}=\left\langle F,R\right\rangle$ . In [2], a separant σf of such a polynomial was defined to be an element of a value group ${\varGamma}_{R_0}$ for any algebraically closed extension ${\mathbb{F}}_0=\left\langle {F}_0,{R}_0\right\rangle \ge \mathbb{F}$ . 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.