In this paper we focus on the study of monic polynomials whose coefficients are quaternions located left-hand side powers, by addressing three fundamental polynomial problems: factor, evaluate and deflate. An algorithm combining a deflaction procedure with Weierstrass-like quaternionic method is presented. Several examples illustrate proposed approach.

Let k be an algebraically closed field of characteristic p > 0. In this note we consider Galois covers g : Y → P1k which are only branched at t = ∞. We call such covers unramified covers of the affine line. It follows from Abhyankar’s conjecture for the affine line proved by Raynaud ([7]) that such a cover exists for a given group G if and only if G is a quasi-p group, i.e. can be generated by ...