Computation of residual polynomial operators of inductive valuations

Let (K,v) be a valued field, and μ an inductive valuation on K[x] extending v. Gμ the graded algebra of over K[x], κ maximal subfield subring formed by homogeneous elements degree zero. In this paper, we find algorithm to compute field residual polynomial operator Rμ:K[x]→κ[y], where y is another indeterminate, without any need perform computations in algebra. This leads OM factorization separable defectless polynomials henselian fields.