An algorithm for doubly unitary Laurent polynomials

Document Type : Original Article

Authors

Ihsen Yengui

Faten Ben Amor

Department of Mathematics, University of Sfax, 3000, Sfax, Tunisia

10.22034/kjm.2022.331453.2498

Abstract

We propose two algorithms that for any ring $R$, given a doubly unitary Laurent polynomial $g \in R[X,X^{-1} ]$, compute $h \in R[X,X^{-1}] $ such that $gh \in R[ X^{-1}+X ]$ and $gh$ is monic. The first algorithm is directly extracted from the classical proof. The second algorithm is more direct and simpler. It relies on a symmetrization technique.

Keywords

Doubly unitary Laurent polynomial

doubly monic Laurent polynomial

integral element

symmetric polynomial

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