An algorithm for doubly unitary Laurent polynomials

[摘要] 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.

[学科分类] 公共、环境与职业健康

[关键词] Doubly unitary Laurent polynomial;doubly monic Laurent polynomial;integral element;Symmetric Polynomial