On the complexity of invariant polynomials under the action of finite reflection groups

2022/03/08 by Vu, Thi Xuan
#FOS: Computer and information sciences #Symbolic Computation (cs.SC)

paper · doi:10.48550/arxiv.2203.04123

Abstract

Let \mathbbK[x₁, …, x_n] be a multivariate polynomial ring over a field \mathbbK. Let (u₁, …, u_n) be a sequence of n algebraically independent elements in \mathbbK[x₁, …, x_n]. Given a polynomial f in \mathbbK[u₁, …, u_n], a subring of \mathbbK[x₁, …, x_n] generated by the u_i's, we are interested infinding the unique polynomial f_{\rm new} in \mathbbK[e₁,…, e_n], where e₁, …, e_n are new variables, such that f_new(u₁, …, u_n) = f(x₁, …, x_n). We provide an algorithm and analyze its arithmetic complexity to compute f_new knowing f and (u₁, …, u_n).

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