Minimal height companion matrices for Euclid polynomials

Eunice Y. S. Chan, Robert M. Corless

We define Euclid polynomials $E_{k+1}(\lambda )=E_k(\lambda )\left(E_k(\lambda )-1\right)+1$ and $E_1(\lambda )=\lambda +1$ in analogy to Euclid numbers $e_k=E_k(1)$. We show how to construct comp…