Abstract
We discuss the generation of polynomials with two bounds-an upper bound and a lower bound-on compact sets in various dimensions. We show that a composition formula based on a weighted 4-squares Euler identity generates all such polynomials in dimension d = 1. Higher dimensions are discussed by means of the 8-squares Degen identity and tensorization, and the connection with quaternions algebras is made explicit. Various numerical results illustrate the potentialities of this approach and some implementation details are provided.
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