Semialgebraic sets and real binary forms decompositions. (November 2021) - Ansola, M.; Díaz-Cano, A.; Zurro, M.A.
Abstract: The Waring Problem over polynomial rings asks how to decompose a homogeneous polynomial p of degree d as a linear combination of d -th powers of linear forms. In this work we give an algorithm to obtain a real Waring decomposition of any given real binary form p of length at most its degree. In fact, we construct a semialgebraic family of Waring decompositions for p . We illustrate our results with some examples.