Ansola, M.Díaz-Cano Ocaña, AntonioZurro, M. A.2023-06-172023-06-1720210747717110.1016/j.jsc.2021.03.001https://hdl.handle.net/20.500.14352/8046The 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.engjournal articlehttps://doi.org/10.1016/j.jsc.2021.03.001https://www.sciencedirect.com/science/article/pii/S0747717121000201#!open access512.622512.7Real binary formsWaring decompositionsSemialgebraic setsÁlgebraGeometria algebraica1201 Álgebra1201.01 Geometría Algebraica