  The Waring Problem over polynomial rings asks how to decompose a homogeneous
polynomial $p$ of degree $d$ as a finite sum 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 $p$. Some
examples are shown to highlight the difference between the real and the complex
case.
