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arXiv · 1910.10771

On real Waring decompositions of real binary forms

Macarena Ansola·Antonio Díaz-Cano·M. Angeles Zurro
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Abstract

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.

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Macarena Ansola, Antonio Díaz-Cano, M. Angeles Zurro. 2019-10-23. On real Waring decompositions of real binary forms. https://arxiv.org/abs/1910.10771

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