Elsevier

Journal of Symbolic Computation

Volume 107, November–December 2021, Pages 209-220
Journal of Symbolic Computation

Semialgebraic sets and real binary forms decompositions

https://doi.org/10.1016/j.jsc.2021.03.001Get rights and content
Under a Creative Commons license
open access

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.

MSC

14P10
12D10

Keywords

Real binary forms
Waring decompositions
Semialgebraic sets

Cited by (0)