On real Waring decompositions of real binary forms
Macarena Ansola, Antonio D\'iaz-Cano, M.Angeles Zurro

TL;DR
This paper presents an algorithm for obtaining real Waring decompositions of real binary forms, constructing a semialgebraic family of solutions and highlighting differences from the complex case.
Contribution
It introduces a novel algorithm for real Waring decompositions of binary forms and constructs a semialgebraic family of such decompositions.
Findings
Algorithm successfully decomposes binary forms of length up to degree.
Constructs a semialgebraic family of decompositions for given forms.
Highlights differences between real and complex Waring decompositions.
Abstract
The Waring Problem over polynomial rings asks how to decompose a homogeneous polynomial of degree as a finite sum of -{th} powers of linear forms. In this work we give an algorithm to obtain a real Waring decomposition of any given real binary form of length at most its degree. In fact, we construct a semialgebraic family of Waring decompositions for . Some examples are shown to highlight the difference between the real and the complex case.
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Taxonomy
TopicsTensor decomposition and applications · Algorithms and Data Compression · Polynomial and algebraic computation
