On real Waring decompositions of real binary forms

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 cons...

Descripción completa

Detalles Bibliográficos
Autores: Ansola Fernández-Enríquez, María Macarena, Díaz-Cano Ocaña, Antonio, Zurro, María Ángeles
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/7228
Acceso en línea:https://hdl.handle.net/20.500.14352/7228
Access Level:acceso abierto
Palabra clave:512.7
Real binary forms
Waring decompositions
Semialgebraic sets
Álgebra
Geometria algebraica
1201 Álgebra
1201.01 Geometría Algebraica
Descripción
Sumario: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.