Semialgebraic sets and real binary forms decompositions
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,...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/8046 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/8046 |
| Access Level: | acceso abierto |
| Palavra-chave: | 512.622 512.7 Real binary forms Waring decompositions Semialgebraic sets Álgebra Geometria algebraica 1201 Álgebra 1201.01 Geometría Algebraica |
| Resumo: | 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. |
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