A family of explicit Waring decompositions of a polynomial
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2023
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910425160876032 |
|---|---|
| author | Han, Kangjin Moon, Hyunsuk |
| author_facet | Han, Kangjin Moon, Hyunsuk |
| contents | In this paper we settle some polynomial identity which provides a family of explicit Waring decompositions of any monomial $X_0^{a_0}X_1^{a_1}\cdots X_n^{a_n}$ over a field $\Bbbk$. This gives an upper bound for the Waring rank of a given monomial and naturally leads to an explicit Waring decomposition of any homogeneous form and, eventually, of any polynomial via (de)homogenization. Note that such decomposition is very useful in many applications dealing with polynomial computations, symmetric tensor problems and so on. We discuss some computational aspect of our result as comparing with other known methods and also present a computer implementation for potential use in the end. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_03177 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A family of explicit Waring decompositions of a polynomial Han, Kangjin Moon, Hyunsuk Commutative Algebra Numerical Analysis Algebraic Geometry Functional Analysis 14P99, 12D05, 13P10, 14A25, 15A21, 14N15 In this paper we settle some polynomial identity which provides a family of explicit Waring decompositions of any monomial $X_0^{a_0}X_1^{a_1}\cdots X_n^{a_n}$ over a field $\Bbbk$. This gives an upper bound for the Waring rank of a given monomial and naturally leads to an explicit Waring decomposition of any homogeneous form and, eventually, of any polynomial via (de)homogenization. Note that such decomposition is very useful in many applications dealing with polynomial computations, symmetric tensor problems and so on. We discuss some computational aspect of our result as comparing with other known methods and also present a computer implementation for potential use in the end. |
| title | A family of explicit Waring decompositions of a polynomial |
| topic | Commutative Algebra Numerical Analysis Algebraic Geometry Functional Analysis 14P99, 12D05, 13P10, 14A25, 15A21, 14N15 |
| url | https://arxiv.org/abs/2301.03177 |