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,...
| Authors: | , , |
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| Format: | article |
| Publication Date: | 2021 |
| Country: | España |
| Institution: | Universidad Complutense de Madrid (UCM) |
| Repository: | Docta Complutense |
| Language: | English |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/8046 |
| Online Access: | https://hdl.handle.net/20.500.14352/8046 |
| Access Level: | Open access |
| Keyword: | 512.622 512.7 Real binary forms Waring decompositions Semialgebraic sets Álgebra Geometria algebraica 1201 Álgebra 1201.01 Geometría Algebraica |
| Summary: | 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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