Groebner basis structure of ideal interpolation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2020
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| _version_ | 1866910296393646080 |
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| author | Gong, Yihe Jiang, Xue |
| author_facet | Gong, Yihe Jiang, Xue |
| contents | We study the relationship between certain Groebner bases for zero dimensional ideals, and the interpolation condition functionals of ideal interpolation. Ideal interpolation is defined by a linear idempotent projector whose kernel is a polynomial ideal. In this paper, we propose the notion of "reverse" complete reduced basis. Based on the notion, we present a fast algorithm to compute the reduced Groebner basis for the kernel of ideal projector under an arbitrary compatible ordering. As an application, we show that knowing the affine variety makes available information concerning the reduced Groebner basis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_11830 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Groebner basis structure of ideal interpolation Gong, Yihe Jiang, Xue Symbolic Computation Numerical Analysis We study the relationship between certain Groebner bases for zero dimensional ideals, and the interpolation condition functionals of ideal interpolation. Ideal interpolation is defined by a linear idempotent projector whose kernel is a polynomial ideal. In this paper, we propose the notion of "reverse" complete reduced basis. Based on the notion, we present a fast algorithm to compute the reduced Groebner basis for the kernel of ideal projector under an arbitrary compatible ordering. As an application, we show that knowing the affine variety makes available information concerning the reduced Groebner basis. |
| title | Groebner basis structure of ideal interpolation |
| topic | Symbolic Computation Numerical Analysis |
| url | https://arxiv.org/abs/2007.11830 |