Algebraic Winding Numbers
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916329839132672 |
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| author | Perrucci, Daniel Roy, Marie-Françoise |
| author_facet | Perrucci, Daniel Roy, Marie-Françoise |
| contents | In this paper, we propose a new algebraic winding number and prove that it computes the number of complex roots of a polynomial in a rectangle, including roots on edges or vertices with appropriate counting. The definition makes sense for the algebraic closure C = R[i] of a real closed field R, and the root counting result also holds in this case. We study in detail the properties of the algebraic winding number defined in [3] with respect to complex root counting in rectangles. We extend both winding numbers to rational functions, obtaining then algebraic versions of the argument principle for rectangles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_08638 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Algebraic Winding Numbers Perrucci, Daniel Roy, Marie-Françoise Algebraic Geometry 12D10, 13J30, 14Q20 In this paper, we propose a new algebraic winding number and prove that it computes the number of complex roots of a polynomial in a rectangle, including roots on edges or vertices with appropriate counting. The definition makes sense for the algebraic closure C = R[i] of a real closed field R, and the root counting result also holds in this case. We study in detail the properties of the algebraic winding number defined in [3] with respect to complex root counting in rectangles. We extend both winding numbers to rational functions, obtaining then algebraic versions of the argument principle for rectangles. |
| title | Algebraic Winding Numbers |
| topic | Algebraic Geometry 12D10, 13J30, 14Q20 |
| url | https://arxiv.org/abs/2305.08638 |