On some Exotic Cylindrical Algebraic Decompositions and Cells
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911376802316288 |
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| author | Michel, Lucas |
| author_facet | Michel, Lucas |
| contents | Cylindrical Algebraic Decompositions (CADs) endowed with additional topological properties have found applications beyond their original logical setting, including algorithmic optimizations in CAD construction, robot motion planning, and the algorithmic study of the topology of semi-algebraic sets. In this paper, we construct explicit examples of CADs and CAD cells that refute several conjectures and open questions of J. H. Davenport, A. Locatelli, and G. K. Sankaran concerning these topological assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09795 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On some Exotic Cylindrical Algebraic Decompositions and Cells Michel, Lucas Algebraic Geometry Symbolic Computation 14P10, 68W30, 14Q30 Cylindrical Algebraic Decompositions (CADs) endowed with additional topological properties have found applications beyond their original logical setting, including algorithmic optimizations in CAD construction, robot motion planning, and the algorithmic study of the topology of semi-algebraic sets. In this paper, we construct explicit examples of CADs and CAD cells that refute several conjectures and open questions of J. H. Davenport, A. Locatelli, and G. K. Sankaran concerning these topological assumptions. |
| title | On some Exotic Cylindrical Algebraic Decompositions and Cells |
| topic | Algebraic Geometry Symbolic Computation 14P10, 68W30, 14Q30 |
| url | https://arxiv.org/abs/2601.09795 |