Cylindrical Algebraic Decomposition in Macaulay2
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910899494715392 |
|---|---|
| author | Lee, Corin del Río, Tereso Rahkooy, Hamid |
| author_facet | Lee, Corin del Río, Tereso Rahkooy, Hamid |
| contents | CylindricalAlgebraicDecomposition.m2 is the first implementation of Cylindrical Algebraic Decomposition (CAD) in Macaulay2. CAD decomposes space into 'cells' where input polynomials are sign-invariant. This package computes an Open CAD (full-dimensional cells only) for sets of real polynomials with rational coefficients, enabling users to solve existential problems involving strict inequalities. With the construction of a full CAD (cells of all dimensions), this tool could be extended to solve any real quantifier elimination problem. The current implementation employs the Lazard projection and introduces a new heuristic for choosing the variable ordering. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21731 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cylindrical Algebraic Decomposition in Macaulay2 Lee, Corin del Río, Tereso Rahkooy, Hamid Symbolic Computation Algebraic Geometry 14Q30 (Primary) 68W30, 14P05, 13P15, 03C10 (Secondary) CylindricalAlgebraicDecomposition.m2 is the first implementation of Cylindrical Algebraic Decomposition (CAD) in Macaulay2. CAD decomposes space into 'cells' where input polynomials are sign-invariant. This package computes an Open CAD (full-dimensional cells only) for sets of real polynomials with rational coefficients, enabling users to solve existential problems involving strict inequalities. With the construction of a full CAD (cells of all dimensions), this tool could be extended to solve any real quantifier elimination problem. The current implementation employs the Lazard projection and introduces a new heuristic for choosing the variable ordering. |
| title | Cylindrical Algebraic Decomposition in Macaulay2 |
| topic | Symbolic Computation Algebraic Geometry 14Q30 (Primary) 68W30, 14P05, 13P15, 03C10 (Secondary) |
| url | https://arxiv.org/abs/2503.21731 |