### Abstract

Given a set of r-variate integral polynomials, a cylindrical algebraic decomposition (cad) of euclidean r-space E^{r }partitions E^{r} into connected subsets compatible with the zeros of the polynomials. Each subset is a cell. Informally, two cells of a cad are adjacent if they touch each other; formally, they are adjacent if their union is connected. In applications of cads one often wishes to know the adjacent pairs of cells. Previous algorithms for cad construction (such as that given in Part I of this paper) have not actually determined them. The authors give here in Part II an algorithm which determines the pairs of adjacent cells as it constructs a cad of E^{2}.

Original language | English |
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Pages (from-to) | 878-889 |

Number of pages | 12 |

Journal | SIAM Journal on Computing |

Volume | 13 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1 Jan 1984 |

Externally published | Yes |

### Keywords

- polynomial zeros
- computer algebra
- computational geometry
- semi-algebraic geometry
- real closed fields
- decision procedures
- real algebraic geometry

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## Cite this

*SIAM Journal on Computing*,

*13*(4), 878-889. https://doi.org/10.1137/0213055