## Algorithms for the Geometry of Semi-algebraic Sets |

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### Contents

The original cylindrical algebraic | 8 |

Cell boundaries and adjacency | 50 |

The clustering cylindrical | 101 |

4 other sections not shown

### Common terms and phrases

1-section 2-space A-adjacent A-adjacent to tz A-cad A-invariant cad adja algebraic stack basis for PP(A basis-determined cad Bl,Bz boundary section cad of E3 clustering cad algorithm coarsest A-clustering contains a limit continuous function Corollary cylindrical algebraic decomposition cylindrical with respect cylindricity-free Definition denote derivative-based defining formula derivative-regular dim(d DIMENSION disjoint EXACT SAMPLE POINT exists finite hence by Lemma hence by Theorem Idcf INDEX integral minimal polynomial Intermediate Value Theorem invariant irreducible polynomial isolating interval L-cluster L'-initial A-cluster L'-outer adjacency multiset nonvanishing nonzero element open ball open interval original cad algorithm pathwise connected positive degree Proof quantifier elimination real algebraic number real roots region in E1"l regular REP CELL representative cell respect to B3 SAMPLE POINT COORDINATES SD(c section boundary property section of Z(c semi-algebraic set So(c So(cz So(d So{c stack subset Suppose unique factorization domain unique limit point UNIQUE ROOT unique section boundary vanishes