### Abstract

Cylindrical algebraic decompositions were introduced as a major component of a new quantifier elimination algorithm for elementary algebra and geometry (G. Collins, 1973). In the present paper we turn the tables and show that one can use quantifier elimination for elementary algebra and geometry to obtain a new version of the cylindrical algebraic decomposition algorithm. A key part of our result is a theorem, of interest in its own right. that relates the multiplicities of the roots of a polynomial to their continuity.

Original language | English |
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Title of host publication | Computer Algebra - EUROCAM 1982, European Computer Algebra Conference |

Editors | Jacques Calmet |

Publisher | Springer-VDI-Verlag GmbH & Co. KG |

Pages | 215-222 |

Number of pages | 8 |

ISBN (Print) | 9783540116073 |

DOIs | |

Publication status | Published - 1 Jan 1982 |

Externally published | Yes |

Event | European Computer Algebra Conference, EUROCAM 1982 - Marseille, France Duration: 5 Apr 1982 → 7 Apr 1982 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 144 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | European Computer Algebra Conference, EUROCAM 1982 |
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Country | France |

City | Marseille |

Period | 5/04/82 → 7/04/82 |

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## Cite this

Arnon, D. S., & McCallum, S. (1982). Cylindrical algebraic decomposition by quantifier elimination. In J. Calmet (Ed.),

*Computer Algebra - EUROCAM 1982, European Computer Algebra Conference*(pp. 215-222). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 144 LNCS). Springer-VDI-Verlag GmbH & Co. KG. https://doi.org/10.1007/3-540-11607-9_25