## Abstract

This article makes the key observation that when using cylindrical algebraic decomposition (CAD) to solve a problem with respect to a set of polynomials, it is not always the signs of those polynomials that are of paramount importance but rather the truth values of certain quantifier free formulae involving them. This motivates our definition of a Truth Table Invariant CAD (TTICAD). We generalise the theory of equational constraints to design an algorithm which will efficiently construct a TTICAD for a wide class of problems, producing stronger results than when using equational constraints alone. The algorithm is implemented fully inMaple and we present promising results from experimentation.

Original language | English |
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Title of host publication | ISSAC 2013 - Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation |

Editors | Manuel Kauers |

Place of Publication | New York |

Publisher | Association for Computing Machinery |

Pages | 125-132 |

Number of pages | 8 |

ISBN (Print) | 9781450320597 |

DOIs | |

Publication status | Published - 2013 |

Event | 38th International Symposium on Symbolic and Algebraic Computation, ISSAC 2013 - Boston, MA, United States Duration: 26 Jun 2013 → 29 Jun 2013 |

### Other

Other | 38th International Symposium on Symbolic and Algebraic Computation, ISSAC 2013 |
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Country | United States |

City | Boston, MA |

Period | 26/06/13 → 29/06/13 |