### Abstract

A real quantifier elimination method based on the theory of real root counting and the computation of comprehensive Gröbner systems introduced by V. Weispfenning is studied in more detail. We introduce a simpler and more intuitive algorithm which is shown to be an improvement of the original algorithm. Our algorithm is implemented on the computer algebra system Maple using a recent algorithm to compute comprehensive Gröbner systems together with several simplification techniques. According to our computation experiments, our program is superior to other existing implementations for many examples which contain many equalities.

Original language | English |
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Title of host publication | ISSAC 2015 - Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation |

Publisher | Association for Computing Machinery |

Pages | 173-180 |

Number of pages | 8 |

ISBN (Electronic) | 9781450334358 |

DOIs | |

Publication status | Published - Jun 24 2015 |

Externally published | Yes |

Event | 40th ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2015 - Bath, United Kingdom Duration: Jul 6 2015 → Jul 9 2015 |

### Publication series

Name | Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC |
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Volume | 2015-June |

### Conference

Conference | 40th ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2015 |
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Country | United Kingdom |

City | Bath |

Period | 7/6/15 → 7/9/15 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*ISSAC 2015 - Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation*(pp. 173-180). (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC; Vol. 2015-June). Association for Computing Machinery. https://doi.org/10.1145/2755996.2756646

**Real quantifier elimination by computation of comprehensive Gröbner systems.** / Fukasaku, Ryoya; Iwane, Hidenao; Sato, Yosuke.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*ISSAC 2015 - Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation.*Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC, vol. 2015-June, Association for Computing Machinery, pp. 173-180, 40th ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2015, Bath, United Kingdom, 7/6/15. https://doi.org/10.1145/2755996.2756646

}

TY - GEN

T1 - Real quantifier elimination by computation of comprehensive Gröbner systems

AU - Fukasaku, Ryoya

AU - Iwane, Hidenao

AU - Sato, Yosuke

PY - 2015/6/24

Y1 - 2015/6/24

N2 - A real quantifier elimination method based on the theory of real root counting and the computation of comprehensive Gröbner systems introduced by V. Weispfenning is studied in more detail. We introduce a simpler and more intuitive algorithm which is shown to be an improvement of the original algorithm. Our algorithm is implemented on the computer algebra system Maple using a recent algorithm to compute comprehensive Gröbner systems together with several simplification techniques. According to our computation experiments, our program is superior to other existing implementations for many examples which contain many equalities.

AB - A real quantifier elimination method based on the theory of real root counting and the computation of comprehensive Gröbner systems introduced by V. Weispfenning is studied in more detail. We introduce a simpler and more intuitive algorithm which is shown to be an improvement of the original algorithm. Our algorithm is implemented on the computer algebra system Maple using a recent algorithm to compute comprehensive Gröbner systems together with several simplification techniques. According to our computation experiments, our program is superior to other existing implementations for many examples which contain many equalities.

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U2 - 10.1145/2755996.2756646

DO - 10.1145/2755996.2756646

M3 - Conference contribution

T3 - Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

SP - 173

EP - 180

BT - ISSAC 2015 - Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation

PB - Association for Computing Machinery

ER -