### Abstract

We develop a probabilistic test for the vanishing of radical expressions, that is, expressions involving the four rational operations (+,−,×,÷) and square root extraction. This extends the well-known Schwartz’s probabilistic test for the vanishing of polynomials. The probabilistic test forms the basis of a new theorem prover for conjectures about ruler & compass constructions. Our implementation uses the Core Library which can perform exact comparison for radical expressions. Some experimental results are presented.

Original language | English (US) |
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Title of host publication | Automated Deduction in Geometry - 3rd International Workshop, ADG 2000, Revised Papers |

Publisher | Springer Verlag |

Pages | 58-82 |

Number of pages | 25 |

Volume | 2061 |

ISBN (Print) | 3540425985, 9783540425984 |

State | Published - 2001 |

Event | 3rd International Workshop on Automated Deduction in Geometry, ADG 2000 - Zurich, Switzerland Duration: Sep 25 2000 → Sep 27 2000 |

### 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 | 2061 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 3rd International Workshop on Automated Deduction in Geometry, ADG 2000 |
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Country | Switzerland |

City | Zurich |

Period | 9/25/00 → 9/27/00 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Automated Deduction in Geometry - 3rd International Workshop, ADG 2000, Revised Papers*(Vol. 2061, pp. 58-82). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2061). Springer Verlag.

**Randomized zero testing of radical expressions and elementary geometry theorem proving.** / Tulone, Daniela; Yap, Chee; Li, Chen.

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

*Automated Deduction in Geometry - 3rd International Workshop, ADG 2000, Revised Papers.*vol. 2061, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2061, Springer Verlag, pp. 58-82, 3rd International Workshop on Automated Deduction in Geometry, ADG 2000, Zurich, Switzerland, 9/25/00.

}

TY - GEN

T1 - Randomized zero testing of radical expressions and elementary geometry theorem proving

AU - Tulone, Daniela

AU - Yap, Chee

AU - Li, Chen

PY - 2001

Y1 - 2001

N2 - We develop a probabilistic test for the vanishing of radical expressions, that is, expressions involving the four rational operations (+,−,×,÷) and square root extraction. This extends the well-known Schwartz’s probabilistic test for the vanishing of polynomials. The probabilistic test forms the basis of a new theorem prover for conjectures about ruler & compass constructions. Our implementation uses the Core Library which can perform exact comparison for radical expressions. Some experimental results are presented.

AB - We develop a probabilistic test for the vanishing of radical expressions, that is, expressions involving the four rational operations (+,−,×,÷) and square root extraction. This extends the well-known Schwartz’s probabilistic test for the vanishing of polynomials. The probabilistic test forms the basis of a new theorem prover for conjectures about ruler & compass constructions. Our implementation uses the Core Library which can perform exact comparison for radical expressions. Some experimental results are presented.

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UR - http://www.scopus.com/inward/citedby.url?scp=84949510783&partnerID=8YFLogxK

M3 - Conference contribution

SN - 3540425985

SN - 9783540425984

VL - 2061

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 58

EP - 82

BT - Automated Deduction in Geometry - 3rd International Workshop, ADG 2000, Revised Papers

PB - Springer Verlag

ER -