Randomized zero testing of radical expressions and elementary geometry theorem proving

Daniela Tulone; Chee Yap; Chen Li

doi:10.1007/3-540-45410-1_5

Randomized zero testing of radical expressions and elementary geometry theorem proving

Daniela Tulone, Chee Yap, Chen Li

Computer Science

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

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)
Title of host publication	Automated Deduction in Geometry - 3rd International Workshop, ADG 2000, Revised Papers
Editors	Jurgen Richter-Gebert, Dongming Wang
Publisher	Springer Verlag
Pages	58-82
Number of pages	25
ISBN (Print)	3540425985, 9783540425984
DOIs	https://doi.org/10.1007/3-540-45410-1_5
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)
Volume	2061
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	3rd International Workshop on Automated Deduction in Geometry, ADG 2000
Country/Territory	Switzerland
City	Zurich
Period	9/25/00 → 9/27/00

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/3-540-45410-1_5

Cite this

Tulone, D., Yap, C., & Li, C. (2001). Randomized zero testing of radical expressions and elementary geometry theorem proving. In J. Richter-Gebert, & D. Wang (Eds.), Automated Deduction in Geometry - 3rd International Workshop, ADG 2000, Revised Papers (pp. 58-82). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2061). Springer Verlag. https://doi.org/10.1007/3-540-45410-1_5

Randomized zero testing of radical expressions and elementary geometry theorem proving. / Tulone, Daniela; Yap, Chee; Li, Chen.
Automated Deduction in Geometry - 3rd International Workshop, ADG 2000, Revised Papers. ed. / Jurgen Richter-Gebert; Dongming Wang. Springer Verlag, 2001. p. 58-82 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2061).

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

Tulone, D, Yap, C & Li, C 2001, Randomized zero testing of radical expressions and elementary geometry theorem proving. in J Richter-Gebert & D Wang (eds), Automated Deduction in Geometry - 3rd International Workshop, ADG 2000, Revised Papers. 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. https://doi.org/10.1007/3-540-45410-1_5

Tulone D, Yap C, Li C. Randomized zero testing of radical expressions and elementary geometry theorem proving. In Richter-Gebert J, Wang D, editors, Automated Deduction in Geometry - 3rd International Workshop, ADG 2000, Revised Papers. Springer Verlag. 2001. p. 58-82. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-45410-1_5

Tulone, Daniela ; Yap, Chee ; Li, Chen. / Randomized zero testing of radical expressions and elementary geometry theorem proving. Automated Deduction in Geometry - 3rd International Workshop, ADG 2000, Revised Papers. editor / Jurgen Richter-Gebert ; Dongming Wang. Springer Verlag, 2001. pp. 58-82 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Randomized zero testing of radical expressions and elementary geometry theorem proving

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