Randomized zero testing of radical expressions and elementary geometry theorem proving

Daniela Tulone, Chee Yap, Chen Li

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish (US)
Title of host publicationAutomated Deduction in Geometry - 3rd International Workshop, ADG 2000, Revised Papers
PublisherSpringer Verlag
Pages58-82
Number of pages25
Volume2061
ISBN (Print)3540425985, 9783540425984
StatePublished - 2001
Event3rd International Workshop on Automated Deduction in Geometry, ADG 2000 - Zurich, Switzerland
Duration: Sep 25 2000Sep 27 2000

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2061
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other3rd International Workshop on Automated Deduction in Geometry, ADG 2000
CountrySwitzerland
CityZurich
Period9/25/009/27/00

Fingerprint

Theorem proving
Theorem Proving
Polynomials
Testing
Geometry
Zero
Ruler
Square root
Polynomial
Experimental Results
Theorem

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Tulone, D., Yap, C., & Li, C. (2001). Randomized zero testing of radical expressions and elementary geometry theorem proving. In 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.

Automated Deduction in Geometry - 3rd International Workshop, ADG 2000, Revised Papers. Vol. 2061 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 proceedingConference contribution

Tulone, D, Yap, C & Li, C 2001, Randomized zero testing of radical expressions and elementary geometry theorem proving. in 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.
Tulone D, Yap C, Li C. Randomized zero testing of radical expressions and elementary geometry theorem proving. In Automated Deduction in Geometry - 3rd International Workshop, ADG 2000, Revised Papers. Vol. 2061. Springer Verlag. 2001. p. 58-82. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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. Vol. 2061 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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