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Randomized Xero Testing of Radical Expressions and Elementary Geometry Theorem Proving

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Automated Deduction in Geometry (ADG 2000)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2061))

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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.

This work was performed while Daniela Tulone was at NYU.

This work is supported in part by NSF Grant #CCR 9402464.

Acknowledgments

Daniela Tulone would like to acknowledge Alfredo Ferro and Pina Carrà for their advice and discussions in the initial stages of this project.

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Tulone, D., Yap, C., Li, C. (2001). Randomized Xero Testing of Radical Expressions and Elementary Geometry Theorem Proving. In: Richter-Gebert, J., Wang, D. (eds) Automated Deduction in Geometry. ADG 2000. Lecture Notes in Computer Science(), vol 2061. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45410-1_5

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  • DOI: https://doi.org/10.1007/3-540-45410-1_5

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