Dynamics of Algorithms pp 1-29 | Cite as

# Complexity and Applications of Parametric Algorithms of Computational Algebraic Geometry

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## Abstract

This article has two main goals. The first goal is to give a tutorial introduction to certain common computations in algebraic geometry which arise in numerous contexts. No prior knowledge of algebraic geometry is assumed. The second goal is to introduce a software package, called *CGBlisp* which is capable of performing these computations. This exposition is enhanced with simple examples which illustrate the package’s usage. The package was developed as a tool to prove a particular theory in billiard theory, but its scope is very general, as our examples demonstrate. All examples of computations with *CGBLisp* discussed in this paper are included in the distribution of *CGBLisp.*

## Key words

Algebraic geometry geometric theorem proving billiards parametric equations Gröbner basis software## Preview

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## References

- [1]T. Becker and V. Weispfenning,
*Gröbner bases—A Computational approach to Commutative Algebra*, Springer-Verlag, New York, Berlin, Heidelberg, 1993.zbMATHGoogle Scholar - [2]D. Cox, J. Little, and D. O’shea,
*Ideals, Varieties and Algorithms—An Introduction to Algebraic Geometry and Commutative Algebra*, Springer-Verlag, New York, Berlin, Heidelberg, 1992.zbMATHGoogle Scholar - [3]W. M. Dunn III,
*Algorithms and Applications of Comprehensive Groebner Bases*, Ph. D. dissertation, University of Arizona, Tucson, 1995.Google Scholar - [4]D. Eisenbud,
*Commutative Algebra with a View Toward Algebraic Geometry*, Springer-Verlag, New York, Berlin, Heidelberg, 1995.zbMATHGoogle Scholar - [5]M. Rychlik,
*Periodic points of period three of the billiard ball map in a convex domain have measure**0*, J. of Diff. Geometry,**30**, 1989, pp. 191 - 205.MathSciNetzbMATHGoogle Scholar - [6]
- [7]V. Weispfenning,
*Comprehensive Gröbner bases*, Journal of Symbolic Computation,**14**, 1992, pp. 1–29.MathSciNetzbMATHCrossRefGoogle Scholar