Complexity and Applications of Parametric Algorithms of Computational Algebraic Geometry

Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 118)


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 


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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ArizonaTucsonUSA

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