, Volume 5, Issue 1–4, pp 147–154 | Cite as

An algorithm for constructing gröbner bases from characteristic sets and its application to geometry

  • Shang-Ching Chou
  • William F. Schelter
  • Jin-Gen Yang


In Ritt's method, a prime ideal is given by a characteristic set. A characteristic set of a prime ideal is generally not a set of generators of this ideal. In this paper we present a simple algorithm for constructing Gröbner bases of a prime ideal from its characteristic set. We give a method for finding new theorems in geometry as an application of this algorithm.

Key words

Polynomial, (Prime) ideal Generators (Irreducible) ascending chain (Irreducible) algebraic set Decomposition of an algebraic set Geometric configuration Nondegenerate component Geometry theorem proving 


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Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • Shang-Ching Chou
    • 1
  • William F. Schelter
    • 2
  • Jin-Gen Yang
    • 2
  1. 1.Institute for Computing ScienceUniversity of Texas at AustinAustinUSA
  2. 2.Department of MathematicsUniversity of Texas at AustinAustinUSA

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