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Software Tool for Polynomial Elimination and Triangular Decomposition

Dongming Wang

School of Science, Beihang University, Beijing 100083, China
Laboratoire d'Informatique de Paris 6, UPMC - CNRS
8 rue du Capitaine Scott, F-75015 Paris, France


Epsilon is a library of functions implemented in Maple and Java for polynomial elimination and triangular decomposition with (geometric) applications. It has 8 modules and contains more than 70 functions, which allow one to

  • triangularize systems of multivariate (differential) polynomials,
  • decompose polynomial systems into triangular systems of various kinds (regular, normal, simple, irreducible, or with projection property),
  • decompose algebraic varieties into irreducible or unmixed subvarieties,
  • decompose polynomial ideals into primary components,
  • factorize polynomials over algebraic extension fields,
  • solve systems of polynomial equations and inequations, and
  • handle and prove geometric theorems automatically.

The entire library with documentation, examples, and Maple worksheets is available at

for download. It has also been published and distributed together with a book entitled "Elimination Practice: Software Tools and Applications" by Imperial College Press, London. Epsilon is completely free for academic and noncommercial use. More information about the library may be found from the above-mentioned book and web page.

In this exhibition, we shall present the main capabilities of Epsilon with a demonstration on its application to geometric reasoning problems.

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