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
http://wwwcalfor.lip6.fr/~wang/epsilon
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 abovementioned 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.
