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
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.