The functions available in the Epsilon library are capable of performing the following computational tasks.

- Triangularize an arbitrary system of multivariate polynomials.
- Decompose any polynomial system into triangular systems; these triangular systems can be regular, normal, simple, or irreducible, or possess the projection property.
- Decompose any algebraic variety into unmixed or irreducible subvarieties.
- Decompose the radical of any polynomial ideal into prime components and any polynomial ideal into primary components.
- Test radical ideal membership in different ways.
- Perform (most of) the above tasks for systems of ordinary differential polynomials.
- Factorize polynomials over successive algebraic extension fields.
- Solve systems of polynomial equations and inequations.
- Prove theorems in elementary geometry and differential geometry automatically.
- Automatic generation of geometric diagrams; the generated diagrams may be modified and animated with a mouse click and dragging.
- Automatic translation of geometric specifications into algebraic expressions and statements in natural languages.
- Automated documentation and demonstration plus on-line help facilities.
- Compute bivariate Bézout resultants, Macaulay resultants, subresultants, and implicit equations of rational surfaces.
- Compute Liapunov constants for a class of plane differential systems.

Last Modification: June 18, 2003