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.