Algebraic Number Comparisons for Robust Geometric Operations

Motivation: Computations with algebraic numbers are of key importance in several geometric computations. Algebraic numbers arise as solutions to systems of polynomials—a common operation in many geometric applications, particularly those involving curved objects. Polynomials regularly describe the relationships between even basic geometric objects, for example the (squared) distance between two points. For more complex curved geometric objects, polynomials are often used to describe the actual shapes. Finding solutions to systems of polynomials thus becomes a key operation in numerous geometric applications.