A repository for CAD Examples

Cylindrical Algebraic Decomposition (CAD, first introduced in [Col75]) of Euclidean space has become an important tool in mathematics and allows for practical quantifier elimination (QE) over the reals. Much research has gone into improving the projection operator (e.g. [McC85]), the use of partial CADs (e.g. [CH91]), or into alternative algorithms (e.g. [CDM+09]). A problem of fundamentally high complexity (doubly-exponential in the number of variables [DH88]) it can be difficult to judge when a problem will be solved quickly, and easy to write down problems that are computationally infeasible. It can therefore be difficult to test new advances in this field, and even harder to 'experiment' with new ideas. We have created a unified machine-readable repository of examples to be used when considering CADs. This allows for quick access to a host of examples, pulled from various theoretical questions and applications. As well as enabling more efficient research, the creation of the repository has prompted us to look deeper at certain questions related to CADs. The example bank currently facilitates quick input for Maple and Qepcad implementations of CAD and QE. Whilst CAD and QE procedures exist in other software, they are not directly involved in our research.