Real quantifier elimination is doubly exponential
Journal of Symbolic Computation
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
An Improved Projection Operation for Cylindrical Algebraic Decomposition
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
QEPCAD B: a program for computing with semi-algebraic sets using CADs
ACM SIGSAM Bulletin
Computing cylindrical algebraic decomposition via triangular decomposition
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Cylindrical algebraic decompositions for boolean combinations
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Optimising problem formulation for cylindrical algebraic decomposition
CICM'13 Proceedings of the 2013 international conference on Intelligent Computer Mathematics
| Hi-index | 0.00 |
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.