Computer Algebra
The team has a broad interest in developing and applying computer algebra to the design, analysis and verification of systems of polynomial equations and/or differential polynomial equations. This covers:
- Data structure for representing and querying such systems. Binary Decision Diagrams (BDD) are perhaps the most known example, but other recent data structures like chordal networks also fall into this topic.
- Automated reasoning about polynomial differential equations. For instance, one wants to know whether a semi-algebraic set is positively invariant under a given polynomial ordinary differential equation.
- Extensions of differential algebra techniques to real closed fields. This allows in particular to consider systems with inequalities in addition to the usual equations. Linear Complementarity Systems (LCS) are of particular interest as they are often used to model idealized physical behaviors.
