Computer Algebra Systems which implement Cylindrical Algebraic Decomposition My understanding is that Mathematica's `Reduce` function is based on Cylindrical Algebraic Decomposition (CAD). The only other system I've seen which implements CAD is QEPCAD. QEPCAD isn't a general CAS like Mathematica or Maple. Do any mainstream CASes feature a solver as powerful as Mathematica's `Reduce`? Are they known to be based on CAD as well? Are any of the open source CASes working on adding a CAD based solver?

In Maple 16, see the commands CylindricalAlgebraicDecompose and CylindricalDecompose