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?