Question: My understanding is that Mathematica's [`Reduce`](http://reference.wolfram.com/mathematica/ref/Reduce.html) function is based on [Cylindrical Algebraic Decomposition](http://en.wikipedia.org/wiki/Cylindrical_algebraic_decomposition) (CAD).

The only other system I've seen which implements CAD is [QEPCAD](http://www.usna.edu/cs/~qepcad/B/QEPCAD.html). 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?

Answer: 
In Maple 16, see the commands [CylindricalAlgebraicDecompose](http://www.maplesoft.com/support/help/Maple/view.aspx?path=RegularChains/SemiAlgebraicSetTools/CylindricalAlgebraicDecompose) and [CylindricalDecompose](http://www.maplesoft.com/support/help/Maple/view.aspx?path=RegularChains/ConstructibleSetTools/CylindricalDecompose)
[Singular](http://www.singular.uni-kl.de/) interfaces with QEPCAD. It's not as powerful as Mathematica, though.