# 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?

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In Maple 16, see the commands CylindricalAlgebraicDecompose and CylindricalDecompose

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Thank you Robert! – dharmatech Aug 1 '12 at 22:26
Also in Maple in the recent versions is SemiAlgebraic (see SolveTools package). It is very user friendly (it takes rational polynomials as input, while the other commands don't accept that. – Sergio Parreiras Apr 26 '14 at 18:28

Open source: In Axiom (also FriCAS and OpenAxiom) see the axiom-developer email list

Re: [Axiom-developer] installing Axiom on Fedora 16
From: Renaud . Rioboo
Date: Fri, 13 Jul 2012 14:15:46 -0700


Dear Axiom Gurus,

there seems to be again some interests on cylindrical algebraic decomposition and I wanted to recompile my CAD package which is available at