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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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3 Answers 3

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In Maple 16, see the commands CylindricalAlgebraicDecompose and CylindricalDecompose

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  • $\begingroup$ 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. $\endgroup$ Commented Apr 26, 2014 at 18:28
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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

http://rioboo.free.fr/CadPub/

The package compiles and runs under open-axiom ...

http://www.ensiie.fr/~renaud.rioboo/

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Singular interfaces with QEPCAD. It's not as powerful as Mathematica, though.

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