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Quantifier Elimination
in
Elementary Algebra and Geometry
by
Partial Cylindrical Algebraic Decomposition
Version B 1.69, 16 Mar 2012
by
Hoon Hong
(hhong@math.ncsu.edu)
With contributions by: Christopher W. Brown, George E.
Collins, Mark J. Encarnacion, Jeremy R. Johnson
Werner Krandick, Richard Liska, Scott McCallum,
Nicolas Robidoux, and Stanly Steinberg
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http://www.usna.edu/CS/~qepcad/B/QEPCAD.html
This is a (shallow) fork of QEPCAD, a program performing cylindrical algebraic decomposition.
I found the library a bit hard to build (especially with Visual Studio), so I added CMake files which makes the process considerably easier.
Given the input
(Ex)[x^2 + a x + b = 0].
the program will output:
An equivalent quantifier-free formula:
4 b - a^2 <= 0
Pretty cool!
There are more examples in the tests folder.
With Visual Studio in Windows, everything is included. Just run the CMake graphical interface and point it to the source root.
In Ubuntu, you may have to execute
sudo apt-get install libreadline-dev
to install a dependency (GNU Readline). Then run
git clone https://github.com/PetterS/qepcad
cd qepcad
mkdir build
cd build
cmake ..
make