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GluCat is a set of templates for Clifford Algebra written by Paul Leopardi. See http://glucat.sourceforge.net/ for details. Paul has designed the templates to work with numeric types. Paul supplies two version of his code.
- framed_multi uses an STL map to store each object.
- matrix_multi uses a sparse matrix representation from the Matrix Template Library to store each object.
Some functions interconvert between the types.
I have been adapting them to work with algebraic symbols. I have explained some of this on my web pages at
From the author of GluCat
GluCat is intended for use in numerical analysis applications, such as solution of PDEs.
GluCat uses a fast real matrix representation for Clifford algebras.
See the paper "A generalized FFT for Clifford algebras", Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 11, Number 5, 2005, pp. 663-688, and the preprint at
I have now released GluCat 0.2.1, which uses Boost 1.33.X uBLAS and compiles with GCC 3.3.X to 4.1.X or Intel C++ 7.X to 9.0.
See also Effective uBLAS and http://www.boost.org/libs/numeric/ublas/doc/index.htm
Also, please note that there are other C++ implementations of Clifford algebras.
- GAIGEN, a C++ code optimized generator
- CLU, a C++ library with OPEN-GL graphics
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