Clifford Algebra Computation

Computation of CliffordAlgebra amounts to building a system capable of doing the multiplications.

There is a review of available software at

One of the items listed there is called Glucat, by Paul Leopardi. (

It provides a set of templated CeePlusPlus classes which can be used to calculate numerical problems in CliffordAlgebra.

I have been developing a symbolic extension to Glucat using GiNac ( to provide the symbolic algebra. One of my objectives has been to use OperatorOverloading to enable the writer of the top-level program to write down any expression which is valid in the algebra and have it compile and give the correct answer. This has led me on a long journey into the use of CeePlusPlus templates (see CategoryCppTemplates). I have largely succeeded in getting to the point where I have working code, making use of FC++ (see FunctoidsInCpp).

The main limitation on the use of this is that the user has to have access to the C++ compiler (in my case GnuCpp), and enter into an edit/compile/run cycle for every change of the program. To get around this problem, I have used the SimplifiedWrapperAndInterfaceGenerator to make an interface to RubyLanguage. I also make use of RubyCoerce. The result is a great aid to exploring the algebra, as I can think of something and just type it into a Ruby program. I would like to extend this use of AlternateHardAndSoftLayers. One way is to deliver the results using a tool such as RubyOnRails to put the calculations onto a web page. -- JohnFletcher

Hitzer has a good mailing list and word press available at

I've found Mathematica well suited for GA work, and have used (and hacked on) Suguru Furuta's Mathematica routines. (also available from link above) -EricLindahl?


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