Clifford Algebra Computation

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

There is a review of available software at http://sinai.mech.fukui-u.ac.jp/gcj/gc_int.html.

One of the items listed there is called Glucat, by Paul Leopardi. (http://glucat.sourceforge.net/)

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 (http://www.ginac.de/) 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

http://www.mrao.cam.ac.uk/~clifford/pages/software.htm

Hitzer has a good mailing list and word press available at http://gaupdate.wordpress.com/

I've found Mathematica well suited for GA work, and have used (and hacked on) Suguru Furuta's Mathematica routines. http://www.mrao.cam.ac.uk/~clifford/pages/software.htm (also available from link above) -EricLindahl?

CategoryMath