Hello Bertfried, > > I am therefore looking for another way to combine these algebras in > > interesting ways. > > If you look at real Clifford algebras, and within them at spinor > modules (vector spaces) > then you can model all of the required number systems as sub Clifford > alegbras. So > if that is your only venue you need only Clifford algebras over > Clifford numbers.
One of the things that I thought would be interesting to do would be to write a program in FriCAS to traverse all the orthogonal and null Clifford algebras and produce a complete map of all these equivalences to these hypercomplex algebras. I have used dual-quaternions to work out kinematics of solid bodies (such as robot arms). I expect this has its limitations, I guess it would not be much use for dynamics as it is not linear, but I get the impression that for certain types of problem it could be a very clean and efficient way to calculate the results. I think some users would just be interested in the application and don't want to learn about Clifford algebras or projective or conformal spaces. So I thought it would be worthwhile to map these algebras to more rigorous methods so people know when it is safe to use them. Also sometimes I come across these hypercomplex algebras in textbooks and on the web so its good to be able to experiment with them using FriCAS. > > zeros of x^2+1, but I can't think how polynomials could represent dual > > or double numbers and so on? > > What about R[x]/<x^2> and R[x]/<x^2-1> ? I guess I would have to add another dimension to combine two Complex algebras: R[x,y]/<(x^2+1)(y^2+1)> ? Would this produce a direct product? I will have to experiment with SimpleAlgebraicExtension and find out how it works, unfortunately it is not very well documented. > Sorry for being short, no problem, I know you are very busy and I appreciate your help. Cheers Martin -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To post to this group, send email to fricas-de...@googlegroups.com. To unsubscribe from this group, send email to fricas-devel+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en.
