[GiNaC-list] Clifford Metric Array

[Vladimir Kisil]

On Thu, 17 Nov 2005, Alan Bromborsky wrote:

> You probably handle this correctly internally, but the documentation example 
> is not consistent.  In section 4.15.1.2, "A Generic Clifford Algebra", you 
> state that e[i]*e[j]+e[j]*e[i] = M(i,j) and then give an example where
>    ex M = diag_matrix(lst(1,-1,0,s));
>    ex e = clifford_unit(nu,M);
> and say M(0,0) = 1 -> e[0]^2 = 1.  I get 2*e[0]^2 = 1 so that e[0]^2 = 1/2. 
> Is M internally multiplied by 2?

Yes, this is a misprint in the earlier version of the documentation: it 
should be read as e[i]*e[j]+e[j]*e[i] = 2 * M(i,j).

The present version of CVS of GiNaC can work with non-symmetric algebras 
and the defined equation is given in the ginac.info by
e~i e~j + e~j e~i = M(i, j) + M(j, i), which is equivalent to the above 
for a symmetric M.

Best wishes,
Vladimir
--
Vladimir Kisil            email: kisilv at amsta.leeds.ac.uk
                             www: http://amsta.leeds.ac.uk/~kisilv