[GiNaC-list] A.i B~i != A.0 B~0 + A.1 B~1 + ... [WAS: Bug or feature?]

[Richard B. Kreckel]

On Wed, 13 Jul 2005, Sheplyakov Alexei wrote:
> On Tue, Jul 12, 2005 at 10:35:22PM +0200, Richard B. Kreckel wrote:
> [...]
> > Can you suggest the wording for such a FAQ entry?
>
> I will try.
>
> ---------------------------- cut here -------------------------------
> Q1: I am wondering how to convince GiNaC that the following to
>   expressions are equal:
>   [[-1,0],[0,1]~mu~mu * a~mu
>   [[-1,0],[0,1].nu~mu * a~nu
>
> A:
> Declare `a' as a matrix. Otherwise, these expressions are meaningless.
>
> The `indexed' class (and most of derived classes) is intended for tensor
> manipulation without referring to a particular basis. Thus, the `indexed'
> class is well suited for calculations involving (formally defined)
> tensor algebra of non-integer-dimensional space.  This is particularly
> useful for evaluation of Feynman integrals in the framework of
> dimensional regularization.
>
> On the other hand, the `matrix' class is _not_ treated as a tensor,
> so mixing matrices with indexed objects typically gives meaningless
> result.
>
> Q2: I'd like to know if is it possible to unroll indexed
> objects. As example, I would like to do something like this
>
>  a_i a~i = (a_1)^2 + (a_2)^2 + (a_3)^2 + ...
>
> A: You should use matrix instead of indexed. See also Q1.

Thanks a lot!  I've coalesced the two Q's and A's into one (each).  Hope
the result is okay: <http://www.ginac.de/FAQ.html#matrix_indexed>.

On a related note: It would be good if the FAQ could be incorporated into
the sources.  I wonder what format would be most convenient.  Maybe just
add it as another chapter to the Texinfo documentation?  This would make
it conveniently searchable from within info.

Regards
  -richy.
-- 
Richard B. Kreckel
<http://www.ginac.de/~kreckel/>