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

Richard B. Kreckel kreckel at ginac.de
Mon Jul 18 22:51:18 CEST 2005

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.

Richard B. Kreckel

More information about the GiNaC-list mailing list