[GiNaC-devel] Re: Bug(?) in reposition_dummy_indices: test case

[Chris Dams]

Dear Alexei,

> First of all, I think it is perfectly sensible for eval() to return zero
> (e.g., what about traceless tensors?).

Yes. However, if we have a traceless tensor both T~mu.mu and T.mu~mu
should evaluated themselves into 0. It does not make sense to only have
one of them evaluate into zero. The point I was trying to make is that
tensors with some index lowered/raised always (?) have the same properties
so that an evaluate step that aplies to the version with an up-index
should also aply to the one with a down-index.

> Secondly, your patch does not catch this:
> [I admit that example is a little bit weird]

Your example is perfectly fine. I should have deleted all indices that are 
dummy indices of the indexed object e that is given as a parameter to 
reposition_dummy_indices in any case, not just when a cyclic symmetry is 
involved. Because you also mentioned the possibility that users would want 
to implement things like the Riemann curvature tensor, it makes sense that 
the evaluation of an indexed object could do any weird kind of 
symmetrization it would want, so I also removed the condition that a 
cyclic symmetry should be involved when trying all combinations of 
repositioning local dummy indices.

> > On the other hand, as a matter of principle you are right that it is
> > best to assume as little about the rest of the code as possbile. For
> > this reason I would accept a patch that would do the substitutions as
> > they are currently but does not cause eval to be called.
>
> The patch I've posted does that. Is there something wrong/stupid/etc 
> with it?

Oh well, the thing seemed rather complicated to me and didn't do all
simplifications possible, as noted in
http://www.ginac.de/pipermail/ginac-devel/2006-August/001055.html. I now
more or less applied it, but with some modifications. I hope that I
haven't broken anything ;-).
(1) Now that the raising and lowering of indices is done on an exvector, 
we do not need to raise/lower both indices at the same time. Another 
reason why this isn't necessary anymore is that indices that occur in 
dummy pairs within the indexed object e should already have been removed 
from the vector variant_dummy_indices. I think this means that the 
for_each that you had can be omitted.
(2) It is not correct to return the indexed object by doing

	indexed ei_ = ex_to<indexed>(e);
	ei_.seq = seq;
	e = ei_; 

This should be e = ex_to<indexed>(e).thiscontainer(seq); because we may be 
dealing with something that inherits from indexed rather than an indexed 
object.

I also simplified the clifford exam by removing a huge macro.

A patch is in CVS.

Best wishes,
Chris