I think that numerical indices should be treated more or less like the
other indices;
for instance consider `A_{m a}` with Lorentz index `m`, flavour index `a`
``T = A^{m 1}*A_m{}^1*A_n{}^a``
is a tensor with two repeated flavor indices.
The first thing to do is to work out the canonicalization in tensor_can;
the indices are ordered as [free, repeated, dummies] so in this case
``ord = [-n,a,F(1),F(1),m,-m]``
To ``T`` is assigned the permutation ``g = [4,2, 5,3, 0,1, 6,7]``
``canonical_free`` is applied to the free indices and the repeated indices .
Then ``double_coset_can_rep`` is applied to the dummy indices and the
repeated indices;
in the above example one adds to the dummy generators the generator
``(2,3)``.
I could do this modification of tensor_can.py
Then one should use this in tensor.py; one has to choose how to represent
numerical indices;
one way could be to add to ``free`` and ``dum`` an attribute ``numeric``
which in the
above example would be ``[(F(1),1,0), (F(1),1,1)]``; the indices are
represented as in ``free``,
but they cannot be summed. Alternatively one can put the numerical indices
together with
the free indices, but putting some logic to distinguish the two kind of
indices.
Finally one has to choose the API; one which I would like is e.g. ``A(m,
F(0))*A(-m, -F(0))``;
one cannot write ``A(m, 0)*A(-m, -0)`` because ``0 = -0``; however one
could print it.
On Thursday, September 19, 2013 8:59:12 PM UTC+2, F. B. wrote:
>
> I am considering introducing numeric indices for tensor expressions. My
> basic idea is that
>
>
> - setting a numeric index is like working on a specific basis for that
> index.
> - setting it breaks the symmetry group of tensor indices, creating a
> new tensor with an index missing (replaced by a fixed number).
> - numeric indices can be numbers and symbols.
>
> By the way, anyone already knows how to handle to symmetry group of tensor
> indices in the case of an index disappearing?
>
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