🚀 go-pugleaf

In article <2185@nikhefh.nikhef.nl> t16@nikhefh.nikhef.nl (Kasper Peeters) writes:

> I was aware of the fact that 'RICCI' can do a lot of these things. However,
> I also need to be able to substitute specific things into the components of
> various tensors, and I do need a system that does automatic dummy relabeling,
> not like 'RICCI' where the only way (correct me if I'm wrong) seems to
> perform every substution after explicit relabeling by 'NewDummy'

>   DefineTensor(a,1,Variance->Con)
>   DefineTensor(b,1) 
>   c=a[U[i]] b[L[i]]
>   e=NewDummy[c] * Newdummy[c]

> This is too complicated for the types of formulea I want to process.

One minor correction.  For the specific computation you wrote above, Ricci
will accept the following:

    e = c^2

You don't have to explicitly call NewDummy to relabel the dummy indices in
this case: Ricci interprets c^2 correctly and will relabel the indices when
necessary (e.g. when differentiating e).  Ricci also calls NewDummy
whenever it automatically performs substitutions containing dummy indices
(for example, in response to a user's DefineRelation command).  However, if
you wanted to multiply together two DIFFERENT expressions that both already
contained i as a dummy index, you would indeed have to use NewDummy
explicitly.  The only way Ricci could save you this trouble would be if it
checked EVERY product to see if the factors had duplicate dummy index
names, which would cost far too much time.

In any case, you're right that Ricci doesn't support substitution of
specific values for components of tensors.  Some day, hopefully.

Jack Lee
--
Jack Lee
Dept. of Mathematics
University of Washington
Seattle, WA