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[Douglas N Arnold <arnold@xxxxxxx>]

Why only three dimensions?  That seems arbitrary. The mathematical 
definition is of course

 epsilon(i_1,...,i_n) =  1, -1, or 0

according to whether (i_1,...,i_n) is an even permutation
of (1,...,n), an odd permutation of (1,...,n), or neither.
It is defined in all dimensions n\ge 1, and is very useful
for all n>1.  The 2-d case is often used in describing finite
element methods for elasticity with weakly imposed symmetry.

The wikipedia article on this is "Levi-Civita symbol",
and the synonyms for the name are "permutation symbol", "antisymmetric
symbol", or "alternating symbol".  I would think

 e = PermutationSymbol()   or  e = PermutationSign()

would be relativitely intuitive.

On 04/13/2011 01:38 PM, Garth N. Wells wrote:
> On 13/04/11 19:31, Martin Sandve Alnæs wrote:
> > That should be fairly easy to do, can be handled similarly to Identity.
>
> Yes - I had a look in the code this afternoon because I thought that it
> may have already been implemented somewhere close to Identity.
>
> > I = Identity(cell.d)
> > f = I[i,j] * ...
> >
> > e = Permutation(cell.d)
> > f = e[i,j,l] * v[j]*w[i]*v[l]*dx
> >
> > Other suggestions for naming?
>
> Maybe
>
>     e = PermutationSymbol()
>
> ? 'Permutation' sounds a bit generic.
>
> I don't think that it needs the cell dimension since it's only defined
> for d = 3.
>
> Garth
>
>
> > Martin
> >
> > On 13 April 2011 20:24, Garth N. Wells<gnw20@xxxxxxxxx
> > <mailto:gnw20@xxxxxxxxx>>  wrote:
> >
> >      The permutation symbol should be added to UFL.
> >
> >      Garth
> >
> >      On 13/04/11 19:20, Martin Sandve Alnæs wrote:
> >      >  Python does not know anything about implicit index summation, so
> >      in your
> >      >  code e() is only called once, and reaches the else condition and thus
> >      >  returns 0.0.
> >      >
> >      >  Similar to as_vector, you can use the as_tensor function, since
> >      you need
> >      >  three dimensions.
> >      >
> >      >  Martin
> >      >
> >      >  On 13 April 2011 19:04, B. Emek Abali
> >      >  <question152702@xxxxxxxxxxxxxxxxxxxxx
> >      <mailto:question152702@xxxxxxxxxxxxxxxxxxxxx>
> >      >  <mailto:question152702@xxxxxxxxxxxxxxxxxxxxx
> >      <mailto:question152702@xxxxxxxxxxxxxxxxxxxxx>>>  wrote:
> >      >
> >      >      New question #152702 on DOLFIN:
> >      >      https://answers.launchpad.net/dolfin/+question/152702
> >      >
> >      >      May be a non-needed trial for some, but I try to define an
> >      >      expression (permutation symbol)
> >      >
> >      >      def e(i,j,k):
> >      >             if (i,j,k) == (1.0,2.0,3.0): return 1.0
> >      >             elif (i,j,k) == (2.0,3.0,1.0): return 1.0
> >      >             elif (i,j,k) == (3.0,1.0,2.0): return 1.0
> >      >             elif (i,j,k) == (3.0,2.0,1.0): return -1.0
> >      >             elif (i,j,k) == (2.0,1.0,3.0): return -1.0
> >      >             elif (i,j,k) == (1.0,3.0,2.0): return -1.0
> >      >             else: return 0.0
> >      >
> >      >      and use (with summation over indices, it is a curl operator
> >      >      contracted with w) in the form like
> >      >
> >      >      f=v[j]*w[i]*e(i,j,l)*v[l]*dx
> >      >
> >      >      which raises:
> >      >      ufl.log.UFLException: Trying to integrate expression of rank 0
> >      with
> >      >      free indices
> >      >
> >      >      Do I have to use as_vector(...) type definition to sum with
> >      indices
> >      >      or is there a nice possibility to let it sum over the arguments of
> >      >      e(...) expression?
> >      >
> >      >      --
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> >      >      DOLFIN Team, which is an answer contact for DOLFIN.
> >      >
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