Question: discrete variational computation

Hi, I need to calculate some discrete variational problems, but it's a hard work just by hand.

Is there any toolboxes about the discrete variational computation? Or how to design a program to do that?

In particular, I need to realize the functions:

1. the linearized operator and the adjoint operator of some expressions.

       For example:

       the linearized operator of u(n,m+1)u(n+1,m) is u(n+1,m)Tm+u(n,m+1)Tn

       the adjoint operator is u(n+1,m-1)T^(-1)m+u(n-1,m+1)T^(-1)n,

       (The latter is just the discrete Euler operator.)

      Tm, Tn is the shift operator, T^(-1) is the inverse operator of T.

2. discrete Euler-Lagrange equation.

I am not familar with the maple, please help!


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