Question: How can the functional derivative/variation of the Ricci Tensor be computed in the Physics package?

Hello Everyone, 

My questions is about a straight forward as my title suggests. I know how to compute the variation by hand and of course it is in plently of books, but I would like to know how I could possibly do it in Maple as I have some terms with non-trivial contributions where I infact need that specific variation. 

I have attached my file I have been working with that has more comments.

Thank you

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