Symbolic tensor product calculation

Question

I am trying to calculate the a symbolic tensor product

$\langle \nabla f\otimes f,\nabla g\otimes g\rangle ^2+(\langle \nabla f\otimes g,\nabla f\otimes g\rangle +\langle \nabla g\otimes f,\nabla g\otimes f\rangle +\langle \nabla g\otimes f,\nabla g\otimes g\rangle ) \langle \nabla f\otimes f,\nabla g\otimes g\rangle +4 \langle \nabla f\otimes g,\nabla f\otimes g\rangle ^2-\langle \nabla f\otimes f,\nabla f\otimes g\rangle \langle \nabla f\otimes g,\nabla g\otimes g\rangle +8 \langle f\otimes g,g\otimes g\rangle \langle \nabla f\otimes \nabla g,\nabla f\otimes \nabla g\rangle +\langle \nabla f\otimes f,\nabla f\otimes f\rangle \langle \nabla g\otimes g,\nabla g\otimes g\rangle$

〈∇f⊗f, ∇g⊗g 〉^2 +  4 〈∇f⊗g, ∇f⊗g〉^2 - 〈∇f⊗f, ∇f⊗g〉 〈∇f⊗g, ∇g⊗g〉 + 
  〈∇f⊗f, ∇g⊗g〉 (〈∇f⊗g, ∇f⊗g〉 + 〈∇g⊗f, ∇g⊗f〉 + 〈∇g⊗f, ∇g⊗g〉) + 
  〈∇f⊗f, ∇f⊗f〉 〈∇g⊗g, ∇g⊗g〉 + 8 〈∇f⊗∇g, ∇f⊗∇g〉 〈f⊗g, g⊗g〉

Is there any Mathematica package to do this?

Welcome to any help

Take a look at related questions and then ask. See e.g. 42966 and 44035. — Artes, May 15 '14 at 16:30
When I need to do some tensor calculcation I use http://www.inp.demokritos.gr/~sbonano/RGTC/ it is designed for general relativity but can handle basic tensor calculation. This one http://www.math.washington.edu/~lee/Ricci/ is often useful to. — mattiav27, May 15 '14 at 16:33

Symbolic tensor product calculation

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