Question: Contraction over Indices

I caught aome serious errors with Maple 22 calculating the Ricci tensor not only wrong for known metrics, but also producing garbage entries in the Ricci tensor e.g. bare thetas where only trigonometric functions of angles are expected. Completely wrong.

That aside,

I need to replace the built in Ricci tensor calculation in Maple and therefore need maple to contract the Christoffel Symbols.

d_[alpha](Christoffel[~alpha, mu, nu]) - d_[nu](Christoffel[~alpha, mu, alpha]) + Christoffel[~beta, mu, nu]*Christoffel[~alpha, beta, alpha] - Christoffel[~beta, mu, alpha]*Christoffel[~alpha, nu, beta]

How do I tell Maple to contract thae alpha and beta indices in above expression, without crudely having to set up Summing.?

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