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+1 vote

The expression in the example should be zero, but how do you get automatically such result? I happen to have similar (but a bit more complex expressions) and I do not know what to do to get Cadabra simplify such sort of expressions automatically for me. T is a once contravariant twice covariant tensor (well, it is the torsion tensor)

{\alpha,\beta,\gamma,\eta,\tau,\nu}::Indices(vector, position=fixed);
HeartOfTheProblem:=T^{\nu}_{\nu \alpha}*T^{\eta}_{\eta \tau} -T^{\nu}_{\nu\tau}*T^{\eta}_{\eta \alpha};

Cadabra almost repeats the input, which although it is not wrong, is not the expected zero:

HeartOfTheProblem := {T}^{\beta}\,_{\beta \alpha} {T}^{\gamma}\,_{\gamma \tau} - {T}^{\beta}\,_{\beta \tau} {T}^{\gamma}\,_{\gamma \alpha};`
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1 Answer

+2 votes

Use @canonicalise!(%) followed by @collect_terms!(%). In Cadabra v2.x, it is just a matter of canonicalise(_).

by (65.1k points)