how can i tell cadabra that the partial derivatives commute upto linear order while calculating Riemann Tensor

Question

i was trying to tell it like the following -

c1:= \partial_{\alpha}{\partial_{\beta}{h_{\mu \nu}} = 
              \partial_{\beta}{\partial_{\alpha}{h_{\mu \nu}};

its showing error " free index is not matching" something like that

Answer 1

That one had me puzzled for a minute... The solution is to match your brackets: both terms should have an additional } to close the argument of the outmost derivative. So

\partial{#}::PartialDerivative;
c1:= \partial_{\alpha}{\partial_{\beta}{h_{\mu \nu}}} = 
             \partial_{\beta}{\partial_{\alpha}{h_{\mu \nu}}};

And to answer the question in the subject: you can then make these terms equal with a call to canonicalise(c1).