I have to do some really long computations of basic riemannian geometry. I am trying to use Mathematica to check them. This is the kind of computations I want to do. Let $M$ be a riemannian manifold and $f:M\rightarrow M$ be given by $f(x)=x$, then I want a code that tells me that $$df_x(e_i)=e_i,$$ for $x\in M$ and $e_i\in T_xM$. Also some of the computations involve and inner product. For exampe, if $f:M\subset (\mathbb{R}^3,\langle, \rangle) \rightarrow \mathbb{R}$ is given by $f(x)=\langle x,x\rangle$ then I would like to have a code that tells me that $$df_x(e_i)=2\langle x,e_i\rangle, $$ for $x\in M$ and $e_i\in T_xM$. I would be thankful for any help.

  • $\begingroup$ Look at that to this end. $\endgroup$
    – user64494
    Commented Jul 28, 2021 at 12:21
  • $\begingroup$ @user64494 I have not been able to find there a solution to my question. There are many other advanced computations but not this simpler one. $\endgroup$ Commented Jul 29, 2021 at 10:19


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