I am curious how differential operators are defined in Mathematica. More specifically, if the Laplacian function wasn't available, how would one go on to define such a function in Mathematica directly without reference to Grad or Div? I am thinking of pure functions, but I haven't been able to reproduce the effect of the Laplacian.

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    $\begingroup$ At the end of this answer mathematica.stackexchange.com/questions/5434/… you can find a definition of the d'Alembertian operator, for the Laplacian one can proceed analogically. $\endgroup$
    – Artes
    Mar 9, 2013 at 19:27
  • $\begingroup$ @Artes Thank you for the interesting link. Reading more about Derivative, I see that Mathematica tries to convert this to a pure function such as D[f[#],{#,n}]& . That was what I was trying to achieve directly. $\endgroup$
    – luftiq
    Mar 9, 2013 at 19:36


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