What is the reason for Mathematica to produce expressions with opposite signs?

Curl[Curl[{X[x, y], Y[x, y], 0}, {x, y, z}], {x, y, z}]

Curl[Curl[{X[x, y], Y[x, y]}, {x, y}], {x, y}]
  • $\begingroup$ Possible duplicate: mathematica.stackexchange.com/q/191373/12 $\endgroup$
    – Szabolcs
    Commented Mar 7, 2019 at 13:34
  • $\begingroup$ Nitpick: that's not a scalar you're taking the curl of. $\endgroup$ Commented Mar 7, 2019 at 14:27
  • $\begingroup$ @MichaelSeifert In the second line, s/he's taking the curl of Curl[{X[x, y], Y[x, y]}, {x, y}], which returns a scalar. $\endgroup$
    – Szabolcs
    Commented Mar 7, 2019 at 15:05
  • $\begingroup$ Yes the second line indeed it is the Curl of a scalar. It is explained in another post actually and has to do with Hodge Duality and Exterior Forms. $\endgroup$
    – user651620
    Commented Mar 7, 2019 at 18:19


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