Curl

As of Version 9.0, vector analysis functionality is built into the Wolfram Language »

Curl[f]

gives the curl, ∇×f, of the vector field f in the default coordinate system.

Curl[f,coordsys]

gives the curl of f in the coordinate system coordsys.

Details and Options

To use Curl, you first need to load the Vector Analysis Package using Needs["VectorAnalysis`"].
The vector field f should be a 3-element list where each element is a function of the coordinates of the appropriate coordinate system.

Wolfram Language code: Needs["VectorAnalysis`"]

Compute the curl of a vector field:

Wolfram Language code: v := {3Xx ^ 2 + 2Yy + (a - 3 b) Zz, (b - 7a)Xx - 5Yy - Zz, 2Xx + c a Yy + 7Zz}

Wolfram Language code: Curl[v]

Find the parameter values for which the vector field is irrotational:

Wolfram Language code: Solve[Curl[v] == 0, {a, b, c}]

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