# Rotational: curl

### 5.21.5 Rotational: curl

The curl of a three-dimensional vector field F=[F1,F2,F3] with variables [x1,x2,x3] is

curl F = [

∂ F3
∂ x2

−

∂ F2
∂ x3

,

∂ F1
∂ x3

−

∂ F3
∂ x1

,

∂ F2
∂ x1

−

∂ F1
∂ x2

]

The curl command computes the curl of a three dimensional vector field (note that it must be three dimensional).

- curl takes two arguments:
  - F, a three-dimensional vector field, given as a list of three expressions depending on three variables.
  - vars, a list of the three variable names.
- curl(F,vars) returns the curl of the vector field.

#### Example.

Input:

curl([x*z,-y^2,2*x^y],[x,y,z])

Output:

⎡ ⎣ | 2 lnx· xy,x−2 y xy−1,0 | ⎤ ⎦