# Wolfram Language & System 11.0 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# Curl

Curl[{f1,f2},{x1,x2}]
gives the curl .

Curl[{f1,f2,f3},{x1,x2,x3}]
gives the curl .

Curl[f,{x1,,xn}]
gives the curl of the ××× array f with respect to the -dimensional vector {x1,,xn}.

Curl[f,x,chart]
gives the curl in the coordinates chart.

## DetailsDetails

• Curl[f,x] can be input as xf. The character can be typed as EscdelEsc or \[Del], and the character can be typed as EsccrossEsc or \[Cross]. The list of variables x is entered as a subscript.
• An empty template can be entered as EscdelxEsc, and Tab moves the cursor from the subscript to the main body.
• All quantities that do not explicitly depend on the variables given are taken to have zero partial derivative.
• In Curl[f,{x1,,xn}], if f is an array with depth k<n, it must have dimensions {n,,n}, and the resulting curl is an array with depth n-k-1 of dimensions {n,,n}.
• If f is a scalar, Curl[f,{x1,,xn},chart] returns an array of depth n-1 in the orthonormal basis associated with chart.
• In Curl[f,{x1,,xn},chart], if f is an array, the components of f are interpreted as being in the orthonormal basis associated with chart.
• Coordinate charts in the third argument of Curl can be specified as triples {coordsys,metric,dim} in the same way as in the first argument of CoordinateChartData. The short form in which dim is omitted may be used.
• Curl works with SparseArray and StructuredArray objects.

## ExamplesExamplesopen allclose all

### Basic Examples  (4)Basic Examples  (4)

Curl of a vector field in Cartesian coordinates:

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Curl of a vector field in cylindrical coordinates:

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Rotational in two dimensions:

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Use EscdelEsc to enter , Ctrl+- for the list of subscripted variables, and EsccrossEsc to enter :

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Use EscdelxEsc to enter the template , fill in the variables, press Tab, and fill in the function:

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