calculus (version 0.1.0)

curl: Numerical and Symbolic Curl

Description

Computes the curl of functions, expressions and characters.

Usage

curl(f, var, accuracy = 2, stepsize = NULL,
  coordinates = "cartesian")
f %curl% var

Arguments

f

function, expression or character array.

var

character vector, giving the variable names with respect to which derivatives will be computed. If a named vector is provided, derivatives will be computed at that point.

accuracy

accuracy degree for numerical derivatives.

stepsize

finite differences stepsize for numerical derivatives. Auto-optimized by default.

coordinates

coordinate system to use. One of: cartesian, polar, spherical, cylindrical, parabolic, parabolic-cylindrical or a character vector of scale factors for each varibale.

Value

curl array.

Functions

• curl: arbitrary coordinate system

• %curl%: cartesian coordinates

Examples

# NOT RUN {
# curl of a vector field
f <- c('x*y','y*z','x*z')
curl(f, var = c('x','y','z'))
f %curl% c('x','y','z')

# irrotational vector field
f <- c('x','-y','z')
curl(f, var = c('x','y','z'))
f %curl% c('x','y','z')

# numerical curl of a vector field
f <- c(function(x,y,z) x*y, function(x,y,z) y*z, function(x,y,z) x*z)
curl(f, var = c('x'=1,'y'=1,'z'=1))
f %curl% c('x'=1,'y'=1,'z'=1)

# curl of array of vector fields
f1 <- c('x*y','y*z','z*x')
f2 <- c('x','-y','z')
a <- matrix(c(f1,f2), nrow = 2, byrow = TRUE)
curl(a, var = c('x','y','z'))
a %curl% c('x','y','z')

# curl in polar coordinates
f <- c('sqrt(r)/10','sqrt(r)')
curl(f, var = c('r','phi'), coordinates = 'polar')

# }