# Evaluate a curl at a point?

I'm trying to create a curl example for my calc III students. I figured out how to compute the curl, but not how to evaluate it at a point. Can someone please advise? Thanks, Albert

from sage.manifolds.operators import *
E.<x,y,z> = EuclideanSpace()
v = E.vector_field(exp(x)*sin(y),-exp(x)*cos(y),0, name='v')
show(v.display())
curl_v = curl(v)
show(type(curl_v))
show(curl_v.display())

edit retag close merge delete

Sort by » oldest newest most voted

It is shown on the bottom of the reference manual page for vector fields, using the at method:

p = E((0,0,0), name='p')
show(curl_v.at(p).display())


$$\mathrm{curl}\left(v\right) = -2 e_{ z }$$

(For some reason, the point is not displayed in the notation. Not sure why this is. I would expect it as a subscript.)

more

I was missing the at(). All of the vector calc stuff upto this point has been pretty easy, but these div and curl operators in sage are going to be really tough for the students. Much more complicated. I appreciate the help.

more

1

The method at() is presented in this vector calculus tutorial. The reason why you cannot just write v(p) is that the call operator () acting on a vector field is expecting a 1-form and returns the contraction with that 1-form (a scalar field).

( 2020-10-01 09:52:15 +0200 )edit