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())
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.)
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.
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).
Asked: 2020-09-30 18:46:55 +0100
Seen: 355 times
Last updated: Sep 30 '20
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