Le jeudi 31 janvier 2019 06:52:10 UTC+1, Tevian Dray a écrit :
>
> >> You can use the plot functionality of vector fields on
> >> Euclidean spaces to get better arrowheads:
>
> OK; I can get jmol to work with some browsers, although it is painfully
> slow. But the results are very nice.
>
>
Hopefully, some day threejs will replace jmol as the default 3d viewer:
https://trac.sagemath.org/ticket/22408
> Finally, is there a simple mechanism to enable Sage to plot vector fields
> with singularities, such as a pole at the origin? I've had no luck yet
> trying to plot something like:
> E.vector_field((-y/(x^2+y^2),x/(x^2+y^2)))
> I've tried piecing together nonsingular domains, although I'm possibly not
> doing it correctly. But there is surely a more elegant solution, such as
> cutting off the vector field at some maximum magnitude.
>
The cut off should definitely be added to the plot method of vector fields,
among many other improvements to be done...
Meanwhile, you can define a subdomain of E, U say, where the vector field
is everywhere regular and plot the restriction of the vector field to U.
For your example, U can be E minus the disk x^2+y^2 <= 0.01:
sage: E.<x,y> = EuclideanSpace()
sage: v = E.vector_field((-y/(x^2+y^2),x/(x^2+y^2)))
sage: U = E.open_subset('U', coord_def={E.cartesian_coordinates():
x^2+y^2>0.01})
sage: v.restrict(U).plot(max_range=1, scale=0.2)
In the above code, "coord_def" stands for the coordinate definition of the
open subset U and "v.restrict(U)" is the restriction of v to U.
Best wishes,
Eric.
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