plot_vector_field : some questions

edit

hi

i dont really know how to do this :

i have a vectori field, say :

y=var('y')#x l'est déjà par défaut
coef=10
g = plot_vector_field((x*coef, 2*y*coef), (x,-4,4), (y,-3,3),
        gridlines=True, gridlinesstyle=dict(color="blue", linestyle=":"),
        frame=False, axes=True)
show(g)

so each point say (k.p,k'.p) with k,k' in Z and p,p choosen by sage, have a vector starting from them, represented by sage.

Now, i would like to show to my students what div and rot mean

for that purpose, i would like to :

• draw some little areas, like circles -> i think i can learn how to do that
• inside this circles i would like to put some text with the value of div and rot at the center of the circle -> also i think, if i do some research i can find
• but now, the point where i am not sure wether it is possible : i would like to modify my vectoriel field, so that no point inside the disk has its vector image represented, but a certain number of points of the circle would have their vector, as in the image C:\fakepath\aj_vect.JPG