3904.sagews

Gradient Fields - Example 2: Cone  $$\sqrt{x^2+y^2}$$
YouTube PlayList on Gradient Vector Fields - http://www.youtube.com/playlist?list=PLF4CB7AB822F21236

var('x y')
g(x,y)=sqrt(x^2+y^2)

V=plot_vector_field(g.gradient(),(x,-5,5),(y,-5,5),color='red')
show(V, figsize=5)

W = plot3d(g,(x,-5,5),(y,-5,5), aspect_ratio=[1,1,1], adaptive=True,color=['red','yellow']) 
S = sphere((0,0,0),size=.3, color='blue', aspect_ratio=[1,1,1])
show(W + S, figsize=5)

C= contour_plot(g,(x,-5,5),(y,-5,5), cmap='hsv',fill=False, contours=10) 
show(C , figsize=5)

show(C+V, figsize=5)