3903.sagews

Gradient Fields of Surfaces - Example 3:  $$4+x^3+y^3-3xy$$
YouTube PlayList on Gradient Vector Fields - http://www.youtube.com/playlist?list=PLF4CB7AB822F21236

var('x y')
g(x,y)=4+x^3+y^3-3*x*y

V=plot_vector_field(g.gradient(),(x,-1,2),(y,-1,2), color='red',plot_points=13)
show(V, figsize=5)

W = plot3d(g,(x,-1,2),(y,-1,2), aspect_ratio=[1,1,.2], adaptive=True,color=['red','yellow']) 
Sm = sphere((1,1,3),size=.2, color='blue', aspect_ratio=[1,1,1])
Ss=sphere((0,0,4),size=.2, color='blue', aspect_ratio=[1,1,1])
show(W + Sm+Ss, figsize=5)

C= contour_plot(g,(x,-1,2),(y,-1,2), cmap='hsv',fill=False, contours=10) 
show(C , figsize=5)

show(C+V, figsize=5)