x,y,z=var('x,y,z')
p1=implicit_plot3d(z==(x*y)/(x^2+y^2),(x,-1,1),(y,-1,1),(z,-1,1))
p2=implicit_plot3d(y==x,(x,-1,1),(y,-1,1),(z,0.47,0.53),color='magenta')
p3=implicit_plot3d(y==-x,(x,-1,1),(y,-1,1),(z,-0.47,-0.53),color='green')
p1+p2+p3