Quelques graphiques accompagnant la solution du devoir n.5

var('x,y')
f(x,y) = y^3 -x^3 -1
G = f.gradient()
G(x,y)

Champ = plot_vector_field([y^2,x^2],(x,-2,2),(y,-2,2), color="blue")
Courbe = implicit_plot(f(x,y) == 0 , (x,-2,2), (y,-2,2), color= "red")
show(Champ + Courbe)

var('s,t')
def x(t) :
	return 10*cos(t)
def y(t) :
	return 10*sin(t)
def z(x,y) :
	return 4+(x^2-y^2)/100
S = parametric_plot3d([x(t),y(t), s*z(x(t),y(t))],(t,0,2*pi),(s,0,1), color= "darkgreen", opacity = 0.35)
C = parametric_plot3d([x(t),y(t), z(x(t),y(t))],(t,0,2*pi), color= "red", thickness= 2)
show(S+C, frame_aspect_ratio = [1,1,3])