CoCalc Public Files201-303-AH / Fichiers Sage pour les Étudiants / Exercice 28 page 124.sagewsOpen with one click!
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%md # Exercice 28 page 124

Exercice 28 page 124

%md ## Traces dans les plans x = k

Traces dans les plans x = k

var('x, y, z') x = 0 eq = z==2-x^2-y^2 r = 10 G = implicit_plot(eq, (y, -r, r), (z, -r, r), color = 'red') for k in range(1,4): x = k eq = z==2-x^2-y^2 G+= implicit_plot(eq, (y, -r, r), (z, -r, r), color = 'red') show(G)
(x, y, z)
%md ## Traces dans les plans y = k

Traces dans les plans y = k

var('x, y, z') y=0 eq = z==2-x^2-y^2 show(eq) r = 10 G = implicit_plot(eq, (x, -r, r), (z, -r, r), color = 'blue') for k in range(1,4): y = k eq = z==2-x^2-y^2 G+= implicit_plot(eq, (x, -r, r), (z, -r, r), color = 'blue') show(G)
(x, y, z)
z=x2+2\displaystyle z = -x^{2} + 2
%md ## Traces dans les plans z = k (courbes de niveau)

Traces dans les plans z = k (courbes de niveau)

var('x, y, z') z=0 eq = z==2-x^2-y^2 show(eq) r=5 G = implicit_plot(eq, (x, -r, r), (y, -r, r), color = 'green') for k in range(-1,5): z = k eq = z==2-x^2-y^2 G+= implicit_plot(eq, (x, -r, r), (y, -r, r), color = 'green') show(G)
(x, y, z)
0=x2y2+2\displaystyle 0 = -x^{2} - y^{2} + 2
%md ## Graphe

Graphe

var('x, y, z') eq = z==2-x^2-y^2 show(eq) r = 10 G = implicit_plot3d(eq, (x, -r, r), (y, -r, r), (z, -r, r), plot_points=30, color='orange', mesh=1, opacity=.7) show(G, spin=1)
(x, y, z)
z=x2y2+2\displaystyle z = -x^{2} - y^{2} + 2
3D rendering not yet implemented