Exercice 28 page 124.sagews

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# Exercice 28 page 124

Exercice 28 page 124

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## 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)

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## 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)

$\displaystyle z = -x^{2} + 2$

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## 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)

$\displaystyle 0 = -x^{2} - y^{2} + 2$

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## 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)

$\displaystyle z = -x^{2} - y^{2} + 2$

3D rendering not yet implemented