CoCalc Public Files201-303-AH / Fichiers Sage pour les Étudiants / Exercice 11 p 142.sagews
Author: Julien Giol
Description: Fichiers Sage
Compute Environment: Ubuntu 18.04 (Deprecated)
%md
# Paraboloïde elliptique


# Paraboloïde elliptique

var('x, y, z')

(x, y, z)
eq = x==y^2+4*z^2
show(eq)

$\displaystyle x = y^{2} + 4 \, z^{2}$
r = 2
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)

3D rendering not yet implemented
%md
# Traces dans les plans x = k


# Traces dans les plans x = k

var('x, y, z')
x=0
eq = x==y^2+4*z^2
show(eq)

(x, y, z)
$\displaystyle 0 = y^{2} + 4 \, z^{2}$
r = 5
G = implicit_plot(eq, (y, -r, r), (z, -r, r), color = 'red')
show(G)

for k in range(1,10):
x = k
eq = x==y^2+4*z^2
G+= implicit_plot(eq, (y, -r, r), (z, -r, r), color = 'red')
show(G)



%md
# Traces dans les plans y = k


# Traces dans les plans y = k

var('x, y, z')
y=0
eq = x==y^2+4*z^2
show(eq)

(x, y, z)
$\displaystyle x = 4 \, z^{2}$
r = 10
G = implicit_plot(eq, (x, -r, r), (z, -r, r), color = 'blue')
show(G)

for k in range(1,4):
y = k
eq = x==y^2+4*z^2
G+= implicit_plot(eq, (x, -r, r), (z, -r, r), color = 'blue')
show(G)

%md
# Traces dans les plans z = k


# Traces dans les plans z = k

var('x, y, z')
z=0
eq = x==y^2+4*z^2
show(eq)

(x, y, z)
$\displaystyle x = y^{2}$
r = 10
G = implicit_plot(eq, (x, -r, r), (y, -r, r), color = 'orange')
show(G)

for k in range(-1,5):
z = k
eq = x==y^2+4*z^2
G+= implicit_plot(eq, (x, -r, r), (y, -r, r), color = 'orange')
show(G)