CoCalc Public Files201-303-AH / Fichiers Sage pour les Étudiants / Exercice 28 page 124.sagews
Author: Julien Giol
Description: Fichiers Sage
Compute Environment: Ubuntu 18.04 (Deprecated)
%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)
$\displaystyle z = -x^{2} + 2$
%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)
$\displaystyle 0 = -x^{2} - y^{2} + 2$
%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)
$\displaystyle z = -x^{2} - y^{2} + 2$
3D rendering not yet implemented