Fichiers Sage
%md # Paraboloïde hyperbolique
var('x, y, z')
eq = z==y^2-x^2 show(eq)
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)
%md # Traces dans les plans x = k
var('x, y, z') x=0 eq = z==y^2-x^2 show(eq)
r = 5 G = implicit_plot(eq, (y, -r, r), (z, -r, r), color = 'red') show(G)
for k in range(1,3): x = k eq = z==y^2-x^2 G+= implicit_plot(eq, (y, -r, r), (z, -r, r), color = 'red') show(G)
%md # Traces dans les plans y = k
var('x, y, z') y=0 eq = z==y^2-x^2 show(eq)
r = 5 G = implicit_plot(eq, (x, -r, r), (z, -r, r), color = 'blue') show(G)
for k in range(1,3): y = k eq = z==y^2-x^2 G+= implicit_plot(eq, (x, -r, r), (z, -r, r), color = 'blue') show(G)
%md # Traces dans les plans z = k
var('x, y, z') z=0 eq = z==y^2-x^2 show(eq)
G = implicit_plot(eq, (x, -r, r), (y, -r, r), color = 'orange') show(G)
for k in range(-1,2): z = k eq = z==y^2-x^2 G+= implicit_plot(eq, (x, -r, r), (y, -r, r), color = 'orange') show(G)