2408.sagews

var('x,y,z')

(x, y, z)

F(x,y) = (-2*y,2*x)
P = point((2,1),color='red', size=30)
P + plot_vector_field( F, (x,-3,3), (y,-3,3))

P + plot_vector_field( F, (x,1.5,2.5), (y,0.5,1.5))

P + plot_vector_field( F, (x,1.95,2.05), (y,0.95,1.05))

g(x,y) = (x^3+y^3)/(x^2+y^2)
plot3d(g, (x,-1,1), (y,-1,1))

plot3d(g, (x,-0.1,0.1), (y,-0.1,0.1))

h(x,y) = (x^3+y^3)/(x^2+y^2)^(3/2)
plot3d(h, (x,-1,1), (y,-1,1))

plot3d(h,(x,-0.1,0.1),(y,-0.1,0.1))

k(x,y) = (x^2-y^2)/(x^2+y^2)
plot3d(k, (x,-1,1), (y,-1,1) )

plot3d(k, (x,-0.1,0.1), (y,-0.1,0.1) )

plot3d(k, (x,-1,1), (y,-1,1)) + implicit_plot3d(y==2*x, (x,-1,1), (y,-1,1), (z,-1,1), color='red')

plot3d(k, (x,-0.01,0.01), (y,-0.01,0.01) )