2501.sagews

# Execute this first to serve notice that we need a lot of variables!
var('x,y,z,t')

(x, y, z, t)

F(x,y) = (1/2,-3/2)
plot_vector_field( F(x,y), (x,-3,3), (y,-3,3))

G(x,y) = (x,y)
plot_vector_field( G(x,y), (x,-3,3), (y,-3,3))

H(x,y) = (-y,x)
plot_vector_field( H(x,y), (x,-3,3), (y,-3,3))

K(x,y) = (x, x)
plot_vector_field( K(x,y), (x,-3,3), (y,-3,3))

L(x,y) = (-x/(x^2+y^2)^(3/2), -y/(x^2+y^2)^(3/2))
plot_vector_field( L(x,y), (x,-3,3), (y,-3,3))

Q(x,y) = (x*(x-1), y*(y-1))
plot_vector_field( Q(x,y), (x,-3,3), (y,-3,3))

H(x,y) = (-y,x)
plot_vector_field( H(x,y), (x,-3,3), (y,-3,3)) + parametric_plot( (2*cos(t)-sin(t),2*sin(t)+cos(t)), (t,0,2*pi), color="red")