16-1 Vector Fields.sagews

var('x', 'y')
plot_vector_field((y, x), (x, -2, 2), (y, -2, 2))

(x, y)

var('y')
A = plot_vector_field((y, x), (x, -5, 5), (y, -5, 5), plot_points = [25, 25], aspect_ratio = 1, figsize = 5)
B = implicit_plot(x^2 + y^2 == 4, (x, -5, 5), (y, -5, 5))
show(A + B)

y

f(x, y) = sin(x*y)
C = contour_plot(f(x, y) == 0, (x, -5, 5), (y, -5, 5), fill = False, contours = 5)
V = plot_vector_field(f.gradient(), (x, -5, 5), (y, -5, 5), color = 'blue')
show(C + V, figsize = 5)

var('x', 'y', 'z')
plot_vector_field3d((y, x, z/5), (x, -2, 2), (y, -2, 2), (z, -2, 2))