Plots (Sage)

# Hover over a plot to read coordinates
plot(sin(x^2), (x, 0, 2*pi), color='red', legend_label='sin(x^2)', title='sin(x^2)')

# Graphics add up
g = plot(x^3 - 3*x, (x, -2.2, 2.2), thickness=2)
g += point([(-1, 2), (1, -2)], size=60, color='red')
g += text('local max', (-1, 2.5)) + text('local min', (1, -2.5))
g

# Drag the slider
@interact
def rose(n=slider(1, 12, 1, 5), color=selector(['blue', 'green', 'purple']), filled=False):
    g = polar_plot(cos(n*x), (x, 0, 2*pi), color=color, thickness=2)
    if filled:
        g += disk((0, 0), 1, alpha=0.1)
    show(g, figsize=4.5)

@interact
def damped(a=(0.1, 3.0), w=(1, 12)):
    show(plot(exp(-a*x)*sin(w*x), (x, 0, 6), fill='axis', gridlines=True, ymin=-1, ymax=1, figsize=(7, 3)))

# The prime counting function against the PNT prediction (press ▶)
@interact
def f(N=(10, 1000, 5)):
    show(list_plot([prime_pi(k) for k in range(3, N)], plotjoined=True, legend_label='prime_pi') +
         plot(x/(log(x) - 1), (x, 3, N), color='red', legend_label='x/(log(x)-1)'))

# animate: frames on common axes; the result is an animated SVG
a = animate([plot(sin(x - k)*exp(-x/6), (x, 0, 4*pi), fill='axis', thickness=2) for k in srange(0, 2*pi, 0.2)], figsize=(7, 3))
a.show(delay=5)

# The Platonic solids; translate, rotate and scale move any 3D graphics
icosahedron(color='orange', opacity=0.5).translate((0, 0, 1)) + tetrahedron()

sum(s(center=(3*k, 0, 0), color=c) for k, (s, c) in enumerate([(tetrahedron, 'red'), (cube, 'gold'), (octahedron, 'green'), (dodecahedron, 'blue'), (icosahedron, 'purple')]))

x, y, z = var('x y z')
implicit_plot3d(x^4 - 5*x^2 + y^4 - 5*y^2 + z^4 - 5*z^2 + 11.8, (x, -2.5, 2.5), (y, -2.5, 2.5), (z, -2.5, 2.5), color='gold')