2423.sagews

x = var('x')
plot((1 - cos(x)^2)/sin(x), x, -1, 5)

x, y = var('x, y')
plot3d( sin(x)^2*cos(y), (x,3,15), (y,5,17))

x = var('x')
parametric_plot((cos(x),sin(x)),(x,0,pi),color="red", aspect_ratio=1)

u = var('u')
parametric_plot3d( (sin(u), cos(u), u/10), (u, 0, 20))

u, v = var('u,v')
fx = u*v
fy = u
fz = v^2
parametric_plot3d([fx, fy, fz], (u, -1, 1), (v, -1, 1), color="yellow")

u, v = var('u,v')
fx = 2/3* (cos(u)* cos(2*v) + sqrt(2)* sin(u)* cos(v))* cos(u) / (sqrt(2) - sin(2*u)* sin(3*v))
fy = 2/3* (cos(u)* sin(2*v) - sqrt(2)* sin(u)* sin(v))* cos(u) / (sqrt(2) - sin(2*u)* sin(3*v))
fz = sqrt(2)* cos(u)* cos(u) / (sqrt(2) - sin(2*u)* sin(3*v))
parametric_plot3d([fx, fy, fz], (u, -2*pi, 2*pi), (v, 0, pi), plot_points = [90,90], frame=False, color="purple")

x,y = var('x y')
plot_vector_field((sin(x), cos(y)), (x,-3,3), (y,-3,3))

x,y,z=var('x y z')
plot_vector_field3d((x*cos(z),-y*cos(z),sin(z)), (x,0,pi), (y,0,pi), (z,0,pi),colors=['red','green','blue'],center_arrows=True)

x,y,t = var('x, y, t')
P1 = plot3d(sqrt(x^2+y^2),(x,-10,10),(y,-10,10))
P2 = plot3d(1+y,(x,-10,10),(y,-10,10), color="red")
P3 = parametric_plot3d([t,(t^2-1)/2,(t^2+1)/2],(t,-5,5), color="green", thickness=3)
show(P1+P2+P3, aspect_ratio=1)