4116.sagews

Welcome to SAGE!  

We can do all sorts of cool things with SAGE.

First, let's plot a few points.

points([(0,0), (1,1), (2,pi)], pointsize=30)

In 3-D!

points([(0,0,0), (1, 1, 1), (2, pi, -4)])

p=vector((0,2,4))
q=vector((1,1,1))

p-q

(-1, 1, 3)

norm gives the length of the vector

norm(p-q)

sqrt(11)

plot(p) + plot(q) + plot(p-q, color='red')

@interact
def _(p=input_box(default=(0,2,4)),q=input_box(default=(1,1,1))):
    show(plot(vector(p)) + plot(vector(q)) + plot(vector(p)-vector(q), color='red'))
    print html('Enter vectors p and q.  This will plot p and q in blue and p-q in red.')

p  q  [removed] [removed] [removed] [removed]

Now we plot the (boundary of) the cylinder we talked about in class!  

Grab it (with your mouse) to rotate it around and view it from different angles.

var('x,y,z')
equation=x^2+z^2==9
equation

x^2 + z^2 == 9

implicit_plot3d(equation, (x,-5,5),(y,-5,5),(z,-5,5))

var('x,y,z')

@interact
def _(equation=input_box(default=(x-1)^2+(y-2)^2+(z+3)^2==16), size=(5)):
    show(implicit_plot3d(equation, (x,-size,size),(y,-size,size),(z,-size,size)))
    print html('Enter implicitly defined surface in 3-d (in variables x, y and z) and size of display box.')

equation  size  [removed] [removed] [removed] [removed]