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)
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In 3-D!
points([(0,0,0), (1, 1, 1), (2, pi, -4)])
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p=vector((0,2,4))
q=vector((1,1,1))
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p-q
(-1, 1, 3) (-1, 1, 3) |
norm gives the length of the vector
norm(p-q)
sqrt(11) sqrt(11) |
plot(p) + plot(q) + plot(p-q, color='red')
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@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.')
Click to the left again to hide and once more to show the dynamic interactive window |
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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 x^2 + z^2 == 9 |
implicit_plot3d(equation, (x,-5,5),(y,-5,5),(z,-5,5))
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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.')
Click to the left again to hide and once more to show the dynamic interactive window |
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