# using @interact

I have this code which works just fine and produces an image:

var('u')
center(x) =sqrt(x)
spin(x) = 2- 1/4 * x^2
r(x) = abs(spin(x) - center(x))
parametric_plot3d((x, r(x)*sin(u)+center(x), r(x)*cos(u)), (u, 0, 2*pi), (x, 0, 2), mesh=True)


However, I would like to use a @interact to be able to change the functions named center and spin. I tried this (and a few variations)

@interact
def _(center =6 -x^2, spin = x):
var('u')
var('t')
r(x) = abs(spin(x) - center(x))
parametric_plot3d((t, r(t)*sin(u)+center(x=t), r(t)*cos(u)), (u, 0, 2*pi), (t, 0, 2), mesh=True)


and while I don't get an error, I also don't get a picture for some reason. Any suggestions?

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You just need to use the show command to force Sage to show the plot. The code below works for me.

@interact
def _(center =6 -x^2, spin = x):
var('u')
var('t')
r(x) = abs(spin(x) - center(x))
p=parametric_plot3d((t, r(t)*sin(u)+center(t), r(t)*cos(u)), (u, 0, 2*pi), (t, 0, 2), mesh=True)
show(p)

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Yup, because all in all an interact is still a definition, and if you don't ask the function definition to output anything, it won't.