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attachment:heckegraph.png 
Sage Interactions
Post code that demonstrates the use of the interact command in Sage here. It should be easy for people to just scroll through and paste examples out of here into their own sage notebooks.
We'll likely restructure and reorganize this once we have some nontrivial content and get a sense of how it is laid out.
Graphics
Calculus
A contour map and 3d plot of two inverse distance functions
@interact def _(q1=(1,(3,3)), q2=(2,(3,3)), cmap=['autumn', 'bone', 'cool', 'copper', 'gray', 'hot', 'hsv', 'jet', 'pink', 'prism', 'spring', 'summer', 'winter']): x,y = var('x,y') f = q1/sqrt((x+1)^2 + y^2) + q2/sqrt((x1)^2+(y+0.5)^2) C = contour_plot(f, (2,2), (2,2), plot_points=30, contours=15, cmap=cmap) show(C, figsize=3, aspect_ratio=1) show(plot3d(f, (x,2,2), (y,2,2)), figsize=5, viewer='tachyon')
attachment:mountains.png
Number Theory
Illustrating of the prime number thoerem
@interact def _(N=(100,(2..2000))): html("<font color='red'>$\pi(x)$</font> and <font color='blue'>$x/(\log(x)1)$</font> for $x < %s$"%N) show(plot(prime_pi, 0, N, rgbcolor='red') + plot(x/(log(x)1), 5, N, rgbcolor='blue'))
attachment:primes.png
Computing the cuspidal subgroup
html('<h1>Cuspidal Subgroups of Modular Jacobians J0(N)</h1>') @interact def _(N=selector([1..8*13], ncols=8, width=10, default=10)): A = J0(N) print A.cuspidal_subgroup()
attachment:cuspgroup.png
A Charpoly and Hecke Operator Graph
# Note  in Sage2.10.3; multiedges are missing in plots; loops are missing in 3d plots @interact def f(N = prime_range(11,400), p = selector(prime_range(2,12),nrows=1), three_d = ("Three Dimensional", False)): S = SupersingularModule(N) T = S.hecke_matrix(p) G = Graph(T, multiedges=True, loops=not three_d) html("<h1>Charpoly and Hecke Graph: Level %s, T_%s</h1>"%(N,p)) show(T.charpoly().factor()) if three_d: show(G.plot3d(), aspect_ratio=[1,1,1]) else: show(G.plot(),figsize=7)
attachment:heckegraph.png