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Post code (and screen shots) of the use of interact in Sage here. We'll likely restructure and reorganize this, or move it out of the wiki (?) once we have some nontrivial content and get a sense of how it is laid out.  This is a collection of pages demonstrating the use of [[http://sagemath.org/doc/reference/sagenb/notebook/interact.html#sagenb.notebook.interact.interactthe interact command]] in Sage. It should be easy to just scroll through and copy/paste examples into Sage notebooks. If you have suggestions on how to improve interact, add them [[interactSuggestionshere]] or email [email protected] . Of course, your own examples are also welcome! 
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== Graphics ==  * [[interact/algebraAlgebra]] * [[interact/bioBioinformatics]] * [[interact/calculusCalculus]] * [[interact/chemistryChemistry]] * [[interact/diffeqDifferential Equations]] * [[interact/graphicsDrawing Graphics]] * [[interact/dynsysDynamical Systems]] * [[interact/fractalFractals]] * [[interact/gamesGames and Diversions]] * [[interact/geometryGeometry]] * [[interact/graph_theoryGraph Theory]] * [[interact/linear_algebraLinear Algebra]] * [[interact/miscMiscellaneous]] * [[interact/number_theoryNumber Theory]] * [[interact/statsStatistics/Probability]] * [[interact/topologyTopology]] * [[interact/webWeb Applications]] 
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== Calculus ==  == Explanatory example: Taylor Series == 
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== Number Theory ==  This is the code and a mockup animation of the interact command. It defines a slider, seen on top, that can be dragged. Once dragged, it changes the value of the variable "order" and the whole block of code gets evaluated. This principle can be seen in various examples presented on the pages above! 
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{{{ html('<h1>Cuspidal Subgroups of Modular Jacobians J0(N)</h1>') 
{{{#!python numbers=none var('x') x0 = 0 f = sin(x)*e^(x) p = plot(f,1,5, thickness=2) dot = point((x0,f(x=x0)),pointsize=80,rgbcolor=(1,0,0)) 
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def _(N=selector([1..8*13], ncols=8, width=10, default=10)): A = J0(N) print A.cuspidal_subgroup() 
def _(order=(1..12)): ft = f.taylor(x,x0,order) pt = plot(ft,1, 5, color='green', thickness=2) html('$f(x)\;=\;%s$'%latex(f)) html('$\hat{f}(x;%s)\;=\;%s+\mathcal{O}(x^{%s})$'%(x0,latex(ft),order+1)) show(dot + p + pt, ymin = .5, ymax = 1) 
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{{attachment:taylor_series_animated.gif}} 
Sage Interactions
This is a collection of pages demonstrating the use of the interact command in Sage. It should be easy to just scroll through and copy/paste examples into Sage notebooks. If you have suggestions on how to improve interact, add them here or email [email protected] . Of course, your own examples are also welcome!
Explanatory example: Taylor Series
This is the code and a mockup animation of the interact command. It defines a slider, seen on top, that can be dragged. Once dragged, it changes the value of the variable "order" and the whole block of code gets evaluated. This principle can be seen in various examples presented on the pages above!
var('x')
x0 = 0
f = sin(x)*e^(x)
p = plot(f,1,5, thickness=2)
dot = point((x0,f(x=x0)),pointsize=80,rgbcolor=(1,0,0))
@interact
def _(order=(1..12)):
ft = f.taylor(x,x0,order)
pt = plot(ft,1, 5, color='green', thickness=2)
html('$f(x)\;=\;%s$'%latex(f))
html('$\hat{f}(x;%s)\;=\;%s+\mathcal{O}(x^{%s})$'%(x0,latex(ft),order+1))
show(dot + p + pt, ymin = .5, ymax = 1)