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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 [:interactSuggestions:here] or email [email protected] . Of course, your own examples are also welcome!  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 [[interactSuggestionshere]] or email [email protected] . Of course, your own examples are also welcome! 
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* [:interact/graph theory:Graph Theory] * [:interact/fractal:Fractals] * [:interact/calculus:Calculus] * [:interact/diffeq:Differential Equations] * [:interact/dynsys:Dynamical Systems] * [:interact/linear algebra:Linear Algebra] * [:interact/algebra:Algebra] * [:interact/number theory:Number Theory] * [:interact/web:Web Applications] * [:interact/bio:Bioinformatics] * [:interact/graphics:Drawing Graphics] * [:interact/misc:Miscellaneous] 
* [[interact/graph_theoryGraph Theory]] * [[interact/fractalFractals]] * [[interact/calculusCalculus]] * [[interact/diffeqDifferential Equations]] * [[interact/dynsysDynamical Systems]] * [[interact/linear_algebraLinear Algebra]] * [[interact/algebraAlgebra]] * [[interact/number_theoryNumber Theory]] * [[interact/webWeb Applications]] * [[interact/bioBioinformatics]] * [[interact/graphicsDrawing Graphics]] * [[interact/miscMiscellaneous]] 
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attachment:taylor_series_animated.gif  {{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(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)