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added link to complex analysis

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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 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 [[interact/Suggestionshere]] or email the sagesupport mailing list. Of course, your own examples are also welcome! 
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== Graphics ==  Documentation links: 
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== Calculus ==  * [[http://doc.sagemath.org/html/en/reference/repl/sage/repl/ipython_kernel/interact.html interacts in the Jupyter notebook]] (see this page and the two following ones) * [[https://github.com/sagemath/sagenb/blob/master/sagenb/notebook/interact.pyinteracts in the legacy SageNB notebook]] (many helpful examples) * [[https://github.com/sagemath/sagecell/blob/master/interact_compatibility.pySage Cell Server implementation]] * [[https://github.com/sagemathinc/cocalc/blob/master/src/smc_sagews/smc_sagews/sage_salvus.py#L348CoCalc Sage worksheet implementation]] 
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== Number Theory ==  Examples: 
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{{{ html('<h1>Cuspidal Subgroups of Modular Jacobians J0(N)</h1>') 
* [[interact/algebraAlgebra]] * [[interact/bioBioinformatics]] * [[interact/calculusCalculus]] * [[interact/complexComplex Analysis]] * [[interact/cryptographyCryptography]] * [[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/Loop Quantum GravityLoop Quantum Gravity]] * [[interact/miscMiscellaneous]] * [[interact/number_theoryNumber Theory]] * [[interact/statsStatistics/Probability]] * [[interact/topologyTopology]] * [[interact/webWeb Applications]] == 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! {{{#!sagecell x = SR.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=slider([1 .. 12])): ft = f.taylor(x, x0, order) pt = plot(ft, 1, 5, color='green', thickness=2) pretty_print(html(r'$f(x)\;=\;%s$' % latex(f))) pretty_print(html(r'$\hat{f}(x;%s)\;=\;%s+\mathcal{O}(x^{%s})$' % (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 the sagesupport mailing list. Of course, your own examples are also welcome!
Documentation links:
interacts in the Jupyter notebook (see this page and the two following ones)
interacts in the legacy SageNB notebook (many helpful examples)
Examples:
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!