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| 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. | 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! |
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| We'll likely restructure and reorganize this once we have some nontrivial content and get a sense of how it is laid out. | * [:interact/graph theory:Graph Theory] * [:interact/calculus:Calculus] * [:interact/diffeq:Differential Equations] * [: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] |
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| == Graphics == | == Explanatory example: Taylor Series == |
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| == Calculus == === A contour map and 3d plot of two inverse distance functions === |
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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| 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)) |
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| 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((x-1)^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') |
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:mountains.png == Number Theory == === 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 |
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 [:interactSuggestions:here] or email [email protected] . Of course, your own examples are also welcome!
- [:interact/graph theory:Graph Theory]
- [:interact/calculus:Calculus]
- [:interact/diffeq:Differential Equations]
- [: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]
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)attachment:taylor_series_animated.gif