Differences between revisions 3 and 124 (spanning 121 versions)
 ⇤ ← Revision 3 as of 2008-03-11 18:19:25 → Size: 1116 Editor: was Comment: ← Revision 124 as of 2011-03-15 14:42:12 → ⇥ Size: 1977 Editor: pang Comment: added category: topology Deletions are marked like this. Additions are marked like this. Line 3: Line 3: 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 [[http://sagemath.org/doc/reference/sagenb/notebook/interact.html#sagenb.notebook.interact.interact|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! Line 5: Line 5: We'll likely restructure and reorganize this once we have some nontrivial content and get a sense of how it is laid out. * [[interact/algebra|Algebra]] * [[interact/bio|Bioinformatics]] * [[interact/calculus|Calculus]] * [[interact/chemistry|Chemistry]] * [[interact/diffeq|Differential Equations]] * [[interact/graphics|Drawing Graphics]] * [[interact/dynsys|Dynamical Systems]] * [[interact/fractal|Fractals]] * [[interact/games|Games and Diversions]] * [[interact/geometry|Geometry]] * [[interact/graph_theory|Graph Theory]] * [[interact/linear_algebra|Linear Algebra]] * [[interact/misc|Miscellaneous]] * [[interact/number_theory|Number Theory]] * [[interact/stats|Statistics/Probability]] * [[interact/topology|Topology]] * [[interact/web|Web Applications]] Line 7: Line 23: == Graphics == == Explanatory example: Taylor Series == Line 9: Line 25: == Calculus =={{{ 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!{{{#!python numbers=nonevar('x')x0 = 0f = sin(x)*e^(-x)p = plot(f,-1,5, thickness=2)dot = point((x0,f(x=x0)),pointsize=80,rgbcolor=(1,0,0)) Line 12: Line 34: 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) Line 21: Line 41: == Number Theory =={{{html('

Cuspidal Subgroups of Modular Jacobians J0(N)

')@interactdef _(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 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)


interact (last edited 2021-08-23 15:58:42 by anewton)