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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. Post code that demonstrates the use of the interact command in Sage here. It should be easy to just scroll through and paste examples out of here into their own sage notebooks.If you have suggestions on how to improve interact, add them [:interactSuggestions: here] or email [email protected].
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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]
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== Graphics == == Miscellaneous ==
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== Calculus ==
=== A contour map and 3d plot of two inverse distance functions ===		 == Profile a snippet of code ==
{{{
html('<h2>Profile the given input</h2>')
import cProfile; import profile
@interact
def _(cmd = ("Statement", '2 + 2'),
      do_preparse=("Preparse?", True), cprof =("cProfile?", False)):
    if do_preparse: cmd = preparse(cmd)
    print "<html>" # trick to avoid word wrap
    if cprof:
        cProfile.run(cmd)
    else:
        profile.run(cmd)
    print "</html>"
}}}
attachment:profile.png


=== Evaluate a bit of code in a given system ===

by William Stein (there is no way yet to make the text box big):
{{{
@interact
def _(system=selector([('sage0', 'Sage'), ('gp', 'PARI'), ('magma', 'Magma')]), code='2+2'):
    print globals()[system].eval(code)
}}}

attachment:evalsys.png

=== A Random Walk ===

by William Stein
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html('<h1>A Random Walk</h1>')
vv = []; nn = 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 foo(pts = checkbox(True, "Show points"),
        refresh = checkbox(False, "New random walk every time"),
        steps = (50,(10..500))):
    # We cache the walk in the global variable vv, so that
    # checking or unchecking the points checkbox doesn't change
    # the random walk.
    html("<h2>%s steps</h2>"%steps)
    global vv
    if refresh or len(vv) == 0:
        s = 0; v = [(0,0)]
        for i in range(steps):
             s += random() - 0.5
             v.append((i, s))
        vv = v
    elif len(vv) != steps:
        # Add or subtract some points
        s = vv[-1][1]; j = len(vv)
        for i in range(steps - len(vv)):
            s += random() - 0.5
            vv.append((i+j,s))
        v = vv[:steps]
    else:
        v = vv
    L = line(v, rgbcolor='#4a8de2')
    if pts: L += points(v, pointsize=10, rgbcolor='red')
    show(L, xmin=0, figsize=[8,3])
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attachment:mountains.png attachment:randomwalk.png
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== Number Theory ==

=== Illustrating of the prime number thoerem ===		 === 3D Random Walk ===
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def _(N=(100,(2..2000))):
    html("<font color='red'>$\pi(x)$</font> and <font color='blue'>$x/(\log(x)-1)$</font> for $x < %s$"%N)
    show(plot(prime_pi, 0, N, rgbcolor='red') + plot(x/(log(x)-1), 5, N, rgbcolor='blue'))		 def rwalk3d(n=(50,1000), frame=True):
    pnt = [0,0,0]
    v = [copy(pnt)]
    for i in range(n):
        pnt[0] += random()-0.5
        pnt[1] += random()-0.5
        pnt[2] += random()-0.5
        v.append(copy(pnt))
    show(line3d(v,color='black'),aspect_ratio=[1,1,1],frame=frame)
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=== 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:randomwalk3d.png

Sage Interactions

Post code that demonstrates the use of the interact command in Sage here. It should be easy to just scroll through and paste examples out of here into their own sage notebooks.If you have suggestions on how to improve interact, add them [:interactSuggestions: here] or email [email protected].

  • [: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]

Miscellaneous

Profile a snippet of code

html('<h2>Profile the given input</h2>')
import cProfile; import profile
@interact
def _(cmd = ("Statement", '2 + 2'), 
      do_preparse=("Preparse?", True), cprof =("cProfile?", False)):
    if do_preparse: cmd = preparse(cmd)
    print "<html>"  # trick to avoid word wrap
    if cprof:
        cProfile.run(cmd)
    else:
        profile.run(cmd)
    print "</html>"

attachment:profile.png

Evaluate a bit of code in a given system

by William Stein (there is no way yet to make the text box big): 

@interact
def _(system=selector([('sage0', 'Sage'), ('gp', 'PARI'), ('magma', 'Magma')]), code='2+2'):
    print globals()[system].eval(code)

attachment:evalsys.png

A Random Walk

by William Stein 

html('<h1>A Random Walk</h1>')
vv = []; nn = 0
@interact
def foo(pts = checkbox(True, "Show points"), 
        refresh = checkbox(False, "New random walk every time"),
        steps = (50,(10..500))):
    # We cache the walk in the global variable vv, so that
    # checking or unchecking the points checkbox doesn't change
    # the random walk. 
    html("<h2>%s steps</h2>"%steps)
    global vv
    if refresh or len(vv) == 0:
        s = 0; v = [(0,0)]
        for i in range(steps): 
             s += random() - 0.5
             v.append((i, s)) 
        vv = v
    elif len(vv) != steps:
        # Add or subtract some points
        s = vv[-1][1]; j = len(vv)
        for i in range(steps - len(vv)):
            s += random() - 0.5
            vv.append((i+j,s))
        v = vv[:steps]
    else:
        v = vv
    L = line(v, rgbcolor='#4a8de2')
    if pts: L += points(v, pointsize=10, rgbcolor='red')
    show(L, xmin=0, figsize=[8,3])

attachment:randomwalk.png

3D Random Walk

@interact
def rwalk3d(n=(50,1000), frame=True):
    pnt = [0,0,0]
    v = [copy(pnt)]
    for i in range(n):
        pnt[0] += random()-0.5
        pnt[1] += random()-0.5
        pnt[2] += random()-0.5
        v.append(copy(pnt))
    show(line3d(v,color='black'),aspect_ratio=[1,1,1],frame=frame)

attachment:randomwalk3d.png

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