Sage Interactions - Miscellaneous

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TableOfContents

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