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Sage Interactions - Miscellaneous
goto [:interact:interact main page]
An Interactive Venn Diagram
def f(s, braces=True):
t = ', '.join(sorted(list(s)))
if braces: return '{' + t + '}'
return t
def g(s): return set(str(s).replace(',',' ').split())
@interact
def _(X='1,2,3,a', Y='2,a,3,4,apple', Z='a,b,10,apple'):
S = [g(X), g(Y), g(Z)]
X,Y,Z = S
XY = X.intersection(Y)
XZ = X.intersection(Z)
YZ = Y.intersection(Z)
XYZ = XY.intersection(Z)
html('<center>')
html("$X \cap Y$ = %s"%f(XY))
html("$X \cap Z$ = %s"%f(XZ))
html("$Y \cap Z$ = %s"%f(YZ))
html("$X \cap Y \cap Z$ = %s"%f(XYZ))
html('</center>')
centers = [(cos(n*2*pi/3), sin(n*2*pi/3)) for n in [0,1,2]]
scale = 1.7
clr = ['yellow', 'blue', 'green']
G = Graphics()
for i in range(len(S)):
G += circle(centers[i], scale, rgbcolor=clr[i],
fill=True, alpha=0.3)
for i in range(len(S)):
G += circle(centers[i], scale, rgbcolor='black')
# Plot what is in one but neither other
for i in range(len(S)):
Z = set(S[i])
for j in range(1,len(S)):
Z = Z.difference(S[(i+j)%3])
G += text(f(Z,braces=False), (1.5*centers[i][0],1.7*centers[i][1]), rgbcolor='black')
# Plot pairs of intersections
for i in range(len(S)):
Z = set(S[i]).intersection(S[(i+1)%3]).difference(set(XYZ))
C = (1.3*cos(i*2*pi/3 + pi/3), 1.3*sin(i*2*pi/3 + pi/3))
G += text(f(Z,braces=False), C, rgbcolor='black')
# Plot intersection of all three
G += text(f(XYZ,braces=False), (0,0), rgbcolor='black')
# Show it
G.show(aspect_ratio=1, axes=False)attachment:veng.png
Unreadable code
by Igor Tolkov
@interact
def _(h=(20,(1,36,1))):
print (lambda f:f(0,f))(
lambda n,f:'%s\n%s'%(
('*'*(2*n+1)).join([' '*(h-n-1)]*2),
((n<h-1 and f(n+1,f)) or '')
)
)attachment:unreadable.png
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