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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 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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attachment:primes.png === 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 === A Charpoly and Hecke Operator Graph === {{{ # Note -- in Sage-2.10.3; multiedges are missing in plots; loops are missing in 3d plots @interact def f(N = prime_range(11,400), p = selector(prime_range(2,12),nrows=1), three_d = ("Three Dimensional", False)): S = SupersingularModule(N) T = S.hecke_matrix(p) G = Graph(T, multiedges=True, loops=not three_d) html("<h1>Charpoly and Hecke Graph: Level %s, T_%s</h1>"%(N,p)) show(T.charpoly().factor()) if three_d: show(G.plot3d(), aspect_ratio=[1,1,1]) else: show(G.plot(),figsize=7) }}} attachment:heckegraph.png === Demonstrating the Diffie-Hellman Key Exchange Protocol === {{{ @interact def diffie_hellman(button=selector(["New example"],label='',buttons=True), bits=("Number of bits of prime", (8,12,..512))): maxp = 2^bits p = random_prime(maxp) k = GF(p) g = k.multiplicative_generator() a = ZZ.random_element(10, maxp) b = ZZ.random_element(10, maxp) print """ <html> <style> .gamodp { background:yellow } .gbmodp { background:orange } .dhsame { color:green; font-weight:bold } </style> <h2>%s-Bit Diffie-Hellman Key Exchange</h2> <ol style="color:#000;font:12px Arial, Helvetica, sans-serif"> <li>Alice and Bob agree to use the prime number p=%s and base g=%s.</li> <li>Alice chooses the secret integer a=%s, then sends Bob (<span class="gamodp">g<sup>a</sup> mod p</span>):<br/>%s<sup>%s</sup> mod %s = <span class="gamodp">%s</span>.</li> <li>Bob chooses the secret integer b=%s, then sends Alice (<span class="gbmodp">g<sup>b</sup> mod p</span>):<br/>%s<sup>%s</sup> mod %s = <span class="gbmodp">%s</span>.</li> <li>Alice computes (<span class="gbmodp">g<sup>b</sup> mod p</span>)<sup>a</sup> mod p:<br/>%s<sup>%s</sup> mod %s = <span class="dhsame">%s</span>.</li> <li>Bob computes (<span class="gamodp">g<sup>a</sup> mod p</span>)<sup>b</sup> mod p:<br/>%s<sup>%s</sup> mod %s = <span class="dhsame">%s</span>.</li> </ol></html> """ % (bits, p, g, a, g, a, p, (g^a), b, g, b, p, (g^b), (g^b), a, p, (g^ b)^a, g^a, b, p, (g^a)^b) }}} attachment:dh.jpg === Somewhat Silly Egg Painter === {{{ var('s,t') g(s) = ((0.57496*sqrt(121 - 16.0*s^2))/sqrt(10.+ s)) def P(color, rng): return parametric_plot3d((cos(t)*g(s), sin(t)*g(s), s), (s,rng[0],rng[1]), (t,0,2*pi), plot_points = [150,150], rgbcolor=color, frame = False, opacity = 1) colorlist = ['red','blue','red','blue'] @interact def _(band_number = selector(range(1,5)), current_color = Color('red')): html('<h1 align=center>Egg Painter</h1>') colorlist[band_number-1] = current_color egg = sum([P(colorlist[i],[-2.75+5.5*(i/4),-2.75+5.5*(i+1)/4]) for i in range(4)]) show(egg) }}} attachment:eggpaint.jpg |
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