Differences between revisions 97 and 99 (spanning 2 versions)
 ⇤ ← Revision 97 as of 2008-05-07 13:28:23 → Size: 24393 Editor: schilly Comment: ← Revision 99 as of 2008-05-07 13:42:39 → ⇥ Size: 16844 Editor: schilly Comment: Deletions are marked like this. Additions are marked like this. Line 9: Line 9: == Algebra ===== Groebner fan of an ideal ===by Marshall Hampton; (needs sage-2.11 or higher, with gfan-0.3 interface){{{@interactdef gfan_browse(p1 = input_box('x^3+y^2',type = str, label='polynomial 1: '), p2 = input_box('y^3+z^2',type = str, label='polynomial 2: '), p3 = input_box('z^3+x^2',type = str, label='polynomial 3: ')):    R. = PolynomialRing(QQ,3)    i1 = ideal(R(p1),R(p2),R(p3))    gf1 = i1.groebner_fan()    testr = gf1.render()     html('Groebner fan of the ideal generated by: ' + str(p1) + ', ' + str(p2) + ', ' + str(p3))    show(testr, axes = False, figsize=[8,8*(3^(.5))/2])}}}attachment:gfan_interact.png== Number Theory ===== Factor Trees ===by William Stein{{{import randomdef ftree(rows, v, i, F):    if len(v) > 0: # add a row to g at the ith level.        rows.append(v)    w = []    for i in range(len(v)):        k, _, _ = v[i]        if k is None or is_prime(k):            w.append((None,None,None))        else:            d = random.choice(divisors(k)[1:-1])            w.append((d,k,i))            e = k//d            if e == 1:                w.append((None,None))            else:                w.append((e,k,i))    if len(w) > len(v):        ftree(rows, w, i+1, F)def draw_ftree(rows,font):    g = Graphics()    for i in range(len(rows)):        cur = rows[i]        for j in range(len(cur)):            e, f, k = cur[j]            if not e is None:                if is_prime(e):                     c = (1,0,0)                else:                     c = (0,0,.4)                g += text(str(e), (j*2-len(cur),-i), fontsize=font, rgbcolor=c)                if not k is None and not f is None:                    g += line([(j*2-len(cur),-i), ((k*2)-len(rows[i-1]),-i+1)],                     alpha=0.5)    return g@interactdef factor_tree(n=100, font=(10, (8..20)), redraw=['Redraw']):    n = Integer(n)    rows = []    v = [(n,None,0)]    ftree(rows, v, 0, factor(n))    show(draw_ftree(rows, font), axes=False)}}}attachment:factortree.png=== Continued Fraction Plotter ===by William Stein{{{@interactdef _(number=e, ymax=selector([None,5,20,..,400],nrows=2), clr=Color('purple'), prec=[500,1000,..,5000]):    c = list(continued_fraction(RealField(prec)(number))); print c    show(line([(i,z) for i, z in enumerate(c)],rgbcolor=clr),ymax=ymax,figsize=[10,2])}}}attachment:contfracplot.png=== Illustrating the prime number thoerem ===by William Stein{{{@interactdef _(N=(100,(2..2000))):    html("$\pi(x)$ and $x/(\log(x)-1)$ for $x < %s$"%N)    show(plot(prime_pi, 0, N, rgbcolor='red') + plot(x/(log(x)-1), 5, N, rgbcolor='blue'))}}}attachment:primes.png=== Computing Generalized Bernoulli Numbers ===by William Stein (Sage-2.10.3){{{@interactdef _(m=selector([1..15],nrows=2), n=(7,(3..10))):    G = DirichletGroup(m)    s = "

First n=%s Bernoulli numbers attached to characters with modulus m=%s

"%(n,m)    s += ''    s += '
$\\chi$Conductor$B_{%s,\chi}$
$%s$
%s%s
' + \           ''.join(''%k for k in [1..n]) + ''    for eps in G.list():        v = ''.join([''%latex(eps.bernoulli(k)) for k in [1..n]])        s += '%s\n'%(             eps, eps.conductor(), v)    s += ''    html(s)}}}attachment:bernoulli.png=== Fundamental Domains of SL_2(ZZ) ===by Robert Miller{{{L = [[-0.5, 2.0^(x/100.0) - 1 + sqrt(3.0)/2] for x in xrange(1000, -1, -1)]R = [[0.5, 2.0^(x/100.0) - 1 + sqrt(3.0)/2] for x in xrange(1000)]xes = [x/1000.0 for x in xrange(-500,501,1)]M = [[x,abs(sqrt(x^2-1))] for x in xes]fundamental_domain = L+M+Rfundamental_domain = [[x-1,y] for x,y in fundamental_domain]@interactdef _(gen = selector(['t+1', 't-1', '-1/t'], nrows=1)):    global fundamental_domain    if gen == 't+1':        fundamental_domain = [[x+1,y] for x,y in fundamental_domain]    elif gen == 't-1':        fundamental_domain = [[x-1,y] for x,y in fundamental_domain]    elif gen == '-1/t':        new_dom = []        for x,y in fundamental_domain:            sq_mod = x^2 + y^2            new_dom.append([(-1)*x/sq_mod, y/sq_mod])        fundamental_domain = new_dom    P = polygon(fundamental_domain)    P.ymax(1.2); P.ymin(-0.1)    P.show()}}}attachment:fund_domain.png=== Computing modular forms ===by William Stein{{{j = 0@interactdef _(N=[1..100], k=selector([2,4,..,12],nrows=1), prec=(3..40),       group=[(Gamma0, 'Gamma0'), (Gamma1, 'Gamma1')]):    M = CuspForms(group(N),k)    print j; global j; j += 1    print M; print '\n'*3    print "Computing basis...\n\n"    if M.dimension() == 0:         print "Space has dimension 0"    else:        prec = max(prec, M.dimension()+1)        for f in M.basis():             view(f.q_expansion(prec))    print "\n\n\nDone computing basis."}}}attachment:modformbasis.png=== Computing the cuspidal subgroup ===by William Stein{{{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=== A Charpoly and Hecke Operator Graph ===by William Stein{{{# Note -- in Sage-2.10.3; multiedges are missing in plots; loops are missing in 3d plots@interactdef 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("

Charpoly and Hecke Graph: Level %s, T_%s

"%(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 ===by Timothy Clemans (refereed by William Stein){{{@interactdef 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)    if bits>100:        g = k(2)    else:        g = k.multiplicative_generator()    a = ZZ.random_element(10, maxp)    b = ZZ.random_element(10, maxp)    print """

%s-Bit Diffie-Hellman Key Exchange

1. Alice and Bob agree to use the prime number p=%s and base g=%s.
2. Alice chooses the secret integer a=%s, then sends Bob (ga mod p):
%s%s mod %s = %s.
3. Bob chooses the secret integer b=%s, then sends Alice (gb mod p):
%s%s mod %s = %s.
4. Alice computes (gb mod p)a mod p:
%s%s mod %s = %s.
5. Bob computes (ga mod p)b mod p:
%s%s mod %s = %s.
""" % (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.png=== Plotting an elliptic curve over a finite field ==={{{E = EllipticCurve('37a')@interactdef _(p=slider(prime_range(1000), default=389)):    show(E)    print "p = %s"%p    show(E.change_ring(GF(p)).plot(),xmin=0,ymin=0)}}}attachment:ellffplot.png * [:interact/algebra:Algebra] * [:interact/number_theory:Number Theory] Line 627: Line 380: ===Miscellaneous===Profile a snippet of code{{{html('

Profile the given input

')import cProfile; import profile@interactdef _(cmd = ("Statement", '2 + 2'),       do_preparse=("Preparse?", True), cprof =("cProfile?", False)):    if do_preparse: cmd = preparse(cmd)    print "" # trick to avoid word wrap    if cprof:        cProfile.run(cmd)    else:        profile.run(cmd)    print ""}}}attachment:profile.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]

## Web applications

### Stock Market data, fetched from Yahoo and Google

by William Stein

import urllib

class Day:
def __init__(self, date, open, high, low, close, volume):
self.date = date
self.open=float(open); self.high=float(high); self.low=float(low); self.close=float(close)
self.volume=int(volume)
def __repr__(self):
return '%10s %4.2f %4.2f %4.2f %4.2f %10d'%(self.date, self.open, self.high,
self.low, self.close, self.volume)

class Stock:
def __init__(self, symbol):
self.symbol = symbol.upper()

def __repr__(self):
return "%s (%s)"%(self.symbol, self.yahoo()['price'])

def yahoo(self):
url = 'http://finance.yahoo.com/d/quotes.csv?s=%s&f=%s' % (self.symbol, 'l1c1va2xj1b4j4dyekjm3m4rr5p5p6s7')
data = {}
data['price'] = values[0]
data['change'] = values[1]
data['volume'] = values[2]
data['avg_daily_volume'] = values[3]
data['stock_exchange'] = values[4]
data['market_cap'] = values[5]
data['book_value'] = values[6]
data['ebitda'] = values[7]
data['dividend_per_share'] = values[8]
data['dividend_yield'] = values[9]
data['earnings_per_share'] = values[10]
data['52_week_high'] = values[11]
data['52_week_low'] = values[12]
data['50day_moving_avg'] = values[13]
data['200day_moving_avg'] = values[14]
data['price_earnings_ratio'] = values[15]
data['price_earnings_growth_ratio'] = values[16]
data['price_sales_ratio'] = values[17]
data['price_book_ratio'] = values[18]
data['short_ratio'] = values[19]
return data

def historical(self):
try:
return self.__historical
except AttributeError:
pass
symbol = self.symbol
def get_data(exchange):
verbose=False)
R = get_data('NASDAQ')
R = get_data("NYSE")
R = R.splitlines()
self.__historical = []
try:
for x in reversed(R[1:]):
date, opn, high, low, close, volume = x.split(',')
self.__historical.append(Day(date, opn,high,low,close,volume))
except ValueError:
pass
self.__historical = Sequence(self.__historical,cr=True,universe=lambda x:x)
return self.__historical

def plot_average(self, spline_samples=10):
d = self.historical()
if len(d) == 0:
avg = list(enumerate([(z.high+z.low)/2 for z in d]))
P = line(avg) + points(avg, rgbcolor='black', pointsize=4) + \
text(self.symbol, (len(d)*1.05, d[-1].low), horizontal_alignment='right', rgbcolor='black')
if spline_samples > 0:
k = 250//spline_samples
spl = spline([avg[i*k] for i in range(len(d)//k)] + [avg[-1]])
P += plot(spl, (0,len(d)+30), color=(0.7,0.7,0.7))
P.xmax(260)
return P

def plot_diff(self):
d = self.historical()
if len(d) == 0:
diff = []
for i in range(1, len(d)):
z1 = d[i]; z0 = d[i-1]
diff.append((i, (z1.high+z1.low)/2 - (z0.high + z0.low)/2))
P = line(diff,thickness=0.5) + points(diff, rgbcolor='black', pointsize=4) + \
text(self.symbol, (len(d)*1.05, 0), horizontal_alignment='right', rgbcolor='black')
P.xmax(260)
return P

symbols = ['bsc', 'vmw', 'sbux', 'aapl', 'amzn', 'goog', 'wfmi', 'msft', 'yhoo', 'ebay', 'java', 'rht', ]; symbols.sort()
stocks = dict([(s,Stock(s)) for s in symbols])

@interact
def data(symbol = symbols, other_symbol='', spline_samples=(8,[0..15])):
if other_symbol != '':
symbol = other_symbol
S = Stock(symbol)
html('<h1 align=center><font color="darkred">%s</font></h1>'%S)
S.plot_average(spline_samples).save('avg.png', figsize=[10,2])
S.plot_diff().save('diff.png', figsize=[10,2])

Y = S.yahoo()
k = Y.keys(); k.sort()
html('Price during last 52 weeks:<br>Grey line is a spline through %s points (do not take seriously!):<br> <img src="cell://avg.png">'%spline_samples)
html('Difference from previous day:<br> <img src="cell://diff.png">')
html('<table align=center>' + '\n'.join('<tr><td>%s</td><td>%s</td></tr>'%(k[i], Y[k[i]]) for i in range(len(k))) + '</table>')

attachment:stocks.png

### CO2 data plot, fetched from NOAA

by Marshall Hampton

While support for R is rapidly improving, scipy.stats has a lot of useful stuff too. This only scratches the surface.

import urllib2 as U
import scipy.stats as Stat
datalines = []
for a_line in co2data:
if a_line.find('Creation:') != -1:
cdate = a_line
if a_line[0] != '#':
temp = a_line.replace('\n','').split(' ')
temp = [float(q) for q in temp if q != '']
datalines.append(temp)
trdf = RealField(16)
@interact
def mauna_loa_co2(start_date = slider(1958,2010,1,1958), end_date = slider(1958, 2010,1,2009)):
htmls1 = '<h3>CO2 monthly averages at Mauna Loa (interpolated), from NOAA/ESRL data</h3>'
htmls2 = '<h4>'+cdate+'</h4>'
sel_data = [[q[2],q[4]] for q in datalines if start_date < q[2] < end_date]
c_max = max([q[1] for q in sel_data])
c_min = min([q[1] for q in sel_data])
slope, intercept, r, ttprob, stderr = Stat.linregress(sel_data)
html(htmls1+htmls2+'<h4>Linear regression slope: ' + str(trdf(slope)) + ' ppm/year; correlation coefficient: ' + str(trdf(r)) + '</h4>')
var('x,y')
show(list_plot(sel_data, plotjoined=True, rgbcolor=(1,0,0)) + plot(slope*x+intercept,start_date,end_date), xmin = start_date, ymin = c_min-2, axes = True, xmax = end_date, ymax = c_max+3, frame = False)

attachment:co2c.png

### Pie Chart from the Google Chart API

by Harald Schilly

# Google Chart API: http://code.google.com/apis/chart
import urllib2 as inet
from pylab import imshow
@interact
def gChart(title="Google Chart API plots Pie Charts!", color1=Color('purple'), color2=Color('black'), color3=Color('yellow'), val1=slider(0,1,.05,.5), val2=slider(0,1,.05,.3), val3=slider(0,1,.05,0.1), label=("Maths Physics Chemistry")):
url += '&chtt=%s&chts=000000,25'%title.replace(" ","+")
url += '&chco=%s'%(','.join([color1.html_color()[1:],color2.html_color()[1:],color3.html_color()[1:]]))
url += '&chl=%s'%label.replace(" ","|")
url += '&chd=t:%s'%(','.join(map(str,[val1,val2,val3])))
print url
html('<div style="border:3px dashed;text-align:center;padding:50px 0 50px 0"><img src="%s"></div>'%url)

## Bioinformatics

### Web app: protein browser

by Marshall Hampton (tested by William Stein)

import urllib2 as U
@interact
def protein_browser(GenBank_ID = input_box('165940577', type = str), file_type = selector([(1,'fasta'),(2,'GenPept')])):
if file_type == 2:
gen_str = 'http://www.ncbi.nlm.nih.gov/entrez/viewer.fcgi?db=protein&sendto=t&id='
else:
gen_str = 'http://www.ncbi.nlm.nih.gov/entrez/viewer.fcgi?db=protein&sendto=t&dopt=fasta&id='
f = U.urlopen(gen_str + GenBank_ID)
f.close()
html(g)

attachment:biobrowse.png

### Coalescent simulator

by Marshall Hampton

def next_gen(x, selection=1.0):
'''Creates the next generation from the previous; also returns parent-child indexing list'''
next_x = []
for ind in range(len(x)):
if random() < (1 + selection)/len(x):
rind = 0
else:
rind = int(round(random()*(len(x)-1)+1/2))
next_x.append((x[rind],rind))
next_x.sort()
return [[x[0] for x in next_x],[x[1] for x in next_x]]
def coal_plot(some_data):
'''Creates a graphics object from coalescent data'''
gens = some_data[0]
inds = some_data[1]
gen_lines = line([[0,0]])
pts = Graphics()
ngens = len(gens)
gen_size = len(gens[0])
for x in range(gen_size):
pts += point((x,ngens-1), hue = gens[0][x]/float(gen_size*1.1))
p_frame = line([[-.5,-.5],[-.5,ngens-.5], [gen_size-.5,ngens-.5], [gen_size-.5,-.5], [-.5,-.5]])
for g in range(1,ngens):
for x in range(gen_size):
old_x = inds[g-1][x]
gen_lines += line([[x,ngens-g-1],[old_x,ngens-g]], hue = gens[g-1][old_x]/float(gen_size*1.1))
pts += point((x,ngens-g-1), hue = gens[g][x]/float(gen_size*1.1))
return pts+gen_lines+p_frame
d_field = RealField(10)
@interact
def coalescents(pop_size = slider(2,100,1,15,'Population size'), selection = slider(-1,1,.1,0, 'Selection for first taxon'), s = selector(['Again!'], label='Refresh', buttons=True)):
print 'Population size: ' + str(pop_size)
print 'Selection coefficient for first taxon: ' + str(d_field(selection))
start = [i for i in range(pop_size)]
gens = [start]
inds = []
while gens[-1][0] != gens[-1][-1]:
g_index = len(gens) - 1
n_gen = next_gen(gens[g_index], selection = selection)
gens.append(n_gen[0])
inds.append(n_gen[1])
coal_data1 = [gens,inds]
print 'Generations until coalescence: ' + str(len(gens))
show(coal_plot(coal_data1), axes = False, figsize = [8,4.0*len(gens)/pop_size], ymax = len(gens)-1)

attachment:coalescent.png

## Miscellaneous Graphics

### Catalog of 3D Parametric Plots

var('u,v')
plots = ['Two Interlinked Tori', 'Star of David', 'Double Heart',
'Heart', 'Green bowtie', "Boy's Surface", "Maeder's Owl",
'Cross cap']
plots.sort()

@interact
def _(example=selector(plots, buttons=True, nrows=2),
tachyon=("Raytrace", False), frame = ('Frame', False),
opacity=(1,(0.1,1))):
url = ''
if example == 'Two Interlinked Tori':
f1 = (4+(3+cos(v))*sin(u), 4+(3+cos(v))*cos(u), 4+sin(v))
f2 = (8+(3+cos(v))*cos(u), 3+sin(v), 4+(3+cos(v))*sin(u))
p1 = parametric_plot3d(f1, (u,0,2*pi), (v,0,2*pi), color="red", opacity=opacity)
p2 = parametric_plot3d(f2, (u,0,2*pi), (v,0,2*pi), color="blue",opacity=opacity)
P = p1 + p2
elif example == 'Star of David':
f_x = cos(u)*cos(v)*(abs(cos(3*v/4))^500 + abs(sin(3*v/4))^500)^(-1/260)*(abs(cos(4*u/4))^200 + abs(sin(4*u/4))^200)^(-1/200)
f_y = cos(u)*sin(v)*(abs(cos(3*v/4))^500 + abs(sin(3*v/4))^500)^(-1/260)*(abs(cos(4*u/4))^200 + abs(sin(4*u/4))^200)^(-1/200)
f_z = sin(u)*(abs(cos(4*u/4))^200 + abs(sin(4*u/4))^200)^(-1/200)
P = parametric_plot3d([f_x, f_y, f_z], (u, -pi, pi), (v, 0, 2*pi),opacity=opacity)
elif example == 'Double Heart':
f_x = ( abs(v) - abs(u) - abs(tanh((1/sqrt(2))*u)/(1/sqrt(2))) + abs(tanh((1/sqrt(2))*v)/(1/sqrt(2))) )*sin(v)
f_y = ( abs(v) - abs(u) - abs(tanh((1/sqrt(2))*u)/(1/sqrt(2))) - abs(tanh((1/sqrt(2))*v)/(1/sqrt(2))) )*cos(v)
f_z = sin(u)*(abs(cos(4*u/4))^1 + abs(sin(4*u/4))^1)^(-1/1)
P = parametric_plot3d([f_x, f_y, f_z], (u, 0, pi), (v, -pi, pi),opacity=opacity)
elif example == 'Heart':
f_x = cos(u)*(4*sqrt(1-v^2)*sin(abs(u))^abs(u))
f_y = sin(u) *(4*sqrt(1-v^2)*sin(abs(u))^abs(u))
f_z = v
P = parametric_plot3d([f_x, f_y, f_z], (u, -pi, pi), (v, -1, 1), frame=False, color="red",opacity=opacity)
elif example == 'Green bowtie':
f_x = sin(u) / (sqrt(2) + sin(v))
f_y = sin(u) / (sqrt(2) + cos(v))
f_z = cos(u) / (1 + sqrt(2))
P = parametric_plot3d([f_x, f_y, f_z], (u, -pi, pi), (v, -pi, pi), frame=False, color="green",opacity=opacity)
elif example == "Boy's Surface":
url = "http://en.wikipedia.org/wiki/Boy's_surface"
fx = 2/3* (cos(u)* cos(2*v) + sqrt(2)* sin(u)* cos(v))* cos(u) / (sqrt(2) - sin(2*u)* sin(3*v))
fy = 2/3* (cos(u)* sin(2*v) - sqrt(2)* sin(u)* sin(v))* cos(u) / (sqrt(2) - sin(2*u)* sin(3*v))
fz = sqrt(2)* cos(u)* cos(u) / (sqrt(2) - sin(2*u)* sin(3*v))
P = parametric_plot3d([fx, fy, fz], (u, -2*pi, 2*pi), (v, 0, pi), plot_points = [90,90], frame=False, color="orange",opacity=opacity)
elif example == "Maeder's Owl":
fx = v *cos(u) - 0.5* v^2 * cos(2* u)
fy = -v *sin(u) - 0.5* v^2 * sin(2* u)
fz = 4 *v^1.5 * cos(3 *u / 2) / 3
P = parametric_plot3d([fx, fy, fz], (u, -2*pi, 2*pi), (v, 0, 1),plot_points = [90,90], frame=False, color="purple",opacity=opacity)
elif example =='Cross cap':
url = 'http://en.wikipedia.org/wiki/Cross-cap'
fx = (1+cos(v))*cos(u)
fy = (1+cos(v))*sin(u)
fz = -tanh((2/3)*(u-pi))*sin(v)
P = parametric_plot3d([fx, fy, fz], (u, 0, 2*pi), (v, 0, 2*pi), frame=False, color="red",opacity=opacity)
else:
print "Bug selecting plot?"
return

html('<h2>%s</h2>'%example)
if url:
html('<h3><a target="_new" href="%s">%s</a></h3>'%(url,url))
show(P, viewer='tachyon' if tachyon else 'jmol', frame=frame)

attachment:parametricplot3d.png

### Interactive rotatable raytracing with Tachyon3d

C = cube(color=['red', 'green', 'blue'], aspect_ratio=[1,1,1],
viewer='tachyon') + sphere((1,0,0),0.2)
@interact
def example(theta=(0,2*pi), phi=(0,2*pi), zoom=(1,(1,4))):
show(C.rotate((0,0,1), theta).rotate((0,1,0),phi), zoom=zoom)

attachment:tachyonrotate.png

### Interactive 3d plotting

var('x,y')
@interact
def example(clr=Color('orange'), f=4*x*exp(-x^2-y^2), xrange='(-2, 2)', yrange='(-2,2)',
zrot=(0,pi), xrot=(0,pi), zoom=(1,(1/2,3)), square_aspect=('Square Frame', False),
tachyon=('Ray Tracer', True)):
xmin, xmax = sage_eval(xrange); ymin, ymax = sage_eval(yrange)
P = plot3d(f, (x, xmin, xmax), (y, ymin, ymax), color=clr)
html('<h1>Plot of $f(x,y) = %s$</h1>'%latex(f))
aspect_ratio = [1,1,1] if square_aspect else [1,1,1/2]
show(P.rotate((0,0,1), -zrot).rotate((1,0,0),xrot),
viewer='tachyon' if tachyon else 'jmol',
figsize=6, zoom=zoom, frame=False,
frame_aspect_ratio=aspect_ratio)

attachment:tachyonplot3d.png

### Somewhat Silly Egg Painter

by Marshall Hampton (refereed by William Stein)

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.png

===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

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