# Def
U = RealDistribution('uniform',[0,1])
U.get_random_element()
C = ComplexField(300)
C(U.get_random_element()) + C(U.get_random_element()) * C(I)
R.<z> = C['z']
import random
random.sample(range(10), 1)
[3] [3] |
import random
rndpoly1 = C(1)
polyOrd = random.sample(range(100), 1)
# print polyOrd
for i in range(polyOrd[0]):
randRoot = C(U.get_random_element()) + C(U.get_random_element())*C(I)
rndpoly1 = rndpoly1 * (z - randRoot)
rootarray = []
for root in rndpoly1.roots():
j = root[1]
for i in range(j):
rootarray.append(root[0])
Gout = Graphics()
Gout += points(rootarray,color='white', markeredgecolor = 'red', pointsize=20,zorder = 1, marker = "o")
show(Gout,aspect_ratio=1)
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# First Derivatives
derpoly = rndpoly1.derivative(z)
cparray = []
for root in derpoly.roots():
j = root[1]
for i in range(j):
cparray.append(root[0])
Gout = Graphics()
Gout += points(rootarray,color='white', markeredgecolor = 'red', pointsize=20,zorder = 1, marker = "o")
Gout += points(cparray,color='white', markeredgecolor = 'blue', pointsize=20,zorder = 1, marker = "*")
show(Gout,aspect_ratio=1)
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# More Derivatives
Gout = Graphics()
Gout += points(rootarray,color='white', markeredgecolor = 'red', pointsize=20,zorder = 1, marker = "o")
for i in range(20):
derpoly = rndpoly1.derivative(z)
cparray = []
for root in derpoly.roots():
j = root[1]
for i in range(j):
cparray.append(root[0])
Gout += points(cparray,color='white', markeredgecolor = 'blue', pointsize=20,zorder = 1, marker = "*")
rndpoly1 = derpoly
show(Gout,aspect_ratio=1)
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# Uniform
import random
rndpoly1 = C(1)
polyOrd = random.sample(range(100), 1)
# print polyOrd
for i in range(polyOrd[0]):
randRoot = C(U.get_random_element()) + C(U.get_random_element())*C(I)
rndpoly1 = rndpoly1 * (z - randRoot)
rootarray = []
for root in rndpoly1.roots():
j = root[1]
for i in range(j):
rootarray.append(root[0])
Gout = Graphics()
Gout += points(rootarray,color='white', markeredgecolor = 'red', pointsize=20,zorder = 1, marker = "o")
#show(Gout,aspect_ratio=1)
for i in range(20):
derpoly = rndpoly1.derivative(z)
cparray = []
for root in derpoly.roots():
j = root[1]
for i in range(j):
cparray.append(root[0])
Gout += points(cparray,color='white', markeredgecolor = 'blue', pointsize=20,zorder = 1, marker = "*")
rndpoly1 = derpoly
show(Gout,aspect_ratio=1)
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#Gaussian
sigma = 1
G = RealDistribution('gaussian', sigma)
import random
rndpoly1 = C(1)
polyOrd = random.sample(range(100), 1)
# print polyOrd
for i in range(polyOrd[0]):
randRoot = C(G.get_random_element()) + C(G.get_random_element())*C(I)
rndpoly1 = rndpoly1 * (z - randRoot)
rootarray = []
for root in rndpoly1.roots():
j = root[1]
for i in range(j):
rootarray.append(root[0])
Gout = Graphics()
Gout += points(rootarray,color='white', markeredgecolor = 'red', pointsize=20,zorder = 1, marker = "o")
for i in range(20):
derpoly = rndpoly1.derivative(z)
cparray = []
for root in derpoly.roots():
j = root[1]
for i in range(j):
cparray.append(root[0])
Gout += points(cparray,color='white', markeredgecolor = 'blue', pointsize=20,zorder = 1, marker = "*")
rndpoly1 = derpoly
show(Gout,aspect_ratio=1)
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P = [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1]
D = GeneralDiscreteDistribution(P)
counts = [0] * len(P)
nr_samples = 10000
for _ in range(nr_samples):
counts[D.get_random_element()] += 1
[1.0*x/nr_samples for x in counts]
import random
rndpoly1 = C(1)
polyOrd = random.sample(range(100), 1)
# print polyOrd
for i in range(polyOrd[0]):
randRoot = C(D.get_random_element()) + C(D.get_random_element())*C(I)
rndpoly1 = rndpoly1 * (z - randRoot)
rootarray = []
for root in rndpoly1.roots():
j = root[1]
for i in range(j):
rootarray.append(root[0])
Gout = Graphics()
Gout += points(rootarray,color='white', markeredgecolor = 'red', pointsize=20,zorder = 1, marker = "o")
for i in range(20):
derpoly = rndpoly1.derivative(z)
cparray = []
for root in derpoly.roots():
j = root[1]
for i in range(j):
cparray.append(root[0])
Gout += points(cparray,color='white', markeredgecolor = 'blue', pointsize=20,zorder = 1, marker = "*")
rndpoly1 = derpoly
show(Gout,aspect_ratio=1)
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