U = RealDistribution('uniform',[0,1])
U.get_random_element()
C = ComplexField(500)
C(U.get_random_element()) + C(U.get_random_element()) * C(I)
R.<z> = C['z']
import random
random.sample(range(10), 1)
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import random
rndpoly1 = C(1)
polyOrd = random.sample(range(100), 1)
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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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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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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import random
rndpoly1 = C(1)
polyOrd = random.sample(range(100), 1)
for i in range(40):
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 m 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])
if m == 19:
Gout += points(root[0],color='white', markeredgecolor = 'blue', pointsize=20,zorder = 1, marker = "*")
else:
Gout += points(root[0],color='white', markeredgecolor = 'blue', pointsize=20,zorder = 1, marker = "*",alpha=.3)
#Gout += points(cparray,color='white', markeredgecolor = 'blue', pointsize=20,zorder = 1, marker = "*")
rndpoly1 = derpoly
Gout += points(sum(cparray)/len(cparray),color='white', markeredgecolor = 'magenta', pointsize=40,zorder = 1, marker = "p")
Gout += points(sum(rootarray)/len(rootarray),color='white', markeredgecolor = 'orange', pointsize=40,zorder = 1, marker = "d")
show(Gout,aspect_ratio=1)
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sigma = 1
G = RealDistribution('gaussian', sigma)
import random
rndpoly1 = C(1)
polyOrd = random.sample(range(100), 1)
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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results=[]
for n in range(1,100):
randpoly = C(1)
rootarray= []
cparray=[]
for j in range(2*n):
randpoly *= (z-(C(U.get_random_element()) + C(U.get_random_element())*C(I)))
derpoly=randpoly
for j in range(n):
derpoly=sage.calculus.functional.derivative(derpoly,z)
for root in randpoly.roots():
j = root[1]
for i in range(j):
rootarray.append(C(root[0]**2))
for root in derpoly.roots():
j = root[1]
for i in range(j):
cparray.append(C(root[0]**2))
results.append(C(sum(rootarray))/C(len(rootarray))-C(sum(cparray))/C(len(cparray)))
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print(rootarray)
[] [] |
Gout1 = list_plot([(2*(i + 1), abs(results[i])) for i in range(len(results))], color="green")
show(Gout1)
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results[1]
0.0000000000000000000000000000000000000000000000000000000000000000000000\ 000000000000000000000000000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 |
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