U=RealDistribution('uniform',[0,1])
R=RealField(5000)
S=RealField(300)
#T=RealDistribution('uniform',[0,2*pi])
P.<z>=R['z']
|
|
plot(0, (0, 1), color="black", axes=False) + point((0,0), color="black", size=100, marker="|") + point((1,0), color="black", size=100, marker="|")
def gen_poly(ord):
poly = R(1)
for i in range(ord):
poly *= (z-R(U.get_random_element()))
return poly
def get_roots(poly):
rootarray = []
for root in poly.roots():
multiplicity=root[1]
for mult in range (multiplicity):
rootarray.append(S(root[0]))
return rootarray
poly = gen_poly(100)
deriv = sage.calculus.functional.derivative(poly, z)
Graph1 = plot(0, (0, 1), color="black", axes=False) + point((0,0), color="black", size=100, marker="|") + point((1,0), color="black", size=100, marker="|") + points([(root, 0) for root in get_roots(poly)], color="red", size=50, marker="|")
Graph1 += plot(-.1, (0, 1), color="black", axes=False) + point((0,0-.1), color="black", size=100, marker="|") + point((1,-.1), color="black", size=100, marker="|") + points([(root, -.1) for root in get_roots(deriv)], color="green", size=50, marker="|")
show(Graph1, aspect_ratio=0.5)
|
from sage.plot.histogram import Histogram
max_roots = []
max_crit_points = []
for i in range(100):
poly = gen_poly(100)
deriv = sage.calculus.functional.derivative(poly, z)
#polyroots = get_roots(poly)
#polyroots.remove(S(1))
max_roots.append(S(max(get_roots(poly))))
max_crit_points.append(S(max(get_roots(deriv))))
show(histogram([100*(1-max_roots[i]) for i in range(len(maxroots))], bins=50))
show(histogram([100*(1-max_crit_points[i]) for i in range(len(maxroots))], bins=50))
show(histogram([100*(max_crit_points[i]-maxroots[i]) for i in range(len(maxroots))], bins=50))
 
|
rootarray=get_roots(gen_poly(100))
rootarray.remove(S(1))
print(max(rootarray))
0.9840200922917574644088745117187500000000000000000000000000000000000000\ 00000000000000000000 0.984020092291757464408874511718750000000000000000000000000000000000000000000000000000000000 |
|
|