Пример #1
0
 def Is(self, x):
     if x < 0:
         return -x - math.log(2) * mpmath.li(2 -
                                             x) + math.log(2) * mpmath.li(2)
     else:
         return x - math.log(2) * mpmath.li(2 +
                                            x) + math.log(2) * mpmath.li(2)
Пример #2
0
def solve_fx(initial, p):
    x = initial  # initial value

    while True:
        fx = f(x, p)
        fpx = fp(x, 1, p)
        xnew = x - (mpmath.li(x) - p) * (math.log(x)) / (1 +
                                                         (mpmath.li(x) - p) /
                                                         (2 * x))
        if abs(xnew - x) <= eps:
            return xnew

        x = xnew
Пример #3
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def pi(n):
	if n < 2657:
		app = int(n/math.log(n))
		for i, x in enumerate(list(sieve(2658))[app:]):
			if x > n:
				return i + app
	else:
		app = int(mpmath.li(n))
		limit = math.ceil(math.sqrt(n)*math.log(n)/(8*math.pi))
		print(app, limit, list(itertools.islice(sieve(10**6), app-limit, app+limit)))
Пример #4
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# Jun/12/2016
# Yurani Melisa Palacios Palacios 

# Integration, being as important as it is, has several highly efficient implementations available for us. 
# Among them are the ones found in scipy 
# "Integracion, siendo tan importante como lo es, tiene varias implementaciones altamente eficientes disponibles para nosotros.
#  Entre ellos se encuentran los que se encuentran en scipy"

import numpy as np
import mpmath
import scipy.integrate as integrate

def function (x):

	return 1 / np.log(x)

result = integrate.quad( function, 2, 10)

print result
print mpmath.li (10, ofsset=True)
Пример #5
0
# Jun/10/2016
# Yurani Melisa Palacios Palacios 

import numpy as np
import mpmath
import scipy.integrate as integrate


def f(x):
	return 1 / np.log(x)

a = 2.0
b = 10.0
N = 1000

d = (b - a) / N
A = 0
for k in range(N):
	
	a1 = a + k * d
	b1 = a1 + d

	A += (b1 - a1) * (f(a1) + f(b1)) / 2.
	
print 'we calculated = ', A
print 'mpmath calculated = ', mpmath.li(b, offset = True)
print 'scipy calculated = ', integrate.quad(f, 2, 10)
Пример #6
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def getLI( n ):
    return li( n )
Пример #7
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def Li(x): return mpmath.li(x, offset=True)

last_printed = -threshold
Пример #8
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def getLIOperator(n):
    return li(n)
Пример #9
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from mpmath import li
from sympy import sieve
import matplotlib.pyplot as plt

li_offset = lambda x: li(x, offset=True)
N = 1000000
step = 1000

xx = [step * (i + 1) for i in range(N // step)]
primes = list(sieve.primerange(1, N))
estimate = list(map(li_offset, xx))
actual = []
for x in xx:
    actual.append(len([prime for prime in primes if prime < x]))

yy = [a / e for a, e in zip(actual, estimate)]

plt.plot(xx, yy)
plt.title('|{primes<x}|/li(x)')
plt.show()
Пример #10
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def f(x, p):
    return mpmath.li(x) - p