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from math import floor, sqrt | |
def lattice_inside(N):#give square of the radius,i.e., R = \sqrt(N) | |
summ = 0; | |
loop_no = int(N/3) + 2 | |
for i in range(0,loop_no+1): | |
a = floor(N/(3*i+1)) | |
b = floor(N/(3*i+2)) | |
# print(a,b,i) | |
summ = summ + 6*(a-b) | |
return summ + 1 |
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from sympy import minimal_polynomial, Poly, root, divisors, pi | |
def check_irrational(m): | |
result = True | |
p = minimal_polynomial(m) | |
print("Minimal Polynomial of ",m , " is = ",p) | |
pol = Poly(p) | |
a_0 = pol.all_coeffs()[-1] | |
print(" The a_0 is = ", a_0) | |
div_p = divisors(a_0) | |
div_n = [-1*i for i in div_p] |
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import numpy as np | |
original_value = np.pi/4 | |
def f(x): | |
return 1/(1+x*x)#1st step is done | |
def trapizoid(f,a,b,tol): | |
fa = f(a); fb = f(b);I = 0 | |
n =10; it = 1#Iteration number | |
while True: | |
h = (b-a)/n |
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import numpy as np | |
import matplotlib.pyplot as plt | |
original = np.pi/4 | |
def f(x): | |
return 1/(1+(x*x)) | |
x_real = np.linspace(0,1,1000)#This and the next line are used to create a plot of the curve represented by our f(x) function. | |
y_real = f(x_real) | |
def traezoid(f,n,a=0,b=1): |