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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
aburousan /
Created August 5, 2022 10:47
check irrationality for any number using integral root theorem (IRT)
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]
aburousan /
Created June 27, 2020 10:38
This shows a program to calculate Integration using Trapezoidal Rule with a desired Accuracy
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
aburousan /
Last active June 29, 2020 12:32
This is a program to Integrate using Trapezoidal Rule. Here you can also see the plot of the Trapezoids
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):