aburousan

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

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

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

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):