R = RealField(2000)              #Using the RealField, I can choose the number of decimal points for my answers

def Chudnovsky(n):
    """
    A function to simulate the Chudnovsky algorithm for pi approximation, consisting mainly of a sum from 0 to the iteration argument n.
    For clarity, I have seperated parts of the quotient into variables x and y.

    Argument n is an integer.
    Output will be a float
    """
    k = var('k')
    x = ((-1)**k * factorial(6*k) * (13591409 + 545140134 * k))
    y = (factorial(3*k) * (factorial(k))**3 * (640320 ** (3 * k + 3/2)))
    a = R(sum(x / y, k, 0, n))
    return R(1 / (12 * a))

listington = []        #An empty list to be appended with values of correct decimal places for a bar chart
rohanna = [['Iterations','Decimal Places']]
#rohanna is defined as a list of lists to be written to a csv file.
#The first list in rohanna contains the titles of the columns

for i in range(7):
    """
    The following for loop iterates the function and finds the absolute difference between the approximation and pi.
    The number is then converted into a string, then converted into a list of its elements.
    """
    a = R(abs(Chudnovsky(i) - pi))
    numlist = [x for x in str(a)]
    b = numlist[604:606]        #Since the number is in standard form, the last two elements of the list gives us the number of decimal places
    intlist = [int(x) for x in b]
    c = intlist[0] * 10 + intlist[1] - 1           #The coding is rather shoddy I'm afraid
    listington.append(c)
    rohanna.append([i, c])


for i in range(7, 31):
    """
    At a certain point, the number that follows e in standard form reaches three digits, and thus the only method I found that worked was
    creating a new for loop.
    """
    a = R(abs(Chudnovsky(i) - pi))
    numlist = [x for x in str(a)]
    b = numlist[604:607]
    intlist = [int(x) for x in b]
    c = intlist[0] * 100 + intlist[1] * 10 + intlist[2] - 1
    listington.append(c)
    rohanna.append([i, c])

#By using the list that only has the accuracy, I can draw a bar graph to show the continuity.

f = bar_chart(listington, ymin = 0, color = ('purple'))
f.save('BarChart.png')

#With the second list, I can use it to write a csv file of the data.

import csv
file = open('decimalpoints.csv', 'w')
a = csv.writer(file)
a.writerows(rohanna)
file.close()