MathLibrary.py

# Math library
# use the .listFeatures() to get a table of all functions and constants
# Created by Arjun Sarao

# ===============================================================================
def pinumber():
    pie = 0
    for i in range(9999999):

        if i % 2 == 0:
            pie += (1 / (2 * i + 1))
        elif i % 2 != 0:
            pie -= (1 / (2 * i + 1))
    return 4 * pie


# Pretty sure this is Leibniz's formula
# ===============================================================================
def eulersNumber():
    e = (1 + (1 / 10000)) ** 10000
    # print(e)
    return e


# Uses e = lim x-> inf (1+(1/x))^x
# ===============================================================================
def goldenRatio():
    phi = (1 + roots(2, 5)) / 2
    return phi


# ===============================================================================
def goldenRatioInv():
    phiInv = (1 - roots(2, 5)) / 2
    return phiInv


# ===============================================================================
def logarithims(b, x):
    ans = naturalLog(x) / naturalLog(b)
    return ans


# Uses logb(x) = ln(x) / ln(b)
# ===============================================================================
def naturalLog(x):
    ln = 10000 * x ** (1 / 10000) - 10000
    return ln


# Some formula I found online
# ===============================================================================
def factorial(n):
    if n == 1:
        return n
    elif n < 1:
        print("Cannot take factorial of numbers less than 1.")
    elif n == 0:
        print("The value of 0! is: 1")
    else:
        return n * factorial(n - 1)
    print("The value of ", n, "! factorial is: ", int(factorial(n)))


# Recursively generates factorial
# ===============================================================================
def powers(a, x):
    ans = a ** x
    return ans


# ===============================================================================
def roots(a, x):
    ans = eulersNumber() ** ((1 / a) * naturalLog(x))
    return ans


# Uses a^x = e^((1/x)*ln(a))
# ===============================================================================
def permutations(n, r):
    perms = factorial(n) / factorial(n - r)
    return perms


# ===============================================================================
def combinations(n, r):
    perms = factorial(n) / (factorial(r) * factorial(n - r))
    return perms


# ===============================================================================
def fibonacci(n):
    number = ((goldenRatio() ** n) - ((goldenRatioInv()) ** n)) / roots(2, 5)
    return number


# ===============================================================================
def circleArea(r):
    area = pinumber() * powers(r, 2)


# ===============================================================================
def Sieve(n):
    primes = []
    numbers = []
    if 2 <= n:
        primes.append(2)
        if 3 <= n:
            primes.append(3)
    for i in range(1, int(n / 6) + 1):
        numbers.append(6 * i - 1)
        numbers.append(6 * i + 1)
    while numbers:
        primes.append(numbers.pop(0))
        for e in numbers:
            if not e % primes[-1]:
                numbers.pop(numbers.index(e))
    return primes


def is_prime(n):
    prime_list = Sieve(n)
    if n in prime_list:
        return True
    return False


# ===============================================================================
def degtoRadians(n):
    return n * (180 / pinumber())


# ===============================================================================
def sine(x):
    sinx = x - (x ** 3 / factorial(3)) + (x ** 5 / factorial(5)) - (x ** 7 / factorial(7)) + (x ** 9 / factorial(9)) - (
            x ** 11 / factorial(11))
    return sinx


# Uses Taylor Series Expansion for Sin(x)
# ===============================================================================
def cosine(x):
    cosx = 1 - (x ** 2 / factorial(2)) + (x ** 4 / factorial(4)) - (x ** 6 / factorial(6)) + (x ** 8 / factorial(8)) - (
            x ** 10 / factorial(10))
    return cosx


# Uses Taylor Series Expansion for Cos(x)
# ===============================================================================
def etothex(x):
    ex = 1 + x + (x ** 2 / factorial(2)) + (x ** 3 / factorial(3)) + (x ** 4 / factorial(4)) + (
                x ** 5 / factorial(5)) + (x ** 6 / factorial(6))+ (x ** 7 / factorial(7))+ (x ** 8 / factorial(8))
    return ex


# Uses Taylor Series Expansion for e^x
# ===============================================================================
def listFunctions():
    print("> Calculates constants such as pi, e, and phi.")
    print("> Can take logarithims of variable bases.")
    print("> Calculate number of permutations and combinations.")
    print("> Returns the number at a specified index of a fibonacci series.")
    print("> Calculates the factorial of a number.")
    print("> Can find the roots or powers of any numbers.")
    print("> Find the values of sin(x), cos(x), and e^x.")
    print("> Returns prime numbers up until a specified index.")