Figurate_Number

Assignment 2.py

#Monica Ionescu and James Park
#Figurate Numbers
#This program tests for characteristics of positive integers (tests for figurate numbers)

import math

#This function compiles all other functions in this program, establishes a range of numbers, \
#and tests the numbers for each specific characteristic. 
def main():
    limit = 100
    for n in range(1, limit + 1):
        print n, \
            "Prime," if is_prime(n) else "Composite,", \
            "Triangular," if is_triangular(n) else "Not Triangular,", \
            "Tetrahedral," if is_tetrahedral(n) else "Not Tetrahedral,", \
            "Square," if is_square(n) else "Not Square,", \
            "Square Pyramidal," if is_square_pyramidal(n) else "Not Square Pyramidal,", \
            "Pentagonal," if is_pentagonal(n) else "Not Pentagonal,", \
            "Prime Oblong," if is_prime_oblong(n) else "Not Prime Oblong,", \
            "Pointy" if is_pointy(n) else "Not Pointy"

#This function tests whether a number is prime. 
def is_prime(n):
    if n == 1:
        return False
    for x in range(2, n):
        if n % x == 0:
            return False 
    return True

#This function tests whether a number is triangular.
def is_triangular(n):
    test_number = 8 * n + 1
    root = math.sqrt(test_number)
    return int(root)**2 == test_number
        
#This function tests whether a number is a tetrahedral number.
def is_tetrahedral(n):
    test_number = 6.0 * n
    cube_root = test_number**(1.0 / 3.0)
    cube_root_floor = int(cube_root)
    return cube_root_floor * (cube_root_floor + 1) * (cube_root_floor + 2) == test_number

#This function tests whether a number is a square number.
def is_square(n):
    root = math.sqrt(n)
    return int(root)**2 == n

#This function test whether a number square pyramidal.
def is_square_pyramidal(n):
    test_number = 3.0 * n
    cube_root = int(test_number**(1.0 / 3.0))
    return cube_root * (cube_root + 1) * (2 * cube_root + 1) == test_number * 2

#This function tests whether a number is pentagonal.
def is_pentagonal(n):
    test_number = (2.0 / 3.0) * n
    square_root = int(test_number ** (1.0 / 2.0))
    return (square_root + 1) * (3 * (square_root + 1) - 1) == test_number * 3

#This function uses the is_prime function to test whether a number is prime oblong.
def is_prime_oblong(n): 
    for x in range (2, n):
        quotient = n / x
        if n % x == 0 and x != quotient and is_prime(x) and is_prime(quotient):
            return True
    return False

#The next two functions test whether a number is pointy.
# generate_tetrahedral generates tetrahedral numbers, which are then used in is_pointy to check if a number is pointy.
def generate_tetrahedral(n):
    return (1.0 / 6.0) * ( n * (n + 1) * (n + 2))

def is_pointy(n):
    x = 1
    tetrahedral = generate_tetrahedral(x)
    while tetrahedral < n:
        difference = n - tetrahedral
        if is_tetrahedral(difference) and difference != tetrahedral:
            return True
        x = x + 1
        tetrahedral = generate_tetrahedral(x)
    return False    

if __name__ == "__main__":
  main()