"""
Demonstrates use of list comprehension, range() and
math.hypot().

This is a brute force algorithm and is practical only
for smallish n.  Much better algorithms are out there.

a,b can never be same length if c is to be an integer.

Since (3,4,5) and (4,3,5) are the same triple, we force
a < b to preserve uniqueness, i.e. find (a,b,c) where
a < b < c.

The gcd check excludes similar triangles e.g. if (3,4,5)
has been found, we don't also want (6,8,10).
"""

from math import hypot

def triples(n):
    """
    Extract Pythagorean triples up to longer leg b = n
    """
    checklist = [(a,b,hypot(a,b))
                 for b in range(1,n+1)
                 for a in range(1,b)
                 if gcd(a,b)==1]
    return [(a,b,int(c))
            for (a,b,c) in checklist
            if eqint(c)]

def gcd(a,b):
    """
    Find greatest common divisor of a,b
    """
    while b:
        a,b = b, a%b
    return a

def eqint(a):
    """
    Determine whether a is an integer
    """
    if int(a)==a:  return 1
    else:          return 0