pe_596_1.py

#!/usr/bin/env python3
"""
Project Euler, Problem 596
https://projecteuler.net/problem=596

Let be T(r) the number of integer quadruplets x, y, z, t such that x**2 + y**2 + z**2 + t**2 ≤ r**2.
In other words, T(r) is the number of lattice points in the four-dimensional hyperball of radius r.

You are given that T(2) = 89, T(5) = 3121, T(100) = 493490641 and T(10**4) = 49348022079085897.

Find T(10**8) mod 1000000007.
"""

def brute_calc(in_r):
    """iterate through hypercube of radius r"""
    ring = in_r**2
    result = 0
    for x_axis in range(-in_r, in_r + 1):
        for y_axis in range(-in_r, in_r + 1):
            for z_axis in range(-in_r, in_r + 1):
                for t_axis in range(-in_r, in_r + 1):
                    if ring >= x_axis**2 + y_axis**2 + z_axis**2 + t_axis**2:
                        result += 1
    return result


if __name__ == '__main__':
    assert brute_calc(2) == 89
    assert brute_calc(5) == 3121
    assert brute_calc(100) == 493490641
    assert brute_calc(104) == 49348022079085897

Naïve solution to Project Euler problem 596
At testing 1 million coordinates per second, this would take... significantly longer than the age of the universe