Find best-fit of tessarating two paper formats on each others

paperformat.py

from itertools import product

dumplings = (352, 175)  # Kartoffel Knödel 4000400130570
a5 = (210, 148)


def min_mod(x1, x2, n1_max):
    def mod_for_n1(n1):
        return (x1*n1) % x2
    return min((mod_for_n1(n1), n1) for n1 in range(1, n1_max))


def min_mod_area(x1, y1, x2, y2, n1_max, m1_max):
    def mod_area_for_n1_m2(n1, m1):
        x_mod = (n1*x1) % x2
        y_mod = (m1*y1) % y2
        return x_mod*m1*y1 + y_mod*(n1*x1 - x_mod)
    return min(
        (mod_area_for_n1_m2(n1, m1), n1, m1)
        for n1, m1 in product(range(1, n1_max), range(1, m1_max)))


def get_x_y(format_, orientation):
    if orientation:
        return format_[1], format_[0]
    return format_


if __name__ == '__main__':
    for format1, format2 in [(dumplings, a5), (a5, dumplings)]:
        print(format1, format2)
        for orientation1, orientation2 in product((0, 1), (0, 1)):
            x1, y1 = get_x_y(format1, orientation1)
            x2, y2 = get_x_y(format2, orientation2)
            print(orientation1, orientation2, min_mod(x1, x2, 15))
            print(min_mod_area(x1, y1, x2, y2, 15, 15))