def test_power_representation():
tests = [
(1729, 3, 2),
(234, 2, 4),
(2, 1, 2),
(3, 1, 3),
(5, 2, 2),
(12352, 2, 4),
(32760, 2, 3),
]
for test in tests:
n, p, k = test
f = power_representation(n, p, k)
while True:
try:
l = next(f)
assert len(l) == k
chk_sum = 0
for l_i in l:
chk_sum = chk_sum + l_i ** p
assert chk_sum == n
except StopIteration:
break
assert list(power_representation(20, 2, 4, True)) == [(1, 1, 3, 3), (0, 0, 2, 4)]
raises(ValueError, lambda: list(power_representation(1.2, 2, 2)))
raises(ValueError, lambda: list(power_representation(2, 0, 2)))
raises(ValueError, lambda: list(power_representation(2, 2, 0)))
assert list(power_representation(-1, 2, 2)) == []
assert list(power_representation(1, 1, 1)) == [(1,)]
assert list(power_representation(3, 2, 1)) == []
assert list(power_representation(4, 2, 1)) == [(2,)]
assert list(power_representation(3 ** 4, 4, 6, zeros=True)) == [
(1, 2, 2, 2, 2, 2),
(0, 0, 0, 0, 0, 3),
]
assert list(power_representation(3 ** 4, 4, 5, zeros=False)) == []
assert list(power_representation(-2, 3, 2)) == [(-1, -1)]
assert list(power_representation(-2, 4, 2)) == []
assert list(power_representation(0, 3, 2, True)) == [(0, 0)]
assert list(power_representation(0, 3, 2, False)) == []
# when we are dealing with squares, do feasibility checks
assert len(list(power_representation(4 ** 10 * (8 * 10 + 7), 2, 3))) == 0
# there will be a recursion error if these aren't recognized
big = 2 ** 30
for i in [13, 10, 7, 5, 4, 2, 1]:
assert list(sum_of_powers(big, 2, big - i)) == []
def test_sum_of_squares_powers():
tru = {
(0, 0, 1, 1, 11),
(0, 0, 5, 7, 7),
(0, 1, 3, 7, 8),
(0, 1, 4, 5, 9),
(0, 3, 4, 7, 7),
(0, 3, 5, 5, 8),
(1, 1, 2, 6, 9),
(1, 1, 6, 6, 7),
(1, 2, 3, 3, 10),
(1, 3, 4, 4, 9),
(1, 5, 5, 6, 6),
(2, 2, 3, 5, 9),
(2, 3, 5, 6, 7),
(3, 3, 4, 5, 8),
}
eq = u ** 2 + v ** 2 + x ** 2 + y ** 2 + z ** 2 - 123
ans = diop_general_sum_of_squares(eq, oo) # allow oo to be used
assert len(ans) == 14
assert ans == tru
raises(ValueError, lambda: list(sum_of_squares(10, -1)))
assert list(sum_of_squares(-10, 2)) == []
assert list(sum_of_squares(2, 3)) == []
assert list(sum_of_squares(0, 3, True)) == [(0, 0, 0)]
assert list(sum_of_squares(0, 3)) == []
assert list(sum_of_squares(4, 1)) == [(2,)]
assert list(sum_of_squares(5, 1)) == []
assert list(sum_of_squares(50, 2)) == [(5, 5), (1, 7)]
assert list(sum_of_squares(11, 5, True)) == [(1, 1, 1, 2, 2), (0, 0, 1, 1, 3)]
assert list(sum_of_squares(8, 8)) == [(1, 1, 1, 1, 1, 1, 1, 1)]
assert [len(list(sum_of_squares(i, 5, True))) for i in range(30)] == [
1,
1,
1,
1,
2,
2,
1,
1,
2,
2,
2,
2,
2,
3,
2,
1,
3,
3,
3,
3,
4,
3,
3,
2,
2,
4,
4,
4,
4,
5,
]
assert [len(list(sum_of_squares(i, 5))) for i in range(30)] == [
0,
0,
0,
0,
0,
1,
0,
0,
1,
0,
0,
1,
0,
1,
1,
0,
1,
1,
0,
1,
2,
1,
1,
1,
1,
1,
1,
1,
1,
3,
]
for i in range(30):
s1 = set(sum_of_squares(i, 5, True))
assert not s1 or all(sum(j ** 2 for j in t) == i for t in s1)
s2 = set(sum_of_squares(i, 5))
assert all(sum(j ** 2 for j in t) == i for t in s2)
raises(ValueError, lambda: list(sum_of_powers(2, -1, 1)))
raises(ValueError, lambda: list(sum_of_powers(2, 1, -1)))
assert list(sum_of_powers(-2, 3, 2)) == [(-1, -1)]
assert list(sum_of_powers(-2, 4, 2)) == []
assert list(sum_of_powers(2, 1, 1)) == [(2,)]
assert list(sum_of_powers(2, 1, 3, True)) == [(0, 0, 2), (0, 1, 1)]
assert list(sum_of_powers(5, 1, 2, True)) == [(0, 5), (1, 4), (2, 3)]
assert list(sum_of_powers(6, 2, 2)) == []
assert list(sum_of_powers(3 ** 5, 3, 1)) == []
assert list(sum_of_powers(3 ** 6, 3, 1)) == [(9,)] and (9 ** 3 == 3 ** 6)
assert list(sum_of_powers(2 ** 1000, 5, 2)) == []