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from __future__ import annotations
from sympy.ntheory import qs
from sympy.ntheory.qs import SievePolynomial, _generate_factor_base, \
_initialize_first_polynomial, _initialize_ith_poly, \
_gen_sieve_array, _check_smoothness, _trial_division_stage, _gauss_mod_2, \
_build_matrix, _find_factor
from sympy.testing.pytest import slow
@slow
def test_qs_1():
assert qs(10009202107, 100, 10000) == {100043, 100049}
assert qs(211107295182713951054568361, 1000, 10000) == \
{13791315212531, 15307263442931}
assert qs(980835832582657*990377764891511, 3000, 50000) == \
{980835832582657, 990377764891511}
assert qs(18640889198609*20991129234731, 1000, 50000) == \
{18640889198609, 20991129234731}
def test_qs_2() -> None:
n = 10009202107
M = 50
# a = 10, b = 15, modified_coeff = [a**2, 2*a*b, b**2 - N]
sieve_poly = SievePolynomial([100, 1600, -10009195707], 10, 80)
assert sieve_poly.eval(10) == -10009169707
assert sieve_poly.eval(5) == -10009185207
idx_1000, idx_5000, factor_base = _generate_factor_base(2000, n)
assert idx_1000 == 82
assert [factor_base[i].prime for i in range(15)] == \
[2, 3, 7, 11, 17, 19, 29, 31, 43, 59, 61, 67, 71, 73, 79]
assert [factor_base[i].tmem_p for i in range(15)] == \
[1, 1, 3, 5, 3, 6, 6, 14, 1, 16, 24, 22, 18, 22, 15]
assert [factor_base[i].log_p for i in range(5)] == \
[710, 1125, 1993, 2455, 2901]
g, B = _initialize_first_polynomial(
n, M, factor_base, idx_1000, idx_5000, seed=0)
assert g.a == 1133107
assert g.b == 682543
assert B == [272889, 409654]
assert [factor_base[i].soln1 for i in range(15)] == \
[0, 0, 3, 7, 13, 0, 8, 19, 9, 43, 27, 25, 63, 29, 19]
assert [factor_base[i].soln2 for i in range(15)] == \
[0, 1, 1, 3, 12, 16, 15, 6, 15, 1, 56, 55, 61, 58, 16]
assert [factor_base[i].a_inv for i in range(15)] == \
[1, 1, 5, 7, 3, 5, 26, 6, 40, 5, 21, 45, 4, 1, 8]
assert [factor_base[i].b_ainv for i in range(5)] == \
[[0, 0], [0, 2], [3, 0], [3, 9], [13, 13]]
g_1 = _initialize_ith_poly(n, factor_base, 1, g, B)
assert g_1.a == 1133107
assert g_1.b == 136765
sieve_array = _gen_sieve_array(M, factor_base)
assert sieve_array[0:5] == [8424, 13603, 1835, 5335, 710]
assert _check_smoothness(9645, factor_base) == (5, False)
assert _check_smoothness(210313, factor_base)[0][0:15] == \
[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1]
assert _check_smoothness(210313, factor_base)[1]
partial_relations: dict[int, tuple[int, int]] = {}
smooth_relation, partial_relation = _trial_division_stage(
n, M, factor_base, sieve_array, sieve_poly, partial_relations,
ERROR_TERM=25*2**10)
assert partial_relations == {
8699: (440, -10009008507),
166741: (490, -10008962007),
131449: (530, -10008921207),
6653: (550, -10008899607)
}
assert [smooth_relation[i][0] for i in range(5)] == [
-250, -670615476700, -45211565844500, -231723037747200, -1811665537200]
assert [smooth_relation[i][1] for i in range(5)] == [
-10009139607, 1133094251961, 5302606761, 53804049849, 1950723889]
assert smooth_relation[0][2][0:15] == [
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
assert _gauss_mod_2(
[[0, 0, 1], [1, 0, 1], [0, 1, 0], [0, 1, 1], [0, 1, 1]]
) == (
[[[0, 1, 1], 3], [[0, 1, 1], 4]],
[True, True, True, False, False],
[[0, 0, 1], [1, 0, 0], [0, 1, 0], [0, 1, 1], [0, 1, 1]]
)
def test_qs_3():
N = 1817
smooth_relations = [
(2455024, 637, [0, 0, 0, 1]),
(-27993000, 81536, [0, 1, 0, 1]),
(11461840, 12544, [0, 0, 0, 0]),
(149, 20384, [0, 1, 0, 1]),
(-31138074, 19208, [0, 1, 0, 0])
]
matrix = _build_matrix(smooth_relations)
assert matrix == [
[0, 0, 0, 1],
[0, 1, 0, 1],
[0, 0, 0, 0],
[0, 1, 0, 1],
[0, 1, 0, 0]
]
dependent_row, mark, gauss_matrix = _gauss_mod_2(matrix)
assert dependent_row == [[[0, 0, 0, 0], 2], [[0, 1, 0, 0], 3]]
assert mark == [True, True, False, False, True]
assert gauss_matrix == [
[0, 0, 0, 1],
[0, 1, 0, 0],
[0, 0, 0, 0],
[0, 1, 0, 0],
[0, 1, 0, 1]
]
factor = _find_factor(
dependent_row, mark, gauss_matrix, 0, smooth_relations, N)
assert factor == 23
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