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