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| from sympy.polys.domains import ZZ, QQ | |
| from sympy.polys.matrices import DM | |
| from sympy.polys.matrices.domainmatrix import DomainMatrix | |
| from sympy.polys.matrices.exceptions import DMRankError, DMValueError, DMShapeError, DMDomainError | |
| from sympy.polys.matrices.lll import _ddm_lll, ddm_lll, ddm_lll_transform | |
| from sympy.testing.pytest import raises | |
| def test_lll(): | |
| normal_test_data = [ | |
| ( | |
| DM([[1, 0, 0, 0, -20160], | |
| [0, 1, 0, 0, 33768], | |
| [0, 0, 1, 0, 39578], | |
| [0, 0, 0, 1, 47757]], ZZ), | |
| DM([[10, -3, -2, 8, -4], | |
| [3, -9, 8, 1, -11], | |
| [-3, 13, -9, -3, -9], | |
| [-12, -7, -11, 9, -1]], ZZ) | |
| ), | |
| ( | |
| DM([[20, 52, 3456], | |
| [14, 31, -1], | |
| [34, -442, 0]], ZZ), | |
| DM([[14, 31, -1], | |
| [188, -101, -11], | |
| [236, 13, 3443]], ZZ) | |
| ), | |
| ( | |
| DM([[34, -1, -86, 12], | |
| [-54, 34, 55, 678], | |
| [23, 3498, 234, 6783], | |
| [87, 49, 665, 11]], ZZ), | |
| DM([[34, -1, -86, 12], | |
| [291, 43, 149, 83], | |
| [-54, 34, 55, 678], | |
| [-189, 3077, -184, -223]], ZZ) | |
| ) | |
| ] | |
| delta = QQ(5, 6) | |
| for basis_dm, reduced_dm in normal_test_data: | |
| reduced = _ddm_lll(basis_dm.rep.to_ddm(), delta=delta)[0] | |
| assert reduced == reduced_dm.rep.to_ddm() | |
| reduced = ddm_lll(basis_dm.rep.to_ddm(), delta=delta) | |
| assert reduced == reduced_dm.rep.to_ddm() | |
| reduced, transform = _ddm_lll(basis_dm.rep.to_ddm(), delta=delta, return_transform=True) | |
| assert reduced == reduced_dm.rep.to_ddm() | |
| assert transform.matmul(basis_dm.rep.to_ddm()) == reduced_dm.rep.to_ddm() | |
| reduced, transform = ddm_lll_transform(basis_dm.rep.to_ddm(), delta=delta) | |
| assert reduced == reduced_dm.rep.to_ddm() | |
| assert transform.matmul(basis_dm.rep.to_ddm()) == reduced_dm.rep.to_ddm() | |
| reduced = basis_dm.rep.lll(delta=delta) | |
| assert reduced == reduced_dm.rep | |
| reduced, transform = basis_dm.rep.lll_transform(delta=delta) | |
| assert reduced == reduced_dm.rep | |
| assert transform.matmul(basis_dm.rep) == reduced_dm.rep | |
| reduced = basis_dm.rep.to_sdm().lll(delta=delta) | |
| assert reduced == reduced_dm.rep.to_sdm() | |
| reduced, transform = basis_dm.rep.to_sdm().lll_transform(delta=delta) | |
| assert reduced == reduced_dm.rep.to_sdm() | |
| assert transform.matmul(basis_dm.rep.to_sdm()) == reduced_dm.rep.to_sdm() | |
| reduced = basis_dm.lll(delta=delta) | |
| assert reduced == reduced_dm | |
| reduced, transform = basis_dm.lll_transform(delta=delta) | |
| assert reduced == reduced_dm | |
| assert transform.matmul(basis_dm) == reduced_dm | |
| def test_lll_linear_dependent(): | |
| linear_dependent_test_data = [ | |
| DM([[0, -1, -2, -3], | |
| [1, 0, -1, -2], | |
| [2, 1, 0, -1], | |
| [3, 2, 1, 0]], ZZ), | |
| DM([[1, 0, 0, 1], | |
| [0, 1, 0, 1], | |
| [0, 0, 1, 1], | |
| [1, 2, 3, 6]], ZZ), | |
| DM([[3, -5, 1], | |
| [4, 6, 0], | |
| [10, -4, 2]], ZZ) | |
| ] | |
| for not_basis in linear_dependent_test_data: | |
| raises(DMRankError, lambda: _ddm_lll(not_basis.rep.to_ddm())) | |
| raises(DMRankError, lambda: ddm_lll(not_basis.rep.to_ddm())) | |
| raises(DMRankError, lambda: not_basis.rep.lll()) | |
| raises(DMRankError, lambda: not_basis.rep.to_sdm().lll()) | |
| raises(DMRankError, lambda: not_basis.lll()) | |
| raises(DMRankError, lambda: _ddm_lll(not_basis.rep.to_ddm(), return_transform=True)) | |
| raises(DMRankError, lambda: ddm_lll_transform(not_basis.rep.to_ddm())) | |
| raises(DMRankError, lambda: not_basis.rep.lll_transform()) | |
| raises(DMRankError, lambda: not_basis.rep.to_sdm().lll_transform()) | |
| raises(DMRankError, lambda: not_basis.lll_transform()) | |
| def test_lll_wrong_delta(): | |
| dummy_matrix = DomainMatrix.ones((3, 3), ZZ) | |
| for wrong_delta in [QQ(-1, 4), QQ(0, 1), QQ(1, 4), QQ(1, 1), QQ(100, 1)]: | |
| raises(DMValueError, lambda: _ddm_lll(dummy_matrix.rep, delta=wrong_delta)) | |
| raises(DMValueError, lambda: ddm_lll(dummy_matrix.rep, delta=wrong_delta)) | |
| raises(DMValueError, lambda: dummy_matrix.rep.lll(delta=wrong_delta)) | |
| raises(DMValueError, lambda: dummy_matrix.rep.to_sdm().lll(delta=wrong_delta)) | |
| raises(DMValueError, lambda: dummy_matrix.lll(delta=wrong_delta)) | |
| raises(DMValueError, lambda: _ddm_lll(dummy_matrix.rep, delta=wrong_delta, return_transform=True)) | |
| raises(DMValueError, lambda: ddm_lll_transform(dummy_matrix.rep, delta=wrong_delta)) | |
| raises(DMValueError, lambda: dummy_matrix.rep.lll_transform(delta=wrong_delta)) | |
| raises(DMValueError, lambda: dummy_matrix.rep.to_sdm().lll_transform(delta=wrong_delta)) | |
| raises(DMValueError, lambda: dummy_matrix.lll_transform(delta=wrong_delta)) | |
| def test_lll_wrong_shape(): | |
| wrong_shape_matrix = DomainMatrix.ones((4, 3), ZZ) | |
| raises(DMShapeError, lambda: _ddm_lll(wrong_shape_matrix.rep)) | |
| raises(DMShapeError, lambda: ddm_lll(wrong_shape_matrix.rep)) | |
| raises(DMShapeError, lambda: wrong_shape_matrix.rep.lll()) | |
| raises(DMShapeError, lambda: wrong_shape_matrix.rep.to_sdm().lll()) | |
| raises(DMShapeError, lambda: wrong_shape_matrix.lll()) | |
| raises(DMShapeError, lambda: _ddm_lll(wrong_shape_matrix.rep, return_transform=True)) | |
| raises(DMShapeError, lambda: ddm_lll_transform(wrong_shape_matrix.rep)) | |
| raises(DMShapeError, lambda: wrong_shape_matrix.rep.lll_transform()) | |
| raises(DMShapeError, lambda: wrong_shape_matrix.rep.to_sdm().lll_transform()) | |
| raises(DMShapeError, lambda: wrong_shape_matrix.lll_transform()) | |
| def test_lll_wrong_domain(): | |
| wrong_domain_matrix = DomainMatrix.ones((3, 3), QQ) | |
| raises(DMDomainError, lambda: _ddm_lll(wrong_domain_matrix.rep)) | |
| raises(DMDomainError, lambda: ddm_lll(wrong_domain_matrix.rep)) | |
| raises(DMDomainError, lambda: wrong_domain_matrix.rep.lll()) | |
| raises(DMDomainError, lambda: wrong_domain_matrix.rep.to_sdm().lll()) | |
| raises(DMDomainError, lambda: wrong_domain_matrix.lll()) | |
| raises(DMDomainError, lambda: _ddm_lll(wrong_domain_matrix.rep, return_transform=True)) | |
| raises(DMDomainError, lambda: ddm_lll_transform(wrong_domain_matrix.rep)) | |
| raises(DMDomainError, lambda: wrong_domain_matrix.rep.lll_transform()) | |
| raises(DMDomainError, lambda: wrong_domain_matrix.rep.to_sdm().lll_transform()) | |
| raises(DMDomainError, lambda: wrong_domain_matrix.lll_transform()) | |