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())