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