def test_DomainMatrix_unify(): Az = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) Aq = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ) assert Az.unify(Az) == (Az, Az) assert Az.unify(Aq) == (Aq, Aq) assert Aq.unify(Az) == (Aq, Aq) assert Aq.unify(Aq) == (Aq, Aq)
def test_DDM_det(): # 0x0 case A = DDM([], (0, 0), ZZ) assert A.det() == ZZ(1) # 1x1 case A = DDM([[ZZ(2)]], (1, 1), ZZ) assert A.det() == ZZ(2) # 2x2 case A = DDM([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) assert A.det() == ZZ(-2) # 3x3 with swap A = DDM([[ZZ(1), ZZ(2), ZZ(3)], [ZZ(1), ZZ(2), ZZ(4)], [ZZ(1), ZZ(2), ZZ(5)]], (3, 3), ZZ) assert A.det() == ZZ(0) # 2x2 QQ case A = DDM([[QQ(1, 2), QQ(1, 2)], [QQ(1, 3), QQ(1, 4)]], (2, 2), QQ) assert A.det() == QQ(-1, 24) # Nonsquare error A = DDM([[ZZ(1)], [ZZ(2)]], (2, 1), ZZ) raises(DDMShapeError, lambda: A.det()) # Nonsquare error with empty matrix A = DDM([], (0, 1), ZZ) raises(DDMShapeError, lambda: A.det())
def test_DomainMatrix_mul(): A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) A2 = DomainMatrix([[ZZ(7), ZZ(10)], [ZZ(15), ZZ(22)]], (2, 2), ZZ) assert A * A == A.matmul(A) == A2 A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) L = [[1, 2], [3, 4]] raises(TypeError, lambda: A * L) raises(TypeError, lambda: L * A) Az = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) Aq = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ) raises(DDMDomainError, lambda: Az * Aq) raises(DDMDomainError, lambda: Aq * Az) raises(DDMDomainError, lambda: Az.matmul(Aq)) raises(DDMDomainError, lambda: Aq.matmul(Az)) A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) AA = DomainMatrix([[ZZ(2), ZZ(4)], [ZZ(6), ZZ(8)]], (2, 2), ZZ) x = ZZ(2) assert A * x == x * A == A.mul(x) == AA A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) AA = DomainMatrix([[ZZ(0), ZZ(0)], [ZZ(0), ZZ(0)]], (2, 2), ZZ) x = ZZ(0) assert A * x == x * A == A.mul(x) == AA
def test_DDM_copy(): ddm1 = DDM([[QQ(1)], [QQ(2)]], (2, 1), QQ) ddm2 = ddm1.copy() assert (ddm1 == ddm2) is True ddm1[0][0] = QQ(-1) assert (ddm1 == ddm2) is False ddm2[0][0] = QQ(-1) assert (ddm1 == ddm2) is True
def test_DomainMatrix_get_domain(): K, items = DomainMatrix.get_domain([1, 2, 3, 4]) assert items == [ZZ(1), ZZ(2), ZZ(3), ZZ(4)] assert K == ZZ K, items = DomainMatrix.get_domain([1, 2, 3, Rational(1, 2)]) assert items == [QQ(1), QQ(2), QQ(3), QQ(1, 2)] assert K == QQ
def test_DomainScalar_floordiv(): A = DomainScalar(ZZ(-5), ZZ) B = DomainScalar(QQ(2), QQ) assert A // B == DomainScalar(QQ(-5, 2), QQ) C = DomainScalar(ZZ(2), ZZ) assert A // C == DomainScalar(ZZ(-3), ZZ) raises(TypeError, lambda: A // 1.5)
def test_DomainScalar_mod(): A = DomainScalar(ZZ(5), ZZ) B = DomainScalar(QQ(2), QQ) assert A % B == DomainScalar(QQ(0), QQ) C = DomainScalar(ZZ(2), ZZ) assert A % C == DomainScalar(ZZ(1), ZZ) raises(TypeError, lambda: A % 1.5)
def test_DomainScalar_mul(): A = DomainScalar(ZZ(1), ZZ) B = DomainScalar(QQ(2), QQ) dm = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) assert A * B == DomainScalar(QQ(2), QQ) assert A * dm == dm assert B * 2 == DomainScalar(QQ(4), QQ) raises(TypeError, lambda: A * 1.5)
def test_DomainScalar_divmod(): A = DomainScalar(ZZ(5), ZZ) B = DomainScalar(QQ(2), QQ) assert divmod(A, B) == (DomainScalar(QQ(5, 2), QQ), DomainScalar(QQ(0), QQ)) C = DomainScalar(ZZ(2), ZZ) assert divmod(A, C) == (DomainScalar(ZZ(2), ZZ), DomainScalar(ZZ(1), ZZ)) raises(TypeError, lambda: divmod(A, 1.5))
def test_DDM_transpose(): ddm = DDM([[QQ(1)], [QQ(2)]], (2, 1), QQ) ddmT = DDM([[QQ(1), QQ(2)]], (1, 2), QQ) assert ddm.transpose() == ddmT ddm02 = DDM([], (0, 2), QQ) ddm02T = DDM([[], []], (2, 0), QQ) assert ddm02.transpose() == ddm02T assert ddm02T.transpose() == ddm02 ddm0 = DDM([], (0, 0), QQ) assert ddm0.transpose() == ddm0
def test_DomainMatrix_from_dict_sympy(): sdm = SDM({0: {0: QQ(1, 2)}, 1: {1: QQ(2, 3)}}, (2, 2), QQ) sympy_dict = {0: {0: Rational(1, 2)}, 1: {1: Rational(2, 3)}} A = DomainMatrix.from_dict_sympy(2, 2, sympy_dict) assert A.rep == sdm assert A.shape == (2, 2) assert A.domain == QQ fds = DomainMatrix.from_dict_sympy raises(DDMBadInputError, lambda: fds(2, 2, {3: {0: Rational(1, 2)}})) raises(DDMBadInputError, lambda: fds(2, 2, {0: {3: Rational(1, 2)}}))
def test_DDM_add(): A = DDM([[ZZ(1)], [ZZ(2)]], (2, 1), ZZ) B = DDM([[ZZ(3)], [ZZ(4)]], (2, 1), ZZ) C = DDM([[ZZ(4)], [ZZ(6)]], (2, 1), ZZ) AQ = DDM([[QQ(1)], [QQ(2)]], (2, 1), QQ) assert A + B == A.add(B) == C raises(DDMShapeError, lambda: A + DDM([[ZZ(5)]], (1, 1), ZZ)) raises(TypeError, lambda: A + ZZ(1)) raises(TypeError, lambda: ZZ(1) + A) raises(DDMDomainError, lambda: A + AQ) raises(DDMDomainError, lambda: AQ + A)
def test_DomainMatrix_from_dict_sympy(): sdm = SDM({0: {0: QQ(1, 2)}, 1: {1: QQ(2, 3)}}, (2, 2), QQ) A = DomainMatrix.from_dict_sympy(2, 2, { 0: { 0: QQ(1, 2) }, 1: { 1: QQ(2, 3) } }) assert A.rep == sdm assert A.shape == (2, 2) assert A.domain == QQ
def test_DomainMatrix_add(): A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) B = DomainMatrix([[ZZ(2), ZZ(4)], [ZZ(6), ZZ(8)]], (2, 2), ZZ) assert A + A == A.add(A) == B A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) L = [[2, 3], [3, 4]] raises(TypeError, lambda: A + L) raises(TypeError, lambda: L + A) A1 = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) A2 = DomainMatrix([[ZZ(1), ZZ(2)]], (1, 2), ZZ) raises(DDMShapeError, lambda: A1 + A2) raises(DDMShapeError, lambda: A2 + A1) raises(DDMShapeError, lambda: A1.add(A2)) raises(DDMShapeError, lambda: A2.add(A1)) Az = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) Aq = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ) Asum = DomainMatrix([[QQ(2), QQ(4)], [QQ(6), QQ(8)]], (2, 2), QQ) assert Az + Aq == Asum assert Aq + Az == Asum raises(DDMDomainError, lambda: Az.add(Aq)) raises(DDMDomainError, lambda: Aq.add(Az)) As = DomainMatrix({0: {1: ZZ(1)}, 1: {0: ZZ(2)}}, (2, 2), ZZ) Ad = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) Asd = As + Ad Ads = Ad + As assert Asd == DomainMatrix([[1, 3], [5, 4]], (2, 2), ZZ) assert Asd.rep == DDM([[1, 3], [5, 4]], (2, 2), ZZ) assert Ads == DomainMatrix([[1, 3], [5, 4]], (2, 2), ZZ) assert Ads.rep == DDM([[1, 3], [5, 4]], (2, 2), ZZ) raises(DDMFormatError, lambda: As.add(Ad))
def test_DomainMatrix_sub(): A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) B = DomainMatrix([[ZZ(0), ZZ(0)], [ZZ(0), ZZ(0)]], (2, 2), ZZ) assert A - A == A.sub(A) == B A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) L = [[2, 3], [3, 4]] raises(TypeError, lambda: A - L) raises(TypeError, lambda: L - A) A1 = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) A2 = DomainMatrix([[ZZ(1), ZZ(2)]], (1, 2), ZZ) raises(DDMShapeError, lambda: A1 - A2) raises(DDMShapeError, lambda: A2 - A1) raises(DDMShapeError, lambda: A1.sub(A2)) raises(DDMShapeError, lambda: A2.sub(A1)) Az = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) Aq = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ) Adiff = DomainMatrix([[QQ(0), QQ(0)], [QQ(0), QQ(0)]], (2, 2), QQ) assert Az - Aq == Adiff assert Aq - Az == Adiff raises(DDMDomainError, lambda: Az.sub(Aq)) raises(DDMDomainError, lambda: Aq.sub(Az)) As = DomainMatrix({0: {1: ZZ(1)}, 1: {0: ZZ(2)}}, (2, 2), ZZ) Ad = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) Asd = As - Ad Ads = Ad - As assert Asd == DomainMatrix([[-1, -1], [-1, -4]], (2, 2), ZZ) assert Asd.rep == DDM([[-1, -1], [-1, -4]], (2, 2), ZZ) assert Asd == -Ads assert Asd.rep == -Ads.rep
def test_DomainMatrix_from_Matrix(): sdm = SDM({0: {0: ZZ(1), 1: ZZ(2)}, 1: {0: ZZ(3), 1: ZZ(4)}}, (2, 2), ZZ) A = DomainMatrix.from_Matrix(Matrix([[1, 2], [3, 4]])) assert A.rep == sdm assert A.shape == (2, 2) assert A.domain == ZZ K = QQ.algebraic_field(sqrt(2)) sdm = SDM( {0: {0: K.convert(1 + sqrt(2)), 1: K.convert(2 + sqrt(2))}, 1: {0: K.convert(3 + sqrt(2)), 1: K.convert(4 + sqrt(2))}}, (2, 2), K ) A = DomainMatrix.from_Matrix( Matrix([[1 + sqrt(2), 2 + sqrt(2)], [3 + sqrt(2), 4 + sqrt(2)]]), extension=True) assert A.rep == sdm assert A.shape == (2, 2) assert A.domain == K A = DomainMatrix.from_Matrix(Matrix([[QQ(1, 2), QQ(3, 4)], [QQ(0, 1), QQ(0, 1)]]), fmt='dense') ddm = DDM([[QQ(1, 2), QQ(3, 4)], [QQ(0, 1), QQ(0, 1)]], (2, 2), QQ) assert A.rep == ddm assert A.shape == (2, 2) assert A.domain == QQ
def test_DomainMatrix_charpoly(): A = DomainMatrix([], (0, 0), ZZ) assert A.charpoly() == [ZZ(1)] A = DomainMatrix([[1]], (1, 1), ZZ) assert A.charpoly() == [ZZ(1), ZZ(-1)] A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) assert A.charpoly() == [ZZ(1), ZZ(-5), ZZ(-2)] A = DomainMatrix([[ZZ(1), ZZ(2), ZZ(3)], [ZZ(4), ZZ(5), ZZ(6)], [ZZ(7), ZZ(8), ZZ(9)]], (3, 3), ZZ) assert A.charpoly() == [ZZ(1), ZZ(-15), ZZ(-18), ZZ(0)] Ans = DomainMatrix([[QQ(1), QQ(2)]], (1, 2), QQ) raises(NonSquareMatrixError, lambda: Ans.charpoly())
def test_PolyElement(): Ruv, u, v = ring("u,v", ZZ) Rxyz, x, y, z = ring("x,y,z", Ruv) Rx_zzi, xz = ring("x", ZZ_I) assert str(x - x) == "0" assert str(x - 1) == "x - 1" assert str(x + 1) == "x + 1" assert str(x**2) == "x**2" assert str(x**(-2)) == "x**(-2)" assert str(x**QQ(1, 2)) == "x**(1/2)" assert str((u**2 + 3 * u * v + 1) * x**2 * y + u + 1) == "(u**2 + 3*u*v + 1)*x**2*y + u + 1" assert str((u**2 + 3 * u * v + 1) * x**2 * y + (u + 1) * x) == "(u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x" assert str((u**2 + 3 * u * v + 1) * x**2 * y + (u + 1) * x + 1) == "(u**2 + 3*u*v + 1)*x**2*y + (u + 1)*x + 1" assert str((-u**2 + 3 * u * v - 1) * x**2 * y - (u + 1) * x - 1) == "-(u**2 - 3*u*v + 1)*x**2*y - (u + 1)*x - 1" assert str(-(v**2 + v + 1) * x + 3 * u * v + 1) == "-(v**2 + v + 1)*x + 3*u*v + 1" assert str(-(v**2 + v + 1) * x - 3 * u * v + 1) == "-(v**2 + v + 1)*x - 3*u*v + 1" assert str((1 + I) * xz + 2) == "(1 + 1*I)*x + (2 + 0*I)"
def test_DomainMatrix_solve(): # XXX: Maybe the _solve method should be changed... A = DomainMatrix([[QQ(1), QQ(2)], [QQ(2), QQ(4)]], (2, 2), QQ) b = DomainMatrix([[QQ(1)], [QQ(2)]], (2, 1), QQ) particular = DomainMatrix([[1, 0]], (1, 2), QQ) nullspace = DomainMatrix([[-2, 1]], (1, 2), QQ) assert A._solve(b) == (particular, nullspace) b3 = DomainMatrix([[QQ(1)], [QQ(1)], [QQ(1)]], (3, 1), QQ) raises(ShapeError, lambda: A._solve(b3)) bz = DomainMatrix([[ZZ(1)], [ZZ(1)]], (2, 1), ZZ) raises(ValueError, lambda: A._solve(bz))
def test_DomainMatrix_setitem(): dM = DomainMatrix({2: {2: ZZ(1)}, 4: {4: ZZ(1)}}, (5, 5), ZZ) dM[2, 2] = ZZ(2) assert dM == DomainMatrix({2: {2: ZZ(2)}, 4: {4: ZZ(1)}}, (5, 5), ZZ) def setitem(i, j, val): dM[i, j] = val raises(TypeError, lambda: setitem(2, 2, QQ(1, 2))) raises(NotImplementedError, lambda: setitem(slice(1, 2), 2, ZZ(1)))
def test_DomainMatrix_det(): A = DomainMatrix([], (0, 0), ZZ) assert A.det() == 1 A = DomainMatrix([[1]], (1, 1), ZZ) assert A.det() == 1 A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) assert A.det() == ZZ(-2) A = DomainMatrix( [[ZZ(1), ZZ(2), ZZ(3)], [ZZ(1), ZZ(2), ZZ(4)], [ZZ(1), ZZ(3), ZZ(5)]], (3, 3), ZZ) assert A.det() == ZZ(-1) A = DomainMatrix( [[ZZ(1), ZZ(2), ZZ(3)], [ZZ(1), ZZ(2), ZZ(4)], [ZZ(1), ZZ(2), ZZ(5)]], (3, 3), ZZ) assert A.det() == ZZ(0) Ans = DomainMatrix([[QQ(1), QQ(2)]], (1, 2), QQ) raises(NonSquareMatrixError, lambda: Ans.det()) A = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ) assert A.det() == QQ(-2)
def test_DomainScalar_eq(): A = DomainScalar(QQ(2), QQ) assert A == A B = DomainScalar(ZZ(-5), ZZ) assert A != B C = DomainScalar(ZZ(2), ZZ) assert A != C D = [1] assert A != D
def test_ddm_idet(): A = [] assert ddm_idet(A, ZZ) == ZZ(1) A = [[ZZ(2)]] assert ddm_idet(A, ZZ) == ZZ(2) A = [[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]] assert ddm_idet(A, ZZ) == ZZ(-2) A = [[ZZ(1), ZZ(2), ZZ(3)], [ZZ(1), ZZ(2), ZZ(4)], [ZZ(1), ZZ(3), ZZ(5)]] assert ddm_idet(A, ZZ) == ZZ(-1) A = [[ZZ(1), ZZ(2), ZZ(3)], [ZZ(1), ZZ(2), ZZ(4)], [ZZ(1), ZZ(2), ZZ(5)]] assert ddm_idet(A, ZZ) == ZZ(0) A = [[QQ(1, 2), QQ(1, 2)], [QQ(1, 3), QQ(1, 4)]] assert ddm_idet(A, QQ) == QQ(-1, 24)
def test_DDM_sub(): A = DDM([[ZZ(1)], [ZZ(2)]], (2, 1), ZZ) B = DDM([[ZZ(3)], [ZZ(4)]], (2, 1), ZZ) C = DDM([[ZZ(-2)], [ZZ(-2)]], (2, 1), ZZ) AQ = DDM([[QQ(1)], [QQ(2)]], (2, 1), QQ) D = DDM([[ZZ(5)]], (1, 1), ZZ) assert A - B == A.sub(B) == C raises(TypeError, lambda: A - ZZ(1)) raises(TypeError, lambda: ZZ(1) - A) raises(DDMShapeError, lambda: A - D) raises(DDMShapeError, lambda: D - A) raises(DDMShapeError, lambda: A.sub(D)) raises(DDMShapeError, lambda: D.sub(A)) raises(DDMDomainError, lambda: A - AQ) raises(DDMDomainError, lambda: AQ - A) raises(DDMDomainError, lambda: A.sub(AQ)) raises(DDMDomainError, lambda: AQ.sub(A))
def test_FiniteExtension_convert(): # Test from_MonogenicFiniteExtension K1 = FiniteExtension(Poly(x**2 + 1)) K2 = QQ[x] x1, x2 = K1(x), K2(x) assert K1.convert(x2) == x1 assert K2.convert(x1) == x2 K = FiniteExtension(Poly(x**2 - 1, domain=QQ)) assert K.convert_from(QQ(1, 2), QQ) == K.one/2
def test_DDM_matmul(): A = DDM([[ZZ(1)], [ZZ(2)]], (2, 1), ZZ) B = DDM([[ZZ(3), ZZ(4)]], (1, 2), ZZ) AB = DDM([[ZZ(3), ZZ(4)], [ZZ(6), ZZ(8)]], (2, 2), ZZ) BA = DDM([[ZZ(11)]], (1, 1), ZZ) assert A @ B == A.matmul(B) == AB assert B @ A == B.matmul(A) == BA raises(TypeError, lambda: A @ 1) raises(TypeError, lambda: A @ [[3, 4]]) Bq = DDM([[QQ(3), QQ(4)]], (1, 2), QQ) raises(DDMDomainError, lambda: A @ Bq) raises(DDMDomainError, lambda: Bq @ A) C = DDM([[ZZ(1)]], (1, 1), ZZ) assert A @ C == A.matmul(C) == A raises(DDMShapeError, lambda: C @ A) raises(DDMShapeError, lambda: C.matmul(A)) Z04 = DDM([], (0, 4), ZZ) Z40 = DDM([[]] * 4, (4, 0), ZZ) Z50 = DDM([[]] * 5, (5, 0), ZZ) Z05 = DDM([], (0, 5), ZZ) Z45 = DDM([[0] * 5] * 4, (4, 5), ZZ) Z54 = DDM([[0] * 4] * 5, (5, 4), ZZ) Z00 = DDM([], (0, 0), ZZ) assert Z04 @ Z45 == Z04.matmul(Z45) == Z05 assert Z45 @ Z50 == Z45.matmul(Z50) == Z40 assert Z00 @ Z04 == Z00.matmul(Z04) == Z04 assert Z50 @ Z00 == Z50.matmul(Z00) == Z50 assert Z00 @ Z00 == Z00.matmul(Z00) == Z00 assert Z50 @ Z04 == Z50.matmul(Z04) == Z54 raises(DDMShapeError, lambda: Z05 @ Z40) raises(DDMShapeError, lambda: Z05.matmul(Z40))
def test_DomainMatrix_nullspace(): A = DomainMatrix([[QQ(1), QQ(1)], [QQ(1), QQ(1)]], (2, 2), QQ) Anull = DomainMatrix([[QQ(-1), QQ(1)]], (1, 2), QQ) assert A.nullspace() == Anull Az = DomainMatrix([[ZZ(1), ZZ(1)], [ZZ(1), ZZ(1)]], (2, 2), ZZ) raises(ValueError, lambda: Az.nullspace())
def test_DomainMatrix_add(): A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) B = DomainMatrix([[ZZ(2), ZZ(4)], [ZZ(6), ZZ(8)]], (2, 2), ZZ) assert A + A == A.add(A) == B A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) L = [[2, 3], [3, 4]] raises(TypeError, lambda: A + L) raises(TypeError, lambda: L + A) A1 = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) A2 = DomainMatrix([[ZZ(1), ZZ(2)]], (1, 2), ZZ) raises(ShapeError, lambda: A1 + A2) raises(ShapeError, lambda: A2 + A1) raises(ShapeError, lambda: A1.add(A2)) raises(ShapeError, lambda: A2.add(A1)) Az = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) Aq = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ) raises(ValueError, lambda: Az + Aq) raises(ValueError, lambda: Aq + Az) raises(ValueError, lambda: Az.add(Aq)) raises(ValueError, lambda: Aq.add(Az))
def test_DomainMatrix_sub(): A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) B = DomainMatrix([[ZZ(0), ZZ(0)], [ZZ(0), ZZ(0)]], (2, 2), ZZ) assert A - A == A.sub(A) == B A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) L = [[2, 3], [3, 4]] raises(TypeError, lambda: A - L) raises(TypeError, lambda: L - A) A1 = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) A2 = DomainMatrix([[ZZ(1), ZZ(2)]], (1, 2), ZZ) raises(ShapeError, lambda: A1 - A2) raises(ShapeError, lambda: A2 - A1) raises(ShapeError, lambda: A1.sub(A2)) raises(ShapeError, lambda: A2.sub(A1)) Az = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) Aq = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ) raises(ValueError, lambda: Az - Aq) raises(ValueError, lambda: Aq - Az) raises(ValueError, lambda: Az.sub(Aq)) raises(ValueError, lambda: Aq.sub(Az))
def test_DomainMatrix_unify(): Az = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) Aq = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ) assert Az.unify(Az) == (Az, Az) assert Az.unify(Aq) == (Aq, Aq) assert Aq.unify(Az) == (Aq, Aq) assert Aq.unify(Aq) == (Aq, Aq) As = DomainMatrix({0: {1: ZZ(1)}, 1:{0:ZZ(2)}}, (2, 2), ZZ) Ad = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) assert As.unify(As) == (As, As) assert Ad.unify(Ad) == (Ad, Ad) Bs, Bd = As.unify(Ad, fmt='dense') assert Bs.rep == DDM([[0, 1], [2, 0]], (2, 2), ZZ) assert Bd.rep == DDM([[1, 2],[3, 4]], (2, 2), ZZ) Bs, Bd = As.unify(Ad, fmt='sparse') assert Bs.rep == SDM({0: {1: 1}, 1: {0: 2}}, (2, 2), ZZ) assert Bd.rep == SDM({0: {0: 1, 1: 2}, 1: {0: 3, 1: 4}}, (2, 2), ZZ) raises(ValueError, lambda: As.unify(Ad, fmt='invalid'))