def test_PolynomialRingBase():
assert srepr(ZZ.old_poly_ring(x)) == \
"GlobalPolynomialRing(ZZ, Symbol('x'))"
assert srepr(ZZ[x].old_poly_ring(y)) == \
"GlobalPolynomialRing(ZZ[x], Symbol('y'))"
assert srepr(QQ.frac_field(x).old_poly_ring(y)) == \
"GlobalPolynomialRing(FractionField(FracField((Symbol('x'),), QQ, lex)), Symbol('y'))"
def test_FreeModule():
M1 = FreeModule(QQ.old_poly_ring(x), 2)
assert M1 == FreeModule(QQ.old_poly_ring(x), 2)
assert M1 != FreeModule(QQ.old_poly_ring(y), 2)
assert M1 != FreeModule(QQ.old_poly_ring(x), 3)
M2 = FreeModule(QQ.old_poly_ring(x, order="ilex"), 2)
assert [x, 1] in M1
assert [x] not in M1
assert [2, y] not in M1
assert [1/(x + 1), 2] not in M1
e = M1.convert([x, x**2 + 1])
X = QQ.old_poly_ring(x).convert(x)
assert e == [X, X**2 + 1]
assert e == [x, x**2 + 1]
assert 2*e == [2*x, 2*x**2 + 2]
assert e*2 == [2*x, 2*x**2 + 2]
assert e/2 == [x/2, (x**2 + 1)/2]
assert x*e == [x**2, x**3 + x]
assert e*x == [x**2, x**3 + x]
assert X*e == [x**2, x**3 + x]
assert e*X == [x**2, x**3 + x]
assert [x, 1] in M2
assert [x] not in M2
assert [2, y] not in M2
assert [1/(x + 1), 2] in M2
e = M2.convert([x, x**2 + 1])
X = QQ.old_poly_ring(x, order="ilex").convert(x)
assert e == [X, X**2 + 1]
assert e == [x, x**2 + 1]
assert 2*e == [2*x, 2*x**2 + 2]
assert e*2 == [2*x, 2*x**2 + 2]
assert e/2 == [x/2, (x**2 + 1)/2]
assert x*e == [x**2, x**3 + x]
assert e*x == [x**2, x**3 + x]
assert e/(1 + x) == [x/(1 + x), (x**2 + 1)/(1 + x)]
assert X*e == [x**2, x**3 + x]
assert e*X == [x**2, x**3 + x]
M3 = FreeModule(QQ.old_poly_ring(x, y), 2)
assert M3.convert(e) == M3.convert([x, x**2 + 1])
assert not M3.is_submodule(0)
assert not M3.is_zero()
raises(NotImplementedError, lambda: ZZ.old_poly_ring(x).free_module(2))
raises(NotImplementedError, lambda: FreeModulePolyRing(ZZ, 2))
raises(CoercionFailed, lambda: M1.convert(QQ.old_poly_ring(x).free_module(3)
.convert([1, 2, 3])))
raises(CoercionFailed, lambda: M3.convert(1))
def test_DDM_hstack():
A = DDM([[ZZ(1), ZZ(2), ZZ(3)]], (1, 3), ZZ)
B = DDM([[ZZ(4), ZZ(5)]], (1, 2), ZZ)
C = DDM([[ZZ(6)]], (1, 1), ZZ)
Ah = A.hstack(B)
assert Ah.shape == (1, 5)
assert Ah.domain == ZZ
assert Ah == DDM([[ZZ(1), ZZ(2), ZZ(3), ZZ(4), ZZ(5)]], (1, 5), ZZ)
Ah = A.hstack(B, C)
assert Ah.shape == (1, 6)
assert Ah.domain == ZZ
assert Ah == DDM([[ZZ(1), ZZ(2), ZZ(3), ZZ(4), ZZ(5), ZZ(6)]], (1, 6), ZZ)
def test_DDM_init():
items = [[ZZ(0), ZZ(1), ZZ(2)], [ZZ(3), ZZ(4), ZZ(5)]]
shape = (2, 3)
ddm = DDM(items, shape, ZZ)
assert ddm.shape == shape
assert ddm.rows == 2
assert ddm.cols == 3
assert ddm.domain == ZZ
raises(DDMBadInputError, lambda: DDM([[ZZ(2), ZZ(3)]], (2, 2), ZZ))
raises(DDMBadInputError, lambda: DDM([[ZZ(1)], [ZZ(2), ZZ(3)]],
(2, 2), ZZ))
def test_DDM_getitem():
dm = DDM([[ZZ(1), ZZ(2), ZZ(3)], [ZZ(4), ZZ(5), ZZ(6)],
[ZZ(7), ZZ(8), ZZ(9)]], (3, 3), ZZ)
assert dm.getitem(1, 1) == ZZ(5)
assert dm.getitem(1, -2) == ZZ(5)
assert dm.getitem(-1, -3) == ZZ(7)
raises(IndexError, lambda: dm.getitem(3, 3))
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_extract():
dM1 = DomainMatrix([
[ZZ(1), ZZ(2), ZZ(3)],
[ZZ(4), ZZ(5), ZZ(6)],
[ZZ(7), ZZ(8), ZZ(9)]], (3, 3), ZZ)
dM2 = DomainMatrix([
[ZZ(1), ZZ(3)],
[ZZ(7), ZZ(9)]], (2, 2), ZZ)
assert dM1.extract([0, 2], [0, 2]) == dM2
assert dM1.to_sparse().extract([0, 2], [0, 2]) == dM2.to_sparse()
assert dM1.extract([0, -1], [0, -1]) == dM2
assert dM1.to_sparse().extract([0, -1], [0, -1]) == dM2.to_sparse()
dM3 = DomainMatrix([
[ZZ(1), ZZ(2), ZZ(2)],
[ZZ(4), ZZ(5), ZZ(5)],
[ZZ(4), ZZ(5), ZZ(5)]], (3, 3), ZZ)
assert dM1.extract([0, 1, 1], [0, 1, 1]) == dM3
assert dM1.to_sparse().extract([0, 1, 1], [0, 1, 1]) == dM3.to_sparse()
empty = [
([], [], (0, 0)),
([1], [], (1, 0)),
([], [1], (0, 1)),
]
for rows, cols, size in empty:
assert dM1.extract(rows, cols) == DomainMatrix.zeros(size, ZZ).to_dense()
assert dM1.to_sparse().extract(rows, cols) == DomainMatrix.zeros(size, ZZ)
dM = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
bad_indices = [([2], [0]), ([0], [2]), ([-3], [0]), ([0], [-3])]
for rows, cols in bad_indices:
raises(IndexError, lambda: dM.extract(rows, cols))
raises(IndexError, lambda: dM.to_sparse().extract(rows, cols))
def test_DomainMatrix_scalarmul():
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
lamda = DomainScalar(QQ(3)/QQ(2), QQ)
assert A * lamda == DomainMatrix([[QQ(3, 2), QQ(3)], [QQ(9, 2), QQ(6)]], (2, 2), QQ)
assert A * 2 == DomainMatrix([[ZZ(2), ZZ(4)], [ZZ(6), ZZ(8)]], (2, 2), ZZ)
assert A * DomainScalar(ZZ(0), ZZ) == DomainMatrix([[ZZ(0)]*2]*2, (2, 2), ZZ)
assert A * DomainScalar(ZZ(1), ZZ) == A
raises(TypeError, lambda: A * 1.5)
def test_DomainMatrix_vstack():
A = DomainMatrix([[ZZ(1), ZZ(2)]], (1, 2), ZZ)
B = DomainMatrix([[QQ(3), QQ(4)], [QQ(5), QQ(6)]], (2, 2), QQ)
AB = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)], [QQ(5), QQ(6)]], (3, 2), QQ)
assert A.vstack(B) == AB
def test_DomainMatrix_flat():
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
assert A.flat() == [ZZ(1), ZZ(2), ZZ(3), ZZ(4)]
def test_DomainMatrix_transpose():
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
AT = DomainMatrix([[ZZ(1), ZZ(3)], [ZZ(2), ZZ(4)]], (2, 2), ZZ)
assert A.transpose() == AT
def test_DomainMatrix_repr():
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
assert repr(A) == 'DomainMatrix([[1, 2], [3, 4]], (2, 2), ZZ)'
def test_DomainMatrix_to_Matrix():
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
assert A.to_Matrix() == Matrix([[1, 2], [3, 4]])
def test_DomainMatrix_to_sparse():
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
A_sparse = A.to_sparse()
assert A_sparse.rep == {0: {0: 1, 1: 2}, 1: {0: 3, 1: 4}}
def test_DomainMatrix_to_field():
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
Aq = A.to_field()
assert Aq == DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ)
def test_DomainMatrix_convert_to():
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
Aq = A.convert_to(QQ)
assert Aq == DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ)
def test_DomainMatrix_is_zero_matrix():
A = DomainMatrix([[ZZ(1)]], (1, 1), ZZ)
B = DomainMatrix([[ZZ(0)]], (1, 1), ZZ)
assert A.is_zero_matrix is False
assert B.is_zero_matrix is True
def test_DomainMatrix_applyfunc():
A = DomainMatrix([[ZZ(1), ZZ(2)]], (1, 2), ZZ)
B = DomainMatrix([[ZZ(2), ZZ(4)]], (1, 2), ZZ)
assert A.applyfunc(lambda x: 2*x) == B
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_getitem():
dM = DomainMatrix([
[ZZ(1), ZZ(2), ZZ(3)],
[ZZ(4), ZZ(5), ZZ(6)],
[ZZ(7), ZZ(8), ZZ(9)]], (3, 3), ZZ)
assert dM[1:,:-2] == DomainMatrix([[ZZ(4)], [ZZ(7)]], (2, 1), ZZ)
assert dM[2,:-2] == DomainMatrix([[ZZ(7)]], (1, 1), ZZ)
assert dM[:-2,:-2] == DomainMatrix([[ZZ(1)]], (1, 1), ZZ)
assert dM[:-1,0:2] == DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(4), ZZ(5)]], (2, 2), ZZ)
assert dM[:, -1] == DomainMatrix([[ZZ(3)], [ZZ(6)], [ZZ(9)]], (3, 1), ZZ)
assert dM[-1, :] == DomainMatrix([[ZZ(7), ZZ(8), ZZ(9)]], (1, 3), ZZ)
assert dM[::-1, :] == DomainMatrix([
[ZZ(7), ZZ(8), ZZ(9)],
[ZZ(4), ZZ(5), ZZ(6)],
[ZZ(1), ZZ(2), ZZ(3)]], (3, 3), ZZ)
raises(IndexError, lambda: dM[4, :-2])
raises(IndexError, lambda: dM[:-2, 4])
assert dM[1, 2] == DomainScalar(ZZ(6), ZZ)
assert dM[-2, 2] == DomainScalar(ZZ(6), ZZ)
assert dM[1, -2] == DomainScalar(ZZ(5), ZZ)
assert dM[-1, -3] == DomainScalar(ZZ(7), ZZ)
raises(IndexError, lambda: dM[3, 3])
raises(IndexError, lambda: dM[1, 4])
raises(IndexError, lambda: dM[-1, -4])
dM = DomainMatrix({0: {0: ZZ(1)}}, (10, 10), ZZ)
assert dM[5, 5] == DomainScalar(ZZ(0), ZZ)
assert dM[0, 0] == DomainScalar(ZZ(1), ZZ)
dM = DomainMatrix({1: {0: 1}}, (2,1), ZZ)
assert dM[0:, 0] == DomainMatrix({1: {0: 1}}, (2, 1), ZZ)
raises(IndexError, lambda: dM[3, 0])
dM = DomainMatrix({2: {2: ZZ(1)}, 4: {4: ZZ(1)}}, (5, 5), ZZ)
assert dM[:2,:2] == DomainMatrix({}, (2, 2), ZZ)
assert dM[2:,2:] == DomainMatrix({0: {0: 1}, 2: {2: 1}}, (3, 3), ZZ)
assert dM[3:,3:] == DomainMatrix({1: {1: 1}}, (2, 2), ZZ)
assert dM[2:, 6:] == DomainMatrix({}, (3, 0), ZZ)
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_pickling():
import pickle
dM = DomainMatrix({2: {2: ZZ(1)}, 4: {4: ZZ(1)}}, (5, 5), ZZ)
assert pickle.loads(pickle.dumps(dM)) == dM
dM = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
assert pickle.loads(pickle.dumps(dM)) == dM
def test_DomainMatrix_neg():
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
Aneg = DomainMatrix([[ZZ(-1), ZZ(-2)], [ZZ(-3), ZZ(-4)]], (2, 2), ZZ)
assert -A == A.neg() == Aneg
def test_DDM_charpoly():
A = DDM([], (0, 0), ZZ)
assert A.charpoly() == [ZZ(1)]
A = DDM([[ZZ(1), ZZ(2), ZZ(3)], [ZZ(4), ZZ(5), ZZ(6)],
[ZZ(7), ZZ(8), ZZ(9)]], (3, 3), ZZ)
Avec = [ZZ(1), ZZ(-15), ZZ(-18), ZZ(0)]
assert A.charpoly() == Avec
A = DDM([[ZZ(1), ZZ(2)]], (1, 2), ZZ)
raises(DDMShapeError, lambda: A.charpoly())
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)
Aprod = DomainMatrix([[QQ(7), QQ(10)], [QQ(15), QQ(22)]], (2, 2), QQ)
assert Az * Aq == Aprod
assert Aq * Az == Aprod
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
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([[3, 4], [2, 4]], (2, 2), ZZ)
assert Asd.rep == DDM([[3, 4], [2, 4]], (2, 2), ZZ)
assert Ads == DomainMatrix([[4, 1], [8, 3]], (2, 2), ZZ)
assert Ads.rep == DDM([[4, 1], [8, 3]], (2, 2), ZZ)
def test_DDM_convert_to():
ddm = DDM([[ZZ(1), ZZ(2)]], (1, 2), ZZ)
assert ddm.convert_to(ZZ) == ddm
ddmq = ddm.convert_to(QQ)
assert ddmq.domain == QQ
def test_DomainMatrix_pow():
eye = DomainMatrix.eye(2, ZZ)
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)
A3 = DomainMatrix([[ZZ(37), ZZ(54)], [ZZ(81), ZZ(118)]], (2, 2), ZZ)
assert A**0 == A.pow(0) == eye
assert A**1 == A.pow(1) == A
assert A**2 == A.pow(2) == A2
assert A**3 == A.pow(3) == A3
raises(TypeError, lambda: A ** Rational(1, 2))
raises(NotImplementedError, lambda: A ** -1)
raises(NotImplementedError, lambda: A.pow(-1))
A = DomainMatrix.zeros((2, 1), ZZ)
raises(NonSquareMatrixError, lambda: A ** 1)
def test_DDM_neg():
A = DDM([[ZZ(1)], [ZZ(2)]], (2, 1), ZZ)
An = DDM([[ZZ(-1)], [ZZ(-2)]], (2, 1), ZZ)
assert -A == A.neg() == An
assert -An == An.neg() == A
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_DDM_vstack():
A = DDM([[ZZ(1)], [ZZ(2)], [ZZ(3)]], (3, 1), ZZ)
B = DDM([[ZZ(4)], [ZZ(5)]], (2, 1), ZZ)
C = DDM([[ZZ(6)]], (1, 1), ZZ)
Ah = A.vstack(B)
assert Ah.shape == (5, 1)
assert Ah.domain == ZZ
assert Ah == DDM([[ZZ(1)], [ZZ(2)], [ZZ(3)], [ZZ(4)], [ZZ(5)]], (5, 1), ZZ)
Ah = A.vstack(B, C)
assert Ah.shape == (6, 1)
assert Ah.domain == ZZ
assert Ah == DDM([[ZZ(1)], [ZZ(2)], [ZZ(3)], [ZZ(4)], [ZZ(5)], [ZZ(6)]],
(6, 1), ZZ)
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_DMP():
assert srepr(DMP([1, 2], ZZ)) == 'DMP([1, 2], ZZ)'
assert srepr(ZZ.old_poly_ring(x)([1, 2])) == \
"DMP([1, 2], ZZ, ring=GlobalPolynomialRing(ZZ, Symbol('x')))"
def test_DomainMatrix_diag():
A = DomainMatrix({0:{0:ZZ(2)}, 1:{1:ZZ(3)}}, (2, 2), ZZ)
assert DomainMatrix.diag([ZZ(2), ZZ(3)], ZZ) == A
A = DomainMatrix({0:{0:ZZ(2)}, 1:{1:ZZ(3)}}, (3, 4), ZZ)
assert DomainMatrix.diag([ZZ(2), ZZ(3)], ZZ, (3, 4)) == A