def test_dmp_mul():
assert dmp_mul([ZZ(5)], [ZZ(7)], 0, ZZ) == \
dup_mul([ZZ(5)], [ZZ(7)], ZZ)
assert dmp_mul([QQ(5, 7)], [QQ(3, 7)], 0, QQ) == \
dup_mul([QQ(5, 7)], [QQ(3, 7)], QQ)
assert dmp_mul([[[]]], [[[]]], 2, ZZ) == [[[]]]
assert dmp_mul([[[ZZ(1)]]], [[[]]], 2, ZZ) == [[[]]]
assert dmp_mul([[[]]], [[[ZZ(1)]]], 2, ZZ) == [[[]]]
assert dmp_mul([[[ZZ(2)]]], [[[ZZ(1)]]], 2, ZZ) == [[[ZZ(2)]]]
assert dmp_mul([[[ZZ(1)]]], [[[ZZ(2)]]], 2, ZZ) == [[[ZZ(2)]]]
assert dmp_mul([[[]]], [[[]]], 2, QQ) == [[[]]]
assert dmp_mul([[[QQ(1, 2)]]], [[[]]], 2, QQ) == [[[]]]
assert dmp_mul([[[]]], [[[QQ(1, 2)]]], 2, QQ) == [[[]]]
assert dmp_mul([[[QQ(2, 7)]]], [[[QQ(1, 3)]]], 2, QQ) == [[[QQ(2, 21)]]]
assert dmp_mul([[[QQ(1, 7)]]], [[[QQ(2, 3)]]], 2, QQ) == [[[QQ(2, 21)]]]
K = FF(6)
assert dmp_mul([[K(2)], [K(1)]], [[K(3)], [K(4)]], 1, K) == [[K(5)],
[K(4)]]
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 2 * A == DomainMatrix([[ZZ(2), ZZ(4)], [ZZ(6), ZZ(8)]], (2, 2), ZZ)
assert A * DomainScalar(ZZ(0), ZZ) == DomainMatrix({}, (2, 2), ZZ)
assert A * DomainScalar(ZZ(1), ZZ) == A
raises(TypeError, lambda: A * 1.5)
def test_DomainMatrix_getitem_sympy():
dM = DomainMatrix({2: {2: ZZ(2)}, 4: {4: ZZ(1)}}, (5, 5), ZZ)
val1 = dM.getitem_sympy(0, 0)
assert val1 is S.Zero
val2 = dM.getitem_sympy(2, 2)
assert val2 == 2 and isinstance(val2, Integer)
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_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_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.zeros((2, 2), ZZ)
x = ZZ(0)
assert A * x == x * A == A.mul(x).to_sparse() == 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_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_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_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_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_to_sympy():
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
assert A.to_sympy() == A.convert_to(EXRAW)
def test_DomainMatrix_eq():
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
assert A == A
B = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(1)]], (2, 2), ZZ)
assert A != B
C = [[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]]
assert A != C
def test_dup_add_term():
f = dup_normal([], ZZ)
assert dup_add_term(f, ZZ(0), 0, ZZ) == dup_normal([], ZZ)
assert dup_add_term(f, ZZ(1), 0, ZZ) == dup_normal([1], ZZ)
assert dup_add_term(f, ZZ(1), 1, ZZ) == dup_normal([1, 0], ZZ)
assert dup_add_term(f, ZZ(1), 2, ZZ) == dup_normal([1, 0, 0], ZZ)
f = dup_normal([1, 1, 1], ZZ)
assert dup_add_term(f, ZZ(1), 0, ZZ) == dup_normal([1, 1, 2], ZZ)
assert dup_add_term(f, ZZ(1), 1, ZZ) == dup_normal([1, 2, 1], ZZ)
assert dup_add_term(f, ZZ(1), 2, ZZ) == dup_normal([2, 1, 1], ZZ)
assert dup_add_term(f, ZZ(1), 3, ZZ) == dup_normal([1, 1, 1, 1], ZZ)
assert dup_add_term(f, ZZ(1), 4, ZZ) == dup_normal([1, 0, 1, 1, 1], ZZ)
assert dup_add_term(f, ZZ(1), 5, ZZ) == dup_normal([1, 0, 0, 1, 1, 1], ZZ)
assert dup_add_term(f, ZZ(1), 6, ZZ) == dup_normal([1, 0, 0, 0, 1, 1, 1],
ZZ)
assert dup_add_term(f, ZZ(-1), 2, ZZ) == dup_normal([1, 1], ZZ)
def test_dup_pow():
assert dup_pow([], 0, ZZ) == [ZZ(1)]
assert dup_pow([], 0, QQ) == [QQ(1)]
assert dup_pow([], 1, ZZ) == []
assert dup_pow([], 7, ZZ) == []
assert dup_pow([ZZ(1)], 0, ZZ) == [ZZ(1)]
assert dup_pow([ZZ(1)], 1, ZZ) == [ZZ(1)]
assert dup_pow([ZZ(1)], 7, ZZ) == [ZZ(1)]
assert dup_pow([ZZ(3)], 0, ZZ) == [ZZ(1)]
assert dup_pow([ZZ(3)], 1, ZZ) == [ZZ(3)]
assert dup_pow([ZZ(3)], 7, ZZ) == [ZZ(2187)]
assert dup_pow([QQ(1, 1)], 0, QQ) == [QQ(1, 1)]
assert dup_pow([QQ(1, 1)], 1, QQ) == [QQ(1, 1)]
assert dup_pow([QQ(1, 1)], 7, QQ) == [QQ(1, 1)]
assert dup_pow([QQ(3, 7)], 0, QQ) == [QQ(1, 1)]
assert dup_pow([QQ(3, 7)], 1, QQ) == [QQ(3, 7)]
assert dup_pow([QQ(3, 7)], 7, QQ) == [QQ(2187, 823543)]
f = dup_normal([2, 0, 0, 1, 7], ZZ)
assert dup_pow(f, 0, ZZ) == dup_normal([1], ZZ)
assert dup_pow(f, 1, ZZ) == dup_normal([2, 0, 0, 1, 7], ZZ)
assert dup_pow(f, 2, ZZ) == dup_normal([4, 0, 0, 4, 28, 0, 1, 14, 49], ZZ)
assert dup_pow(f, 3, ZZ) == dup_normal(
[8, 0, 0, 12, 84, 0, 6, 84, 294, 1, 21, 147, 343], 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_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_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_DomainMatrix_to_list():
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
assert A.to_list() == [[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]]
def test_DomainMatrix_mul_elementwise():
A = DomainMatrix([[ZZ(2), ZZ(2)], [ZZ(0), ZZ(0)]], (2, 2), ZZ)
B = DomainMatrix([[ZZ(4), ZZ(0)], [ZZ(3), ZZ(0)]], (2, 2), ZZ)
C = DomainMatrix([[ZZ(8), ZZ(0)], [ZZ(0), ZZ(0)]], (2, 2), ZZ)
assert A.mul_elementwise(B) == C
assert B.mul_elementwise(A) == C
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_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_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_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
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_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_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_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_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_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_dup_mul():
assert dup_mul([], [], ZZ) == []
assert dup_mul([], [ZZ(1)], ZZ) == []
assert dup_mul([ZZ(1)], [], ZZ) == []
assert dup_mul([ZZ(1)], [ZZ(1)], ZZ) == [ZZ(1)]
assert dup_mul([ZZ(5)], [ZZ(7)], ZZ) == [ZZ(35)]
assert dup_mul([], [], QQ) == []
assert dup_mul([], [QQ(1, 2)], QQ) == []
assert dup_mul([QQ(1, 2)], [], QQ) == []
assert dup_mul([QQ(1, 2)], [QQ(4, 7)], QQ) == [QQ(2, 7)]
assert dup_mul([QQ(5, 7)], [QQ(3, 7)], QQ) == [QQ(15, 49)]
f = dup_normal([3, 0, 0, 6, 1, 2], ZZ)
g = dup_normal([4, 0, 1, 0], ZZ)
h = dup_normal([12, 0, 3, 24, 4, 14, 1, 2, 0], ZZ)
assert dup_mul(f, g, ZZ) == h
assert dup_mul(g, f, ZZ) == h
f = dup_normal([2, 0, 0, 1, 7], ZZ)
h = dup_normal([4, 0, 0, 4, 28, 0, 1, 14, 49], ZZ)
assert dup_mul(f, f, ZZ) == h
K = FF(6)
assert dup_mul([K(2), K(1)], [K(3), K(4)], K) == [K(5), K(4)]
p1 = dup_normal([
79, -1, 78, -94, -10, 11, 32, -19, 78, 2, -89, 30, 73, 42, 85, 77, 83,
-30, -34, -2, 95, -81, 37, -49, -46, -58, -16, 37, 35, -11, -57, -15,
-31, 67, -20, 27, 76, 2, 70, 67, -65, 65, -26, -93, -44, -12, -92, 57,
-90, -57, -11, -67, -98, -69, 97, -41, 89, 33, 89, -50, 81, -31, 60,
-27, 43, 29, -77, 44, 21, -91, 32, -57, 33, 3, 53, -51, -38, -99, -84,
23, -50, 66, -100, 1, -75, -25, 27, -60, 98, -51, -87, 6, 8, 78, -28,
-95, -88, 12, -35, 26, -9, 16, -92, 55, -7, -86, 68, -39, -46, 84, 94,
45, 60, 92, 68, -75, -74, -19, 8, 75, 78, 91, 57, 34, 14, -3, -49, 65,
78, -18, 6, -29, -80, -98, 17, 13, 58, 21, 20, 9, 37, 7, -30, -53, -20,
34, 67, -42, 89, -22, 73, 43, -6, 5, 51, -8, -15, -52, -22, -58, -72,
-3, 43, -92, 82, 83, -2, -13, -23, -60, 16, -94, -8, -28, -95, -72, 63,
-90, 76, 6, -43, -100, -59, 76, 3, 3, 46, -85, 75, 62, -71, -76, 88,
97, -72, -1, 30, -64, 72, -48, 14, -78, 58, 63, -91, 24, -87, -27, -80,
-100, -44, 98, 70, 100, -29, -38, 11, 77, 100, 52, 86, 65, -5, -42,
-81, -38, -42, 43, -2, -70, -63, -52
], ZZ)
p2 = dup_normal([
65, -19, -47, 1, 90, 81, -15, -34, 25, -75, 9, -83, 50, -5, -44, 31, 1,
70, -7, 78, 74, 80, 85, 65, 21, 41, 66, 19, -40, 63, -21, -27, 32, 69,
83, 34, -35, 14, 81, 57, -75, 32, -67, -89, -100, -61, 46, 84, -78,
-29, -50, -94, -24, -32, -68, -16, 100, -7, -72, -89, 35, 82, 58, 81,
-92, 62, 5, -47, -39, -58, -72, -13, 84, 44, 55, -25, 48, -54, -31,
-56, -11, -50, -84, 10, 67, 17, 13, -14, 61, 76, -64, -44, -40, -96,
11, -11, -94, 2, 6, 27, -6, 68, -54, 66, -74, -14, -1, -24, -73, 96,
89, -11, -89, 56, -53, 72, -43, 96, 25, 63, -31, 29, 68, 83, 91, -93,
-19, -38, -40, 40, -12, -19, -79, 44, 100, -66, -29, -77, 62, 39, -8,
11, -97, 14, 87, 64, 21, -18, 13, 15, -59, -75, -99, -88, 57, 54, 56,
-67, 6, -63, -59, -14, 28, 87, -20, -39, 84, -91, -2, 49, -75, 11, -24,
-95, 36, 66, 5, 25, -72, -40, 86, 90, 37, -33, 57, -35, 29, -18, 4,
-79, 64, -17, -27, 21, 29, -5, -44, -87, -24, 52, 78, 11, -23, -53, 36,
42, 21, -68, 94, -91, -51, -21, 51, -76, 72, 31, 24, -48, -80, -9, 37,
-47, -6, -8, -63, -91, 79, -79, -100, 38, -20, 38, 100, 83, -90, 87,
63, -36, 82, -19, 18, -98, -38, 26, 98, -70, 79, 92, 12, 12, 70, 74,
36, 48, -13, 31, 31, -47, -71, -12, -64, 36, -42, 32, -86, 60, 83, 70,
55, 0, 1, 29, -35, 8, -82, 8, -73, -46, -50, 43, 48, -5, -86, -72, 44,
-90, 19, 19, 5, -20, 97, -13, -66, -5, 5, -69, 64, -30, 41, 51, 36, 13,
-99, -61, 94, -12, 74, 98, 68, 24, 46, -97, -87, -6, -27, 82, 62, -11,
-77, 86, 66, -47, -49, -50, 13, 18, 89, -89, 46, -80, 13, 98, -35, -36,
-25, 12, 20, 26, -52, 79, 27, 79, 100, 8, 62, -58, -28, 37
], ZZ)
res = dup_normal([
5135, -1566, 1376, -7466, 4579, 11710, 8001, -7183, -3737, -7439, 345,
-10084, 24522, -1201, 1070, -10245, 9582, 9264, 1903, 23312, 18953,
10037, -15268, -5450, 6442, -6243, -3777, 5110, 10936, -16649, -6022,
16255, 31300, 24818, 31922, 32760, 7854, 27080, 15766, 29596, 7139,
31945, -19810, 465, -38026, -3971, 9641, 465, -19375, 5524, -30112,
-11960, -12813, 13535, 30670, 5925, -43725, -14089, 11503, -22782,
6371, 43881, 37465, -33529, -33590, -39798, -37854, -18466, -7908,
-35825, -26020, -36923, -11332, -5699, 25166, -3147, 19885, 12962,
-20659, -1642, 27723, -56331, -24580, -11010, -20206, 20087, -23772,
-16038, 38580, 20901, -50731, 32037, -4299, 26508, 18038, -28357,
31846, -7405, -20172, -15894, 2096, 25110, -45786, 45918, -55333,
-31928, -49428, -29824, -58796, -24609, -15408, 69, -35415, -18439,
10123, -20360, -65949, 33356, -20333, 26476, -32073, 33621, 930, 28803,
-42791, 44716, 38164, 12302, -1739, 11421, 73385, -7613, 14297, 38155,
-414, 77587, 24338, -21415, 29367, 42639, 13901, -288, 51027, -11827,
91260, 43407, 88521, -15186, 70572, -12049, 5090, -12208, -56374,
15520, -623, -7742, 50825, 11199, -14894, 40892, 59591, -31356, -28696,
-57842, -87751, -33744, -28436, -28945, -40287, 37957, -35638, 33401,
-61534, 14870, 40292, 70366, -10803, 102290, -71719, -85251, 7902,
-22409, 75009, 99927, 35298, -1175, -762, -34744, -10587, -47574,
-62629, -19581, -43659, -54369, -32250, -39545, 15225, -24454, 11241,
-67308, -30148, 39929, 37639, 14383, -73475, -77636, -81048, -35992,
41601, -90143, 76937, -8112, 56588, 9124, -40094, -32340, 13253, 10898,
-51639, 36390, 12086, -1885, 100714, -28561, -23784, -18735, 18916,
16286, 10742, -87360, -13697, 10689, -19477, -29770, 5060, 20189,
-8297, 112407, 47071, 47743, 45519, -4109, 17468, -68831, 78325, -6481,
-21641, -19459, 30919, 96115, 8607, 53341, 32105, -16211, 23538, 57259,
-76272, -40583, 62093, 38511, -34255, -40665, -40604, -37606, -15274,
33156, -13885, 103636, 118678, -14101, -92682, -100791, 2634, 63791,
98266, 19286, -34590, -21067, -71130, 25380, -40839, -27614, -26060,
52358, -15537, 27138, -6749, 36269, -33306, 13207, -91084, -5540,
-57116, 69548, 44169, -57742, -41234, -103327, -62904, -8566, 41149,
-12866, 71188, 23980, 1838, 58230, 73950, 5594, 43113, -8159, -15925,
6911, 85598, -75016, -16214, -62726, -39016, 8618, -63882, -4299,
23182, 49959, 49342, -3238, -24913, -37138, 78361, 32451, 6337, -11438,
-36241, -37737, 8169, -3077, -24829, 57953, 53016, -31511, -91168,
12599, -41849, 41576, 55275, -62539, 47814, -62319, 12300, -32076,
-55137, -84881, -27546, 4312, -3433, -54382, 113288, -30157, 74469,
18219, 79880, -2124, 98911, 17655, -33499, -32861, 47242, -37393,
99765, 14831, -44483, 10800, -31617, -52710, 37406, 22105, 29704,
-20050, 13778, 43683, 36628, 8494, 60964, -22644, 31550, -17693, 33805,
-124879, -12302, 19343, 20400, -30937, -21574, -34037, -33380, 56539,
-24993, -75513, -1527, 53563, 65407, -101, 53577, 37991, 18717, -23795,
-8090, -47987, -94717, 41967, 5170, -14815, -94311, 17896, -17734,
-57718, -774, -38410, 24830, 29682, 76480, 58802, -46416, -20348,
-61353, -68225, -68306, 23822, -31598, 42972, 36327, 28968, -65638,
-21638, 24354, -8356, 26777, 52982, -11783, -44051, -26467, -44721,
-28435, -53265, -25574, -2669, 44155, 22946, -18454, -30718, -11252,
58420, 8711, 67447, 4425, 41749, 67543, 43162, 11793, -41907, 20477,
-13080, 6559, -6104, -13244, 42853, 42935, 29793, 36730, -28087, 28657,
17946, 7503, 7204, 21491, -27450, -24241, -98156, -18082, -42613,
-24928, 10775, -14842, -44127, 55910, 14777, 31151, -2194, 39206,
-2100, -4211, 11827, -8918, -19471, 72567, 36447, -65590, -34861,
-17147, -45303, 9025, -7333, -35473, 11101, 11638, 3441, 6626, -41800,
9416, 13679, 33508, 40502, -60542, 16358, 8392, -43242, -35864, -34127,
-48721, 35878, 30598, 28630, 20279, -19983, -14638, -24455, -1851,
-11344, 45150, 42051, 26034, -28889, -32382, -3527, -14532, 22564,
-22346, 477, 11706, 28338, -25972, -9185, -22867, -12522, 32120, -4424,
11339, -33913, -7184, 5101, -23552, -17115, -31401, -6104, 21906,
25708, 8406, 6317, -7525, 5014, 20750, 20179, 22724, 11692, 13297,
2493, -253, -16841, -17339, -6753, -4808, 2976, -10881, -10228, -13816,
-12686, 1385, 2316, 2190, -875, -1924
], ZZ)
assert dup_mul(p1, p2, ZZ) == res
p1 = dup_normal([
83, -61, -86, -24, 12, 43, -88, -9, 42, 55, -66, 74, 95, -25, -12, 68,
-99, 4, 45, 6, -15, -19, 78, 65, -55, 47, -13, 17, 86, 81, -58, -27,
50, -40, -24, 39, -41, -92, 75, 90, -1, 40, -15, -27, -35, 68, 70, -64,
-40, 78, -88, -58, -39, 69, 46, 12, 28, -94, -37, -50, -80, -96, -61,
25, 1, 71, 4, 12, 48, 4, 34, -47, -75, 5, 48, 82, 88, 23, 98, 35, 17,
-10, 48, -61, -95, 47, 65, -19, -66, -57, -6, -51, -42, -89, 66, -13,
18, 37, 90, -23, 72, 96, -53, 0, 40, -73, -52, -68, 32, -25, -53, 79,
-52, 18, 44, 73, -81, 31, -90, 70, 3, 36, 48, 76, -24, -44, 23, 98, -4,
73, 69, 88, -70, 14, -68, 94, -78, -15, -64, -97, -70, -35, 65, 88, 49,
-53, -7, 12, -45, -7, 59, -94, 99, -2, 67, -60, -71, 29, -62, -77, 1,
51, 17, 80, -20, -47, -19, 24, -9, 39, -23, 21, -84, 10, 84, 56, -17,
-21, -66, 85, 70, 46, -51, -22, -95, 78, -60, -96, -97, -45, 72, 35,
30, -61, -92, -93, -60, -61, 4, -4, -81, -73, 46, 53, -11, 26, 94, 45,
14, -78, 55, 84, -68, 98, 60, 23, 100, -63, 68, 96, -16, 3, 56, 21,
-58, 62, -67, 66, 85, 41, -79, -22, 97, -67, 82, 82, -96, -20, -7, 48,
-67, 48, -9, -39, 78
], ZZ)
p2 = dup_normal([
52, 88, 76, 66, 9, -64, 46, -20, -28, 69, 60, 96, -36, -92, -30, -11,
-35, 35, 55, 63, -92, -7, 25, -58, 74, 55, -6, 4, 47, -92, -65, 67,
-45, 74, -76, 59, -6, 69, 39, 24, -71, -7, 39, -45, 60, -68, 98, 97,
-79, 17, 4, 94, -64, 68, -100, -96, -2, 3, 22, 96, 54, -77, -86, 67, 6,
57, 37, 40, 89, -78, 64, -94, -45, -92, 57, 87, -26, 36, 19, 97, 25,
77, -87, 24, 43, -5, 35, 57, 83, 71, 35, 63, 61, 96, -22, 8, -1, 96,
43, 45, 94, -93, 36, 71, -41, -99, 85, -48, 59, 52, -17, 5, 87, -16,
-68, -54, 76, -18, 100, 91, -42, -70, -66, -88, -12, 1, 95, -82, 52,
43, -29, 3, 12, 72, -99, -43, -32, -93, -51, 16, -20, -12, -11, 5, 33,
-38, 93, -5, -74, 25, 74, -58, 93, 59, -63, -86, 63, -20, -4, -74, -73,
-95, 29, -28, 93, -91, -2, -38, -62, 77, -58, -85, -28, 95, 38, 19,
-69, 86, 94, 25, -2, -4, 47, 34, -59, 35, -48, 29, -63, -53, 34, 29,
66, 73, 6, 92, -84, 89, 15, 81, 93, 97, 51, -72, -78, 25, 60, 90, -45,
39, 67, -84, -62, 57, 26, -32, -56, -14, -83, 76, 5, -2, 99, -100, 28,
46, 94, -7, 53, -25, 16, -23, -36, 89, -78, -63, 31, 1, 84, -99, -52,
76, 48, 90, -76, 44, -19, 54, -36, -9, -73, -100, -69, 31, 42, 25, -39,
76, -26, -8, -14, 51, 3, 37, 45, 2, -54, 13, -34, -92, 17, -25, -65,
53, -63, 30, 4, -70, -67, 90, 52, 51, 18, -3, 31, -45, -9, 59, 63, -87,
22, -32, 29, -38, 21, 36, -82, 27, -11
], ZZ)
res = dup_normal([
4316, 4132, -3532, -7974, -11303, -10069, 5484, -3330, -5874, 7734,
4673, 11327, -9884, -8031, 17343, 21035, -10570, -9285, 15893, 3780,
-14083, 8819, 17592, 10159, 7174, -11587, 8598, -16479, 3602, 25596,
9781, 12163, 150, 18749, -21782, -12307, 27578, -2757, -12573, 12565,
6345, -18956, 19503, -15617, 1443, -16778, 36851, 23588, -28474, 5749,
40695, -7521, -53669, -2497, -18530, 6770, 57038, 3926, -6927, -15399,
1848, -64649, -27728, 3644, 49608, 15187, -8902, -9480, -7398, -40425,
4824, 23767, -7594, -6905, 33089, 18786, 12192, 24670, 31114, 35334,
-4501, -14676, 7107, -59018, -21352, 20777, 19661, 20653, 33754, -885,
-43758, 6269, 51897, -28719, -97488, -9527, 13746, 11644, 17644,
-21720, 23782, -10481, 47867, 20752, 33810, -1875, 39918, -7710,
-40840, 19808, -47075, 23066, 46616, 25201, 9287, 35436, -1602, 9645,
-11978, 13273, 15544, 33465, 20063, 44539, 11687, 27314, -6538, -37467,
14031, 32970, -27086, 41323, 29551, 65910, -39027, -37800, -22232,
8212, 46316, -28981, -55282, 50417, -44929, -44062, 73879, 37573,
-2596, -10877, -21893, -133218, -33707, -25753, -9531, 17530, 61126,
2748, -56235, 43874, -10872, -90459, -30387, 115267, -7264, -44452,
122626, 14839, -599, 10337, 57166, -67467, -54957, 63669, 1202, 18488,
52594, 7205, -97822, 612, 78069, -5403, -63562, 47236, 36873, -154827,
-26188, 82427, -39521, 5628, 7416, 5276, -53095, 47050, 26121, -42207,
79021, -13035, 2499, -66943, 29040, -72355, -23480, 23416, -12885,
-44225, -42688, -4224, 19858, 55299, 15735, 11465, 101876, -39169,
51786, 14723, 43280, -68697, 16410, 92295, 56767, 7183, 111850, 4550,
115451, -38443, -19642, -35058, 10230, 93829, 8925, 63047, 3146, 29250,
8530, 5255, -98117, -115517, -76817, -8724, 41044, 1312, -35974, 79333,
-28567, 7547, -10580, -24559, -16238, 10794, -3867, 24848, 57770,
-51536, -35040, 71033, 29853, 62029, -7125, -125585, -32169, -47907,
156811, -65176, -58006, -15757, -57861, 11963, 30225, -41901, -41681,
31310, 27982, 18613, 61760, 60746, -59096, 33499, 30097, -17997, 24032,
56442, -83042, 23747, -20931, -21978, -158752, -9883, -73598, -7987,
-7333, -125403, -116329, 30585, 53281, 51018, -29193, 88575, 8264,
-40147, -16289, 113088, 12810, -6508, 101552, -13037, 34440, -41840,
101643, 24263, 80532, 61748, 65574, 6423, -20672, 6591, -10834, -71716,
86919, -92626, 39161, 28490, 81319, 46676, 106720, 43530, 26998, 57456,
-8862, 60989, 13982, 3119, -2224, 14743, 55415, -49093, -29303, 28999,
1789, 55953, -84043, -7780, -65013, 57129, -47251, 61484, 61994,
-78361, -82778, 22487, -26894, 9756, -74637, -15519, -4360, 30115,
42433, 35475, 15286, 69768, 21509, -20214, 78675, -21163, 13596, 11443,
-10698, -53621, -53867, -24155, 64500, -42784, -33077, -16500, 873,
-52788, 14546, -38011, 36974, -39849, -34029, -94311, 83068, -50437,
-26169, -46746, 59185, 42259, -101379, -12943, 30089, -59086, 36271,
22723, -30253, -52472, -70826, -23289, 3331, -31687, 14183, -857,
-28627, 35246, -51284, 5636, -6933, 66539, 36654, 50927, 24783, 3457,
33276, 45281, 45650, -4938, -9968, -22590, 47995, 69229, 5214, -58365,
-17907, -14651, 18668, 18009, 12649, -11851, -13387, 20339, 52472,
-1087, -21458, -68647, 52295, 15849, 40608, 15323, 25164, -29368,
10352, -7055, 7159, 21695, -5373, -54849, 101103, -24963, -10511,
33227, 7659, 41042, -69588, 26718, -20515, 6441, 38135, -63, 24088,
-35364, -12785, -18709, 47843, 48533, -48575, 17251, -19394, 32878,
-9010, -9050, 504, -12407, 28076, -3429, 25324, -4210, -26119, 752,
-29203, 28251, -11324, -32140, -3366, -25135, 18702, -31588, -7047,
-24267, 49987, -14975, -33169, 37744, -7720, -9035, 16964, -2807, -421,
14114, -17097, -13662, 40628, -12139, -9427, 5369, 17551, -13232,
-16211, 9804, -7422, 2677, 28635, -8280, -4906, 2908, -22558, 5604,
12459, 8756, -3980, -4745, -18525, 7913, 5970, -16457, 20230, -6247,
-13812, 2505, 11899, 1409, -15094, 22540, -18863, 137, 11123, -4516,
2290, -8594, 12150, -10380, 3005, 5235, -7350, 2535, -858
], ZZ)
assert dup_mul(p1, p2, ZZ) == res
