def test_DDM_str():
sdm = SDM({0: {0: ZZ(1)}, 1: {1: ZZ(1)}}, (2, 2), ZZ)
assert str(sdm) == '{0: {0: 1}, 1: {1: 1}}'
if HAS_GMPY: # pragma: no cover
assert repr(sdm) == 'SDM({0: {0: mpz(1)}, 1: {1: mpz(1)}}, (2, 2), ZZ)'
else: # pragma: no cover
assert repr(sdm) == 'SDM({0: {0: 1}, 1: {1: 1}}, (2, 2), ZZ)'
def test_SDM():
A = SDM({0: {0: ZZ(1)}}, (2, 2), ZZ)
assert A.domain == ZZ
assert A.shape == (2, 2)
assert dict(A) == {0: {0: ZZ(1)}}
raises(DDMBadInputError, lambda: SDM({5: {1: ZZ(0)}}, (2, 2), ZZ))
raises(DDMBadInputError, lambda: SDM({0: {5: ZZ(0)}}, (2, 2), ZZ))
def test_SDM_mul():
A = SDM({0: {0: ZZ(2)}}, (2, 2), ZZ)
B = SDM({0: {0: ZZ(4)}}, (2, 2), ZZ)
assert A * ZZ(2) == B
assert ZZ(2) * A == B
raises(TypeError, lambda: A * QQ(1, 2))
raises(TypeError, lambda: QQ(1, 2) * A)
def test_SDM_to_list():
A = SDM({0: {1: ZZ(1)}}, (2, 2), ZZ)
assert A.to_list() == [[ZZ(0), ZZ(1)], [ZZ(0), ZZ(0)]]
A = SDM({}, (0, 2), ZZ)
assert A.to_list() == []
A = SDM({}, (2, 0), ZZ)
assert A.to_list() == [[], []]
def test_SDM_convert_to():
A = SDM({0: {1: ZZ(1)}, 1: {0: ZZ(2), 1: ZZ(3)}}, (2, 2), ZZ)
B = SDM({0: {1: QQ(1)}, 1: {0: QQ(2), 1: QQ(3)}}, (2, 2), QQ)
C = A.convert_to(QQ)
assert C == B
assert C.domain == QQ
D = A.convert_to(ZZ)
assert D == A
assert D.domain == ZZ
def test_SDM_sub():
A = SDM({0: {1: ZZ(1)}, 1: {0: ZZ(2), 1: ZZ(3)}}, (2, 2), ZZ)
B = SDM({0: {0: ZZ(1)}, 1: {0: ZZ(-2), 1: ZZ(3)}}, (2, 2), ZZ)
C = SDM({0: {0: ZZ(-1), 1: ZZ(1)}, 1: {0: ZZ(4)}}, (2, 2), ZZ)
assert A.sub(B) == A - B == C
raises(TypeError, lambda: A - [])
def test_QuotientRing():
I = QQ.old_poly_ring(x).ideal(x**2 + 1)
R = QQ.old_poly_ring(x) / I
assert R == QQ.old_poly_ring(x) / [x**2 + 1]
assert R == QQ.old_poly_ring(x) / QQ.old_poly_ring(x).ideal(x**2 + 1)
assert R != QQ.old_poly_ring(x)
assert R.convert(1) / x == -x + I
assert -1 + I == x**2 + I
assert R.convert(ZZ(1), ZZ) == 1 + I
assert R.convert(R.convert(x), R) == R.convert(x)
X = R.convert(x)
Y = QQ.old_poly_ring(x).convert(x)
assert -1 + I == X**2 + I
assert -1 + I == Y**2 + I
assert R.to_sympy(X) == x
raises(ValueError,
lambda: QQ.old_poly_ring(x) / QQ.old_poly_ring(x, y).ideal(x))
R = QQ.old_poly_ring(x, order="ilex")
I = R.ideal(x)
assert R.convert(1) + I == (R / I).convert(1)
def test_SDM_getitem():
A = SDM({0: {1: ZZ(1)}}, (2, 2), ZZ)
assert A.getitem(0, 0) == ZZ.zero
assert A.getitem(0, 1) == ZZ.one
assert A.getitem(1, 0) == ZZ.zero
assert A.getitem(-2, -2) == ZZ.zero
assert A.getitem(-2, -1) == ZZ.one
assert A.getitem(-1, -2) == ZZ.zero
raises(IndexError, lambda: A.getitem(2, 0))
raises(IndexError, lambda: A.getitem(0, 2))
def test_pickling_polys_polyclasses():
from sympy.polys.polyclasses import DMP, DMF, ANP
for c in (DMP, DMP([[ZZ(1)], [ZZ(2)], [ZZ(3)]], ZZ)):
check(c)
for c in (DMF, DMF(([ZZ(1), ZZ(2)], [ZZ(1), ZZ(3)]), ZZ)):
check(c)
for c in (ANP, ANP([QQ(1), QQ(2)], [QQ(1), QQ(2), QQ(3)], QQ)):
check(c)
def test_SDM_vstack():
A = SDM({0: {1: ZZ(1)}}, (2, 2), ZZ)
B = SDM({1: {1: ZZ(1)}}, (2, 2), ZZ)
AA = SDM({0: {1: ZZ(1)}, 2: {1: ZZ(1)}}, (4, 2), ZZ)
AB = SDM({0: {1: ZZ(1)}, 3: {1: ZZ(1)}}, (4, 2), ZZ)
assert SDM.vstack(A) == A
assert SDM.vstack(A, A) == AA
assert SDM.vstack(A, B) == AB
def test_SDM_hstack():
A = SDM({0: {1: ZZ(1)}}, (2, 2), ZZ)
B = SDM({1: {1: ZZ(1)}}, (2, 2), ZZ)
AA = SDM({0: {1: ZZ(1), 3: ZZ(1)}}, (2, 4), ZZ)
AB = SDM({0: {1: ZZ(1)}, 1: {3: ZZ(1)}}, (2, 4), ZZ)
assert SDM.hstack(A) == A
assert SDM.hstack(A, A) == AA
assert SDM.hstack(A, B) == AB
def test_add():
a = [[ZZ(3), ZZ(7), ZZ(4)], [ZZ(2), ZZ(4), ZZ(5)], [ZZ(6), ZZ(2), ZZ(3)]]
b = [[ZZ(5), ZZ(4), ZZ(9)], [ZZ(3), ZZ(7), ZZ(1)],
[ZZ(12), ZZ(13), ZZ(14)]]
c = [[ZZ(12)], [ZZ(17)], [ZZ(21)]]
d = [[ZZ(3)], [ZZ(4)], [ZZ(5)]]
e = [[ZZ(12), ZZ(78)], [ZZ(56), ZZ(79)]]
f = [[ZZ.zero, ZZ.zero], [ZZ.zero, ZZ.zero]]
assert add(a, b, ZZ) == [[ZZ(8), ZZ(11), ZZ(13)], [ZZ(5),
ZZ(11),
ZZ(6)],
[ZZ(18), ZZ(15), ZZ(17)]]
assert add(c, d, ZZ) == [[ZZ(15)], [ZZ(21)], [ZZ(26)]]
assert add(e, f, ZZ) == e
def test_SDM_matmul():
A = SDM({0: {0: ZZ(2)}}, (2, 2), ZZ)
B = SDM({0: {0: ZZ(4)}}, (2, 2), ZZ)
assert A.matmul(A) == B
C = SDM({0: {0: ZZ(2)}}, (2, 2), QQ)
raises(DDMDomainError, lambda: A.matmul(C))
A = SDM({0: {0: ZZ(1), 1: ZZ(2)}, 1: {0: ZZ(3), 1: ZZ(4)}}, (2, 2), ZZ)
B = SDM({0: {0: ZZ(7), 1: ZZ(10)}, 1: {0: ZZ(15), 1: ZZ(22)}}, (2, 2), ZZ)
assert A.matmul(A) == B
A22 = SDM({0: {0: ZZ(4)}}, (2, 2), ZZ)
A32 = SDM({0: {0: ZZ(2)}}, (3, 2), ZZ)
A23 = SDM({0: {0: ZZ(4)}}, (2, 3), ZZ)
A33 = SDM({0: {0: ZZ(8)}}, (3, 3), ZZ)
A22 = SDM({0: {0: ZZ(8)}}, (2, 2), ZZ)
assert A32.matmul(A23) == A33
assert A23.matmul(A32) == A22
# XXX: @ not supported by SDM...
#assert A32.matmul(A23) == A32 @ A23 == A33
#assert A23.matmul(A32) == A23 @ A32 == A22
#raises(DDMShapeError, lambda: A23 @ A22)
raises(DDMShapeError, lambda: A23.matmul(A22))
A = SDM({0: {0: ZZ(-1), 1: ZZ(1)}}, (1, 2), ZZ)
B = SDM({0: {0: ZZ(-1)}, 1: {0: ZZ(-1)}}, (2, 1), ZZ)
assert A.matmul(B) == SDM({}, (1, 1), ZZ)
def test_SDM_transpose():
A = SDM({0: {0: ZZ(1), 1: ZZ(2)}, 1: {0: ZZ(3), 1: ZZ(4)}}, (2, 2), ZZ)
B = SDM({0: {0: ZZ(1), 1: ZZ(3)}, 1: {0: ZZ(2), 1: ZZ(4)}}, (2, 2), ZZ)
assert A.transpose() == B
A = SDM({0: {1: ZZ(2)}}, (2, 2), ZZ)
B = SDM({1: {0: ZZ(2)}}, (2, 2), ZZ)
assert A.transpose() == B
A = SDM({0: {1: ZZ(2)}}, (1, 2), ZZ)
B = SDM({1: {0: ZZ(2)}}, (2, 1), ZZ)
assert A.transpose() == B
def test_SDM_neg():
A = SDM({0: {1: ZZ(1)}, 1: {0: ZZ(2), 1: ZZ(3)}}, (2, 2), ZZ)
B = SDM({0: {1: ZZ(-1)}, 1: {0: ZZ(-2), 1: ZZ(-3)}}, (2, 2), ZZ)
assert A.neg() == B
def test_trace():
a = [[ZZ(3), ZZ(7), ZZ(4)], [ZZ(2), ZZ(4), ZZ(5)], [ZZ(6), ZZ(2), ZZ(3)]]
b = eye(2, ZZ)
assert trace(a, ZZ) == ZZ(10)
assert trace(b, ZZ) == ZZ(2)
def test_mulmatscaler():
a = eye(3, ZZ)
b = [[ZZ(3), ZZ(7), ZZ(4)], [ZZ(2), ZZ(4), ZZ(5)], [ZZ(6), ZZ(2), ZZ(3)]]
assert mulmatscaler(a, ZZ(4), ZZ) == [[ZZ(4), ZZ(0), ZZ(0)],
[ZZ(0), ZZ(4), ZZ(0)],
[ZZ(0), ZZ(0), ZZ(4)]]
assert mulmatscaler(b, ZZ(1), ZZ) == [[ZZ(3), ZZ(7), ZZ(4)],
[ZZ(2), ZZ(4), ZZ(5)],
[ZZ(6), ZZ(2), ZZ(3)]]
def test_SDM_copy():
A = SDM({0: {0: ZZ(1)}}, (2, 2), ZZ)
B = A.copy()
assert A == B
A[0][0] = ZZ(2)
assert A != B
def test_SDM_matmul():
A = SDM({0: {0: ZZ(2)}}, (2, 2), ZZ)
B = SDM({0: {0: ZZ(4)}}, (2, 2), ZZ)
assert A.matmul(A) == B
C = SDM({0: {0: ZZ(2)}}, (2, 2), QQ)
raises(DDMDomainError, lambda: A.matmul(C))
A = SDM({0: {0: ZZ(1), 1: ZZ(2)}, 1: {0: ZZ(3), 1: ZZ(4)}}, (2, 2), ZZ)
B = SDM({0: {0: ZZ(7), 1: ZZ(10)}, 1: {0: ZZ(15), 1: ZZ(22)}}, (2, 2), ZZ)
assert A.matmul(A) == B
def test_SDM_new():
A = SDM({0: {0: ZZ(1)}}, (2, 2), ZZ)
B = A.new({}, (2, 2), ZZ)
assert B == SDM({}, (2, 2), ZZ)
def test_SDM_charpoly():
A = SDM({0: {0: ZZ(1), 1: ZZ(2)}, 1: {0: ZZ(3), 1: ZZ(4)}}, (2, 2), ZZ)
assert A.charpoly() == [ZZ(1), ZZ(-5), ZZ(-2)]
def test_SDM_add():
A = SDM({0: {1: ZZ(1)}, 1: {0: ZZ(2), 1: ZZ(3)}}, (2, 2), ZZ)
B = SDM({0: {0: ZZ(1)}, 1: {0: ZZ(-2), 1: ZZ(3)}}, (2, 2), ZZ)
C = SDM({0: {0: ZZ(1), 1: ZZ(1)}, 1: {1: ZZ(6)}}, (2, 2), ZZ)
assert A.add(B) == C
A = SDM({0: {1: ZZ(1)}}, (2, 2), ZZ)
B = SDM({0: {0: ZZ(1)}, 1: {0: ZZ(-2), 1: ZZ(3)}}, (2, 2), ZZ)
C = SDM({0: {0: ZZ(1), 1: ZZ(1)}, 1: {0: ZZ(-2), 1: ZZ(3)}}, (2, 2), ZZ)
assert A.add(B) == C
assert B.add(A) == C
def test_sub():
a = [[ZZ(3), ZZ(7), ZZ(4)], [ZZ(2), ZZ(4), ZZ(5)], [ZZ(6), ZZ(2), ZZ(3)]]
b = [[ZZ(5), ZZ(4), ZZ(9)], [ZZ(3), ZZ(7), ZZ(1)],
[ZZ(12), ZZ(13), ZZ(14)]]
c = [[ZZ(12)], [ZZ(17)], [ZZ(21)]]
d = [[ZZ(3)], [ZZ(4)], [ZZ(5)]]
e = [[ZZ(12), ZZ(78)], [ZZ(56), ZZ(79)]]
f = [[ZZ.zero, ZZ.zero], [ZZ.zero, ZZ.zero]]
assert sub(a, b, ZZ) == [[ZZ(-2), ZZ(3), ZZ(-5)], [ZZ(-1),
ZZ(-3),
ZZ(4)],
[ZZ(-6), ZZ(-11), ZZ(-11)]]
assert sub(c, d, ZZ) == [[ZZ(9)], [ZZ(13)], [ZZ(16)]]
assert sub(e, f, ZZ) == e
def test_SDM_from_ddm():
A = DDM([[ZZ(1), ZZ(0)], [ZZ(1), ZZ(0)]], (2, 2), ZZ)
B = SDM.from_ddm(A)
assert B.domain == ZZ
assert B.shape == (2, 2)
assert dict(B) == {0: {0: ZZ(1)}, 1: {0: ZZ(1)}}
def test_mulmatmat():
a = [[ZZ(3), ZZ(4)], [ZZ(5), ZZ(6)]]
b = [[ZZ(1), ZZ(2)], [ZZ(7), ZZ(8)]]
c = eye(2, ZZ)
d = [[ZZ(6)], [ZZ(7)]]
assert mulmatmat(a, b, ZZ) == [[ZZ(31), ZZ(38)], [ZZ(47), ZZ(58)]]
assert mulmatmat(b, d, ZZ) == [[ZZ(20)], [ZZ(98)]]
def test_SDM_to_ddm():
A = SDM({0: {1: ZZ(1)}}, (2, 2), ZZ)
B = DDM([[ZZ(0), ZZ(1)], [ZZ(0), ZZ(0)]], (2, 2), ZZ)
assert A.to_ddm() == B
def test_transpose():
a = [[ZZ(3), ZZ(7), ZZ(4)], [ZZ(2), ZZ(4), ZZ(5)], [ZZ(6), ZZ(2), ZZ(3)]]
b = eye(4, ZZ)
assert transpose(a, ZZ) == ([[ZZ(3), ZZ(2), ZZ(6)], [ZZ(7), ZZ(4), ZZ(2)], [ZZ(4), ZZ(5), ZZ(3)]])
assert transpose(b, ZZ) == b
def test_SDM_eye():
A = SDM.eye(2, ZZ)
assert A.domain == ZZ
assert A.shape == (2, 2)
assert dict(A) == {0: {0: ZZ(1)}, 1: {1: ZZ(1)}}
def test_SDM_from_list():
A = SDM.from_list([[ZZ(0), ZZ(1)], [ZZ(1), ZZ(0)]], (2, 2), ZZ)
assert A == SDM({0: {1: ZZ(1)}, 1: {0: ZZ(1)}}, (2, 2), ZZ)
raises(DDMBadInputError,
lambda: SDM.from_list([[ZZ(0)], [ZZ(0), ZZ(1)]], (2, 2), ZZ))
raises(DDMBadInputError, lambda: SDM.from_list([[ZZ(0), ZZ(1)]],
(2, 2), ZZ))
def test_SDM_sub():
A = SDM({0: {1: ZZ(1)}, 1: {0: ZZ(2), 1: ZZ(3)}}, (2, 2), ZZ)
B = SDM({0: {0: ZZ(1)}, 1: {0: ZZ(-2), 1: ZZ(3)}}, (2, 2), ZZ)
C = SDM({0: {0: ZZ(-1), 1: ZZ(1)}, 1: {0: ZZ(4)}}, (2, 2), ZZ)
assert A.sub(B) == C
