def test_Domain_get_ring():
assert ZZ.has_assoc_Ring is True
assert QQ.has_assoc_Ring is True
assert ZZ[x].has_assoc_Ring is True
assert QQ[x].has_assoc_Ring is True
assert ZZ[x, y].has_assoc_Ring is True
assert QQ[x, y].has_assoc_Ring is True
assert ZZ.frac_field(x).has_assoc_Ring is True
assert QQ.frac_field(x).has_assoc_Ring is True
assert ZZ.frac_field(x, y).has_assoc_Ring is True
assert QQ.frac_field(x, y).has_assoc_Ring is True
assert EX.has_assoc_Ring is False
assert RR.has_assoc_Ring is False
assert ALG.has_assoc_Ring is False
assert ZZ.get_ring() == ZZ
assert QQ.get_ring() == ZZ
assert ZZ[x].get_ring() == ZZ[x]
assert QQ[x].get_ring() == QQ[x]
assert ZZ[x, y].get_ring() == ZZ[x, y]
assert QQ[x, y].get_ring() == QQ[x, y]
assert ZZ.frac_field(x).get_ring() == ZZ[x]
assert QQ.frac_field(x).get_ring() == QQ[x]
assert ZZ.frac_field(x, y).get_ring() == ZZ[x, y]
assert QQ.frac_field(x, y).get_ring() == QQ[x, y]
assert EX.get_ring() == EX
pytest.raises(DomainError, lambda: RR.get_ring())
pytest.raises(DomainError, lambda: ALG.get_ring())
def test_Domain_preprocess():
assert Domain.preprocess(ZZ) == ZZ
assert Domain.preprocess(QQ) == QQ
assert Domain.preprocess(EX) == EX
assert Domain.preprocess(FF(2)) == FF(2)
assert Domain.preprocess(ZZ[x, y]) == ZZ[x, y]
assert Domain.preprocess('Z') == ZZ
assert Domain.preprocess('Q') == QQ
assert Domain.preprocess('ZZ') == ZZ
assert Domain.preprocess('QQ') == QQ
assert Domain.preprocess('EX') == EX
assert Domain.preprocess('FF(23)') == FF(23)
assert Domain.preprocess('GF(23)') == GF(23)
pytest.raises(OptionError, lambda: Domain.preprocess('Z[]'))
assert Domain.preprocess('Z[x]') == ZZ[x]
assert Domain.preprocess('Q[x]') == QQ[x]
assert Domain.preprocess('ZZ[x]') == ZZ[x]
assert Domain.preprocess('QQ[x]') == QQ[x]
assert Domain.preprocess('Z[x,y]') == ZZ[x, y]
assert Domain.preprocess('Q[x,y]') == QQ[x, y]
assert Domain.preprocess('ZZ[x,y]') == ZZ[x, y]
assert Domain.preprocess('QQ[x,y]') == QQ[x, y]
pytest.raises(OptionError, lambda: Domain.preprocess('Z()'))
assert Domain.preprocess('Z(x)') == ZZ.frac_field(x)
assert Domain.preprocess('Q(x)') == QQ.frac_field(x)
assert Domain.preprocess('ZZ(x)') == ZZ.frac_field(x)
assert Domain.preprocess('QQ(x)') == QQ.frac_field(x)
assert Domain.preprocess('Z(x,y)') == ZZ.frac_field(x, y)
assert Domain.preprocess('Q(x,y)') == QQ.frac_field(x, y)
assert Domain.preprocess('ZZ(x,y)') == ZZ.frac_field(x, y)
assert Domain.preprocess('QQ(x,y)') == QQ.frac_field(x, y)
assert Domain.preprocess('Q<I>') == QQ.algebraic_field(I)
assert Domain.preprocess('QQ<I>') == QQ.algebraic_field(I)
assert Domain.preprocess('Q<sqrt(2), I>') == QQ.algebraic_field(sqrt(2), I)
assert Domain.preprocess('QQ<sqrt(2), I>') == QQ.algebraic_field(
sqrt(2), I)
pytest.raises(OptionError, lambda: Domain.preprocess('abc'))
def test_Domain___eq__():
assert (ZZ[x, y] == ZZ[x, y]) is True
assert (QQ[x, y] == QQ[x, y]) is True
assert (ZZ[x, y] == QQ[x, y]) is False
assert (QQ[x, y] == ZZ[x, y]) is False
assert (ZZ.frac_field(x, y) == ZZ.frac_field(x, y)) is True
assert (QQ.frac_field(x, y) == QQ.frac_field(x, y)) is True
assert (ZZ.frac_field(x, y) == QQ.frac_field(x, y)) is False
assert (QQ.frac_field(x, y) == ZZ.frac_field(x, y)) is False
def test_Domain_get_exact():
assert EX.get_exact() == EX
assert ZZ.get_exact() == ZZ
assert QQ.get_exact() == QQ
assert RR.get_exact() == QQ
assert ALG.get_exact() == ALG
assert ZZ[x].get_exact() == ZZ[x]
assert QQ[x].get_exact() == QQ[x]
assert ZZ[x, y].get_exact() == ZZ[x, y]
assert QQ[x, y].get_exact() == QQ[x, y]
assert ZZ.frac_field(x).get_exact() == ZZ.frac_field(x)
assert QQ.frac_field(x).get_exact() == QQ.frac_field(x)
assert ZZ.frac_field(x, y).get_exact() == ZZ.frac_field(x, y)
assert QQ.frac_field(x, y).get_exact() == QQ.frac_field(x, y)
def test_Domain_get_field():
assert EX.has_assoc_Field is True
assert ZZ.has_assoc_Field is True
assert QQ.has_assoc_Field is True
assert RR.has_assoc_Field is True
assert ALG.has_assoc_Field is True
assert ZZ[x].has_assoc_Field is True
assert QQ[x].has_assoc_Field is True
assert ZZ[x, y].has_assoc_Field is True
assert QQ[x, y].has_assoc_Field is True
assert EX.get_field() == EX
assert ZZ.get_field() == QQ
assert QQ.get_field() == QQ
assert RR.get_field() == RR
assert ALG.get_field() == ALG
assert ZZ[x].get_field() == ZZ.frac_field(x)
assert QQ[x].get_field() == QQ.frac_field(x)
assert ZZ[x, y].get_field() == ZZ.frac_field(x, y)
assert QQ[x, y].get_field() == QQ.frac_field(x, y)
def test_localring():
Qxy = QQ.frac_field(x, y)
R = QQ.poly_ring(x, y, order="ilex")
X = R.convert(x)
Y = R.convert(y)
assert x in R
assert 1/x not in R
assert Y in R
assert X.ring == R.ring
assert X + Y == R.convert(x + y)
assert X - Y == R.convert(x - y)
assert X + 1 == R.convert(x + 1)
assert X**2 / X == X
assert R.from_PolynomialRing(ZZ.poly_ring(x, y).convert(x), ZZ.poly_ring(x, y)) == X
assert R.from_FractionField(Qxy.convert(x), Qxy) == X
def test_globalring():
Qxy = QQ.frac_field(x, y)
R = QQ.poly_ring(x, y)
X = R.convert(x)
Y = R.convert(y)
assert x in R
assert 1/x not in R
assert 1/(1 + x) not in R
assert Y in R
assert X.ring == R.ring
assert X * (Y**2 + 1) == R.convert(x * (y**2 + 1))
assert X * Y == R.convert(x * y)
assert X + Y == R.convert(x + y)
assert X - Y == R.convert(x - y)
assert X + 1 == R.convert(x + 1)
assert X**2 / X == X
assert R.from_PolynomialRing(ZZ.poly_ring(x, y).convert(x), ZZ.poly_ring(x, y)) == X
assert R.from_FractionField(Qxy.convert(x), Qxy) == X
def test___eq__():
assert not QQ[x] == ZZ[x]
assert not QQ.frac_field(x) == ZZ.frac_field(x)
def test_Domain_unify():
F3 = GF(3)
assert unify(F3, F3) == F3
assert unify(F3, ZZ) == ZZ
assert unify(F3, QQ) == QQ
assert unify(F3, ALG) == ALG
assert unify(F3, RR) == RR
assert unify(F3, CC) == CC
assert unify(F3, ZZ[x]) == ZZ[x]
assert unify(F3, ZZ.frac_field(x)) == ZZ.frac_field(x)
assert unify(F3, EX) == EX
assert unify(ZZ, F3) == ZZ
assert unify(ZZ, ZZ) == ZZ
assert unify(ZZ, QQ) == QQ
assert unify(ZZ, ALG) == ALG
assert unify(ZZ, RR) == RR
assert unify(ZZ, CC) == CC
assert unify(ZZ, ZZ[x]) == ZZ[x]
assert unify(ZZ, ZZ.frac_field(x)) == ZZ.frac_field(x)
assert unify(ZZ, EX) == EX
assert unify(QQ, F3) == QQ
assert unify(QQ, ZZ) == QQ
assert unify(QQ, QQ) == QQ
assert unify(QQ, ALG) == ALG
assert unify(QQ, RR) == RR
assert unify(QQ, CC) == CC
assert unify(QQ, ZZ[x]) == QQ[x]
assert unify(QQ, ZZ.frac_field(x)) == QQ.frac_field(x)
assert unify(QQ, EX) == EX
assert unify(RR, F3) == RR
assert unify(RR, ZZ) == RR
assert unify(RR, QQ) == RR
assert unify(RR, ALG) == RR
assert unify(RR, RR) == RR
assert unify(RR, CC) == CC
assert unify(RR, ZZ[x]) == RR[x]
assert unify(RR, ZZ.frac_field(x)) == RR.frac_field(x)
assert unify(RR, EX) == EX
assert unify(CC, F3) == CC
assert unify(CC, ZZ) == CC
assert unify(CC, QQ) == CC
assert unify(CC, ALG) == CC
assert unify(CC, RR) == CC
assert unify(CC, CC) == CC
assert unify(CC, ZZ[x]) == CC[x]
assert unify(CC, ZZ.frac_field(x)) == CC.frac_field(x)
assert unify(CC, EX) == EX
assert unify(ZZ[x], F3) == ZZ[x]
assert unify(ZZ[x], ZZ) == ZZ[x]
assert unify(ZZ[x], QQ) == QQ[x]
assert unify(ZZ[x], ALG) == ALG[x]
assert unify(ZZ[x], RR) == RR[x]
assert unify(ZZ[x], CC) == CC[x]
assert unify(ZZ[x], ZZ[x]) == ZZ[x]
assert unify(ZZ[x], ZZ.frac_field(x)) == ZZ.frac_field(x)
assert unify(ZZ[x], EX) == EX
assert unify(ZZ.frac_field(x), F3) == ZZ.frac_field(x)
assert unify(ZZ.frac_field(x), ZZ) == ZZ.frac_field(x)
assert unify(ZZ.frac_field(x), QQ) == QQ.frac_field(x)
assert unify(ZZ.frac_field(x), ALG) == ALG.frac_field(x)
assert unify(ZZ.frac_field(x), RR) == RR.frac_field(x)
assert unify(ZZ.frac_field(x), CC) == CC.frac_field(x)
assert unify(ZZ.frac_field(x), ZZ[x]) == ZZ.frac_field(x)
assert unify(ZZ.frac_field(x), ZZ.frac_field(x)) == ZZ.frac_field(x)
assert unify(ZZ.frac_field(x), EX) == EX
assert unify(EX, F3) == EX
assert unify(EX, ZZ) == EX
assert unify(EX, QQ) == EX
assert unify(EX, ALG) == EX
assert unify(EX, RR) == EX
assert unify(EX, CC) == EX
assert unify(EX, ZZ[x]) == EX
assert unify(EX, ZZ.frac_field(x)) == EX
assert unify(EX, EX) == EX
def test_Domain_unify_composite():
assert unify(ZZ.poly_ring(x), ZZ) == ZZ.poly_ring(x)
assert unify(ZZ.poly_ring(x), QQ) == QQ.poly_ring(x)
assert unify(QQ.poly_ring(x), ZZ) == QQ.poly_ring(x)
assert unify(QQ.poly_ring(x), QQ) == QQ.poly_ring(x)
assert unify(ZZ, ZZ.poly_ring(x)) == ZZ.poly_ring(x)
assert unify(QQ, ZZ.poly_ring(x)) == QQ.poly_ring(x)
assert unify(ZZ, QQ.poly_ring(x)) == QQ.poly_ring(x)
assert unify(QQ, QQ.poly_ring(x)) == QQ.poly_ring(x)
assert unify(ZZ.poly_ring(x, y), ZZ) == ZZ.poly_ring(x, y)
assert unify(ZZ.poly_ring(x, y), QQ) == QQ.poly_ring(x, y)
assert unify(QQ.poly_ring(x, y), ZZ) == QQ.poly_ring(x, y)
assert unify(QQ.poly_ring(x, y), QQ) == QQ.poly_ring(x, y)
assert unify(ZZ, ZZ.poly_ring(x, y)) == ZZ.poly_ring(x, y)
assert unify(QQ, ZZ.poly_ring(x, y)) == QQ.poly_ring(x, y)
assert unify(ZZ, QQ.poly_ring(x, y)) == QQ.poly_ring(x, y)
assert unify(QQ, QQ.poly_ring(x, y)) == QQ.poly_ring(x, y)
assert unify(ZZ.frac_field(x), ZZ) == ZZ.frac_field(x)
assert unify(ZZ.frac_field(x), QQ) == QQ.frac_field(x)
assert unify(QQ.frac_field(x), ZZ) == QQ.frac_field(x)
assert unify(QQ.frac_field(x), QQ) == QQ.frac_field(x)
assert unify(ZZ, ZZ.frac_field(x)) == ZZ.frac_field(x)
assert unify(QQ, ZZ.frac_field(x)) == QQ.frac_field(x)
assert unify(ZZ, QQ.frac_field(x)) == QQ.frac_field(x)
assert unify(QQ, QQ.frac_field(x)) == QQ.frac_field(x)
assert unify(ZZ.frac_field(x, y), ZZ) == ZZ.frac_field(x, y)
assert unify(ZZ.frac_field(x, y), QQ) == QQ.frac_field(x, y)
assert unify(QQ.frac_field(x, y), ZZ) == QQ.frac_field(x, y)
assert unify(QQ.frac_field(x, y), QQ) == QQ.frac_field(x, y)
assert unify(ZZ, ZZ.frac_field(x, y)) == ZZ.frac_field(x, y)
assert unify(QQ, ZZ.frac_field(x, y)) == QQ.frac_field(x, y)
assert unify(ZZ, QQ.frac_field(x, y)) == QQ.frac_field(x, y)
assert unify(QQ, QQ.frac_field(x, y)) == QQ.frac_field(x, y)
assert unify(ZZ.poly_ring(x), ZZ.poly_ring(x)) == ZZ.poly_ring(x)
assert unify(ZZ.poly_ring(x), QQ.poly_ring(x)) == QQ.poly_ring(x)
assert unify(QQ.poly_ring(x), ZZ.poly_ring(x)) == QQ.poly_ring(x)
assert unify(QQ.poly_ring(x), QQ.poly_ring(x)) == QQ.poly_ring(x)
assert unify(ZZ.poly_ring(x, y), ZZ.poly_ring(x)) == ZZ.poly_ring(x, y)
assert unify(ZZ.poly_ring(x, y), QQ.poly_ring(x)) == QQ.poly_ring(x, y)
assert unify(QQ.poly_ring(x, y), ZZ.poly_ring(x)) == QQ.poly_ring(x, y)
assert unify(QQ.poly_ring(x, y), QQ.poly_ring(x)) == QQ.poly_ring(x, y)
assert unify(ZZ.poly_ring(x), ZZ.poly_ring(x, y)) == ZZ.poly_ring(x, y)
assert unify(ZZ.poly_ring(x), QQ.poly_ring(x, y)) == QQ.poly_ring(x, y)
assert unify(QQ.poly_ring(x), ZZ.poly_ring(x, y)) == QQ.poly_ring(x, y)
assert unify(QQ.poly_ring(x), QQ.poly_ring(x, y)) == QQ.poly_ring(x, y)
assert unify(ZZ.poly_ring(x, y), ZZ.poly_ring(x,
z)) == ZZ.poly_ring(x, y, z)
assert unify(ZZ.poly_ring(x, y), QQ.poly_ring(x,
z)) == QQ.poly_ring(x, y, z)
assert unify(QQ.poly_ring(x, y), ZZ.poly_ring(x,
z)) == QQ.poly_ring(x, y, z)
assert unify(QQ.poly_ring(x, y), QQ.poly_ring(x,
z)) == QQ.poly_ring(x, y, z)
assert unify(ZZ.frac_field(x), ZZ.frac_field(x)) == ZZ.frac_field(x)
assert unify(ZZ.frac_field(x), QQ.frac_field(x)) == QQ.frac_field(x)
assert unify(QQ.frac_field(x), ZZ.frac_field(x)) == QQ.frac_field(x)
assert unify(QQ.frac_field(x), QQ.frac_field(x)) == QQ.frac_field(x)
assert unify(ZZ.frac_field(x, y), ZZ.frac_field(x)) == ZZ.frac_field(x, y)
assert unify(ZZ.frac_field(x, y), QQ.frac_field(x)) == QQ.frac_field(x, y)
assert unify(QQ.frac_field(x, y), ZZ.frac_field(x)) == QQ.frac_field(x, y)
assert unify(QQ.frac_field(x, y), QQ.frac_field(x)) == QQ.frac_field(x, y)
assert unify(ZZ.frac_field(x), ZZ.frac_field(x, y)) == ZZ.frac_field(x, y)
assert unify(ZZ.frac_field(x), QQ.frac_field(x, y)) == QQ.frac_field(x, y)
assert unify(QQ.frac_field(x), ZZ.frac_field(x, y)) == QQ.frac_field(x, y)
assert unify(QQ.frac_field(x), QQ.frac_field(x, y)) == QQ.frac_field(x, y)
assert unify(ZZ.frac_field(x, y),
ZZ.frac_field(x, z)) == ZZ.frac_field(x, y, z)
assert unify(ZZ.frac_field(x, y),
QQ.frac_field(x, z)) == QQ.frac_field(x, y, z)
assert unify(QQ.frac_field(x, y),
ZZ.frac_field(x, z)) == QQ.frac_field(x, y, z)
assert unify(QQ.frac_field(x, y),
QQ.frac_field(x, z)) == QQ.frac_field(x, y, z)
assert unify(ZZ.poly_ring(x), ZZ.frac_field(x)) == ZZ.frac_field(x)
assert unify(ZZ.poly_ring(x), QQ.frac_field(x)) == ZZ.frac_field(x)
assert unify(QQ.poly_ring(x), ZZ.frac_field(x)) == ZZ.frac_field(x)
assert unify(QQ.poly_ring(x), QQ.frac_field(x)) == QQ.frac_field(x)
assert unify(ZZ.poly_ring(x, y), ZZ.frac_field(x)) == ZZ.frac_field(x, y)
assert unify(ZZ.poly_ring(x, y), QQ.frac_field(x)) == ZZ.frac_field(x, y)
assert unify(QQ.poly_ring(x, y), ZZ.frac_field(x)) == ZZ.frac_field(x, y)
assert unify(QQ.poly_ring(x, y), QQ.frac_field(x)) == QQ.frac_field(x, y)
assert unify(ZZ.poly_ring(x), ZZ.frac_field(x, y)) == ZZ.frac_field(x, y)
assert unify(ZZ.poly_ring(x), QQ.frac_field(x, y)) == ZZ.frac_field(x, y)
assert unify(QQ.poly_ring(x), ZZ.frac_field(x, y)) == ZZ.frac_field(x, y)
assert unify(QQ.poly_ring(x), QQ.frac_field(x, y)) == QQ.frac_field(x, y)
assert unify(ZZ.poly_ring(x, y),
ZZ.frac_field(x, z)) == ZZ.frac_field(x, y, z)
assert unify(ZZ.poly_ring(x, y),
QQ.frac_field(x, z)) == ZZ.frac_field(x, y, z)
assert unify(QQ.poly_ring(x, y),
ZZ.frac_field(x, z)) == ZZ.frac_field(x, y, z)
assert unify(QQ.poly_ring(x, y),
QQ.frac_field(x, z)) == QQ.frac_field(x, y, z)
assert unify(ZZ.frac_field(x), ZZ.poly_ring(x)) == ZZ.frac_field(x)
assert unify(ZZ.frac_field(x), QQ.poly_ring(x)) == ZZ.frac_field(x)
assert unify(QQ.frac_field(x), ZZ.poly_ring(x)) == ZZ.frac_field(x)
assert unify(QQ.frac_field(x), QQ.poly_ring(x)) == QQ.frac_field(x)
assert unify(ZZ.frac_field(x, y), ZZ.poly_ring(x)) == ZZ.frac_field(x, y)
assert unify(ZZ.frac_field(x, y), QQ.poly_ring(x)) == ZZ.frac_field(x, y)
assert unify(QQ.frac_field(x, y), ZZ.poly_ring(x)) == ZZ.frac_field(x, y)
assert unify(QQ.frac_field(x, y), QQ.poly_ring(x)) == QQ.frac_field(x, y)
assert unify(ZZ.frac_field(x), ZZ.poly_ring(x, y)) == ZZ.frac_field(x, y)
assert unify(ZZ.frac_field(x), QQ.poly_ring(x, y)) == ZZ.frac_field(x, y)
assert unify(QQ.frac_field(x), ZZ.poly_ring(x, y)) == ZZ.frac_field(x, y)
assert unify(QQ.frac_field(x), QQ.poly_ring(x, y)) == QQ.frac_field(x, y)
assert unify(ZZ.frac_field(x, y),
ZZ.poly_ring(x, z)) == ZZ.frac_field(x, y, z)
assert unify(ZZ.frac_field(x, y),
QQ.poly_ring(x, z)) == ZZ.frac_field(x, y, z)
assert unify(QQ.frac_field(x, y),
ZZ.poly_ring(x, z)) == ZZ.frac_field(x, y, z)
assert unify(QQ.frac_field(x, y),
QQ.poly_ring(x, z)) == QQ.frac_field(x, y, z)
def test_poly_frac():
pytest.raises(GeneratorsNeeded, lambda: QQ.poly_ring())
pytest.raises(GeneratorsNeeded, lambda: QQ.frac_field())
