def test_Algebra_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_Algebra_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_Algebra_get_field():
assert EX.has_assoc_Field == True
assert ZZ.has_assoc_Field == True
assert QQ.has_assoc_Field == True
assert ALG.has_assoc_Field == True
assert ZZ[x].has_assoc_Field == True
assert QQ[x].has_assoc_Field == True
assert ZZ[x, y].has_assoc_Field == True
assert QQ[x, y].has_assoc_Field == True
assert RR.has_assoc_Field == False
assert EX.get_field() == EX
assert ZZ.get_field() == QQ
assert QQ.get_field() == QQ
assert ALG.get_field() == ALG
assert ZZ[x].get_field() == ZZ.frac_field(x)
assert QQ[x].get_field() == ZZ.frac_field(x)
assert ZZ[x, y].get_field() == ZZ.frac_field(x, y)
assert QQ[x, y].get_field() == ZZ.frac_field(x, y)
raises(DomainError, "RR.get_field()")
def test_Algebra_get_field():
assert EX.has_assoc_Field == True
assert ZZ.has_assoc_Field == True
assert QQ.has_assoc_Field == True
assert ALG.has_assoc_Field == True
assert ZZ[x].has_assoc_Field == True
assert QQ[x].has_assoc_Field == True
assert ZZ[x,y].has_assoc_Field == True
assert QQ[x,y].has_assoc_Field == True
assert RR.has_assoc_Field == False
assert EX.get_field() == EX
assert ZZ.get_field() == QQ
assert QQ.get_field() == QQ
assert ALG.get_field() == ALG
assert ZZ[x].get_field() == ZZ.frac_field(x)
assert QQ[x].get_field() == ZZ.frac_field(x)
assert ZZ[x,y].get_field() == ZZ.frac_field(x,y)
assert QQ[x,y].get_field() == ZZ.frac_field(x,y)
raises(DomainError, "RR.get_field()")
def test_Algebra__unify():
assert ZZ.unify(ZZ) == ZZ
assert QQ.unify(QQ) == QQ
assert ZZ.unify(QQ) == QQ
assert QQ.unify(ZZ) == QQ
assert EX.unify(EX) == EX
assert ZZ.unify(EX) == EX
assert QQ.unify(EX) == EX
assert EX.unify(ZZ) == EX
assert EX.unify(QQ) == EX
assert ZZ.poly_ring('x').unify(EX) == EX
assert ZZ.frac_field('x').unify(EX) == EX
assert EX.unify(ZZ.poly_ring('x')) == EX
assert EX.unify(ZZ.frac_field('x')) == EX
assert ZZ.poly_ring('x', 'y').unify(EX) == EX
assert ZZ.frac_field('x', 'y').unify(EX) == EX
assert EX.unify(ZZ.poly_ring('x', 'y')) == EX
assert EX.unify(ZZ.frac_field('x', 'y')) == EX
assert QQ.poly_ring('x').unify(EX) == EX
assert QQ.frac_field('x').unify(EX) == EX
assert EX.unify(QQ.poly_ring('x')) == EX
assert EX.unify(QQ.frac_field('x')) == EX
assert QQ.poly_ring('x', 'y').unify(EX) == EX
assert QQ.frac_field('x', 'y').unify(EX) == EX
assert EX.unify(QQ.poly_ring('x', 'y')) == EX
assert EX.unify(QQ.frac_field('x', 'y')) == EX
assert ZZ.poly_ring('x').unify(ZZ) == ZZ.poly_ring('x')
assert ZZ.poly_ring('x').unify(QQ) == QQ.poly_ring('x')
assert QQ.poly_ring('x').unify(ZZ) == QQ.poly_ring('x')
assert QQ.poly_ring('x').unify(QQ) == QQ.poly_ring('x')
assert ZZ.unify(ZZ.poly_ring('x')) == ZZ.poly_ring('x')
assert QQ.unify(ZZ.poly_ring('x')) == QQ.poly_ring('x')
assert ZZ.unify(QQ.poly_ring('x')) == QQ.poly_ring('x')
assert QQ.unify(QQ.poly_ring('x')) == QQ.poly_ring('x')
assert ZZ.poly_ring('x', 'y').unify(ZZ) == ZZ.poly_ring('x', 'y')
assert ZZ.poly_ring('x', 'y').unify(QQ) == QQ.poly_ring('x', 'y')
assert QQ.poly_ring('x', 'y').unify(ZZ) == QQ.poly_ring('x', 'y')
assert QQ.poly_ring('x', 'y').unify(QQ) == QQ.poly_ring('x', 'y')
assert ZZ.unify(ZZ.poly_ring('x', 'y')) == ZZ.poly_ring('x', 'y')
assert QQ.unify(ZZ.poly_ring('x', 'y')) == QQ.poly_ring('x', 'y')
assert ZZ.unify(QQ.poly_ring('x', 'y')) == QQ.poly_ring('x', 'y')
assert QQ.unify(QQ.poly_ring('x', 'y')) == QQ.poly_ring('x', 'y')
assert ZZ.frac_field('x').unify(ZZ) == ZZ.frac_field('x')
assert ZZ.frac_field('x').unify(QQ) == EX # QQ.frac_field('x')
assert QQ.frac_field('x').unify(ZZ) == EX # QQ.frac_field('x')
assert QQ.frac_field('x').unify(QQ) == QQ.frac_field('x')
assert ZZ.unify(ZZ.frac_field('x')) == ZZ.frac_field('x')
assert QQ.unify(ZZ.frac_field('x')) == EX # QQ.frac_field('x')
assert ZZ.unify(QQ.frac_field('x')) == EX # QQ.frac_field('x')
assert QQ.unify(QQ.frac_field('x')) == QQ.frac_field('x')
assert ZZ.frac_field('x', 'y').unify(ZZ) == ZZ.frac_field('x', 'y')
assert ZZ.frac_field('x', 'y').unify(QQ) == EX # QQ.frac_field('x','y')
assert QQ.frac_field('x', 'y').unify(ZZ) == EX # QQ.frac_field('x','y')
assert QQ.frac_field('x', 'y').unify(QQ) == QQ.frac_field('x', 'y')
assert ZZ.unify(ZZ.frac_field('x', 'y')) == ZZ.frac_field('x', 'y')
assert QQ.unify(ZZ.frac_field('x', 'y')) == EX # QQ.frac_field('x','y')
assert ZZ.unify(QQ.frac_field('x', 'y')) == EX # QQ.frac_field('x','y')
assert QQ.unify(QQ.frac_field('x', 'y')) == QQ.frac_field('x', 'y')
assert ZZ.poly_ring('x').unify(ZZ.poly_ring('x')) == ZZ.poly_ring('x')
assert ZZ.poly_ring('x').unify(QQ.poly_ring('x')) == QQ.poly_ring('x')
assert QQ.poly_ring('x').unify(ZZ.poly_ring('x')) == QQ.poly_ring('x')
assert QQ.poly_ring('x').unify(QQ.poly_ring('x')) == QQ.poly_ring('x')
assert ZZ.poly_ring('x', 'y').unify(ZZ.poly_ring('x')) == ZZ.poly_ring(
'x', 'y')
assert ZZ.poly_ring('x', 'y').unify(QQ.poly_ring('x')) == QQ.poly_ring(
'x', 'y')
assert QQ.poly_ring('x', 'y').unify(ZZ.poly_ring('x')) == QQ.poly_ring(
'x', 'y')
assert QQ.poly_ring('x', 'y').unify(QQ.poly_ring('x')) == QQ.poly_ring(
'x', 'y')
assert ZZ.poly_ring('x').unify(ZZ.poly_ring('x', 'y')) == ZZ.poly_ring(
'x', 'y')
assert ZZ.poly_ring('x').unify(QQ.poly_ring('x', 'y')) == QQ.poly_ring(
'x', 'y')
assert QQ.poly_ring('x').unify(ZZ.poly_ring('x', 'y')) == QQ.poly_ring(
'x', 'y')
assert QQ.poly_ring('x').unify(QQ.poly_ring('x', 'y')) == QQ.poly_ring(
'x', 'y')
assert ZZ.poly_ring('x', 'y').unify(ZZ.poly_ring('x',
'z')) == ZZ.poly_ring(
'x', 'y', 'z')
assert ZZ.poly_ring('x', 'y').unify(QQ.poly_ring('x',
'z')) == QQ.poly_ring(
'x', 'y', 'z')
assert QQ.poly_ring('x', 'y').unify(ZZ.poly_ring('x',
'z')) == QQ.poly_ring(
'x', 'y', 'z')
assert QQ.poly_ring('x', 'y').unify(QQ.poly_ring('x',
'z')) == QQ.poly_ring(
'x', 'y', 'z')
assert ZZ.frac_field('x').unify(ZZ.frac_field('x')) == ZZ.frac_field('x')
assert ZZ.frac_field('x').unify(QQ.frac_field('x')) == QQ.frac_field('x')
assert QQ.frac_field('x').unify(ZZ.frac_field('x')) == QQ.frac_field('x')
assert QQ.frac_field('x').unify(QQ.frac_field('x')) == QQ.frac_field('x')
assert ZZ.frac_field('x', 'y').unify(ZZ.frac_field('x')) == ZZ.frac_field(
'x', 'y')
assert ZZ.frac_field('x', 'y').unify(QQ.frac_field('x')) == QQ.frac_field(
'x', 'y')
assert QQ.frac_field('x', 'y').unify(ZZ.frac_field('x')) == QQ.frac_field(
'x', 'y')
assert QQ.frac_field('x', 'y').unify(QQ.frac_field('x')) == QQ.frac_field(
'x', 'y')
assert ZZ.frac_field('x').unify(ZZ.frac_field('x', 'y')) == ZZ.frac_field(
'x', 'y')
assert ZZ.frac_field('x').unify(QQ.frac_field('x', 'y')) == QQ.frac_field(
'x', 'y')
assert QQ.frac_field('x').unify(ZZ.frac_field('x', 'y')) == QQ.frac_field(
'x', 'y')
assert QQ.frac_field('x').unify(QQ.frac_field('x', 'y')) == QQ.frac_field(
'x', 'y')
assert ZZ.frac_field('x', 'y').unify(ZZ.frac_field('x',
'z')) == ZZ.frac_field(
'x', 'y', 'z')
assert ZZ.frac_field('x', 'y').unify(QQ.frac_field('x',
'z')) == QQ.frac_field(
'x', 'y', 'z')
assert QQ.frac_field('x', 'y').unify(ZZ.frac_field('x',
'z')) == QQ.frac_field(
'x', 'y', 'z')
assert QQ.frac_field('x', 'y').unify(QQ.frac_field('x',
'z')) == QQ.frac_field(
'x', 'y', 'z')
assert ZZ.poly_ring('x').unify(ZZ.frac_field('x')) == ZZ.frac_field('x')
assert ZZ.poly_ring('x').unify(
QQ.frac_field('x')) == EX # QQ.frac_field('x')
assert QQ.poly_ring('x').unify(
ZZ.frac_field('x')) == EX # QQ.frac_field('x')
assert QQ.poly_ring('x').unify(QQ.frac_field('x')) == QQ.frac_field('x')
assert ZZ.poly_ring('x', 'y').unify(ZZ.frac_field('x')) == ZZ.frac_field(
'x', 'y')
assert ZZ.poly_ring('x', 'y').unify(
QQ.frac_field('x')) == EX # QQ.frac_field('x','y')
assert QQ.poly_ring('x', 'y').unify(
ZZ.frac_field('x')) == EX # QQ.frac_field('x','y')
assert QQ.poly_ring('x', 'y').unify(QQ.frac_field('x')) == QQ.frac_field(
'x', 'y')
assert ZZ.poly_ring('x').unify(ZZ.frac_field('x', 'y')) == ZZ.frac_field(
'x', 'y')
assert ZZ.poly_ring('x').unify(QQ.frac_field(
'x', 'y')) == EX # QQ.frac_field('x','y')
assert QQ.poly_ring('x').unify(ZZ.frac_field(
'x', 'y')) == EX # QQ.frac_field('x','y')
assert QQ.poly_ring('x').unify(QQ.frac_field('x', 'y')) == QQ.frac_field(
'x', 'y')
assert ZZ.poly_ring('x', 'y').unify(ZZ.frac_field('x',
'z')) == ZZ.frac_field(
'x', 'y', 'z')
assert ZZ.poly_ring('x', 'y').unify(QQ.frac_field(
'x', 'z')) == EX # QQ.frac_field('x','y','z')
assert QQ.poly_ring('x', 'y').unify(ZZ.frac_field(
'x', 'z')) == EX # QQ.frac_field('x','y','z')
assert QQ.poly_ring('x', 'y').unify(QQ.frac_field('x',
'z')) == QQ.frac_field(
'x', 'y', 'z')
assert ZZ.frac_field('x').unify(ZZ.poly_ring('x')) == ZZ.frac_field('x')
assert ZZ.frac_field('x').unify(
QQ.poly_ring('x')) == EX # QQ.frac_field('x')
assert QQ.frac_field('x').unify(
ZZ.poly_ring('x')) == EX # QQ.frac_field('x')
assert QQ.frac_field('x').unify(QQ.poly_ring('x')) == QQ.frac_field('x')
assert ZZ.frac_field('x', 'y').unify(ZZ.poly_ring('x')) == ZZ.frac_field(
'x', 'y')
assert ZZ.frac_field('x', 'y').unify(
QQ.poly_ring('x')) == EX # QQ.frac_field('x','y')
assert QQ.frac_field('x', 'y').unify(
ZZ.poly_ring('x')) == EX # QQ.frac_field('x','y')
assert QQ.frac_field('x', 'y').unify(QQ.poly_ring('x')) == QQ.frac_field(
'x', 'y')
assert ZZ.frac_field('x').unify(ZZ.poly_ring('x', 'y')) == ZZ.frac_field(
'x', 'y')
assert ZZ.frac_field('x').unify(QQ.poly_ring(
'x', 'y')) == EX # QQ.frac_field('x','y')
assert QQ.frac_field('x').unify(ZZ.poly_ring(
'x', 'y')) == EX # QQ.frac_field('x','y')
assert QQ.frac_field('x').unify(QQ.poly_ring('x', 'y')) == QQ.frac_field(
'x', 'y')
assert ZZ.frac_field('x', 'y').unify(ZZ.poly_ring('x',
'z')) == ZZ.frac_field(
'x', 'y', 'z')
assert ZZ.frac_field('x', 'y').unify(QQ.poly_ring(
'x', 'z')) == EX # QQ.frac_field('x','y','z')
assert QQ.frac_field('x', 'y').unify(ZZ.poly_ring(
'x', 'z')) == EX # QQ.frac_field('x','y','z')
assert QQ.frac_field('x', 'y').unify(QQ.poly_ring('x',
'z')) == QQ.frac_field(
'x', 'y', 'z')
raises(UnificationFailed,
"ZZ.poly_ring('x','y').unify(ZZ, gens=('y', 'z'))")
raises(UnificationFailed,
"ZZ.unify(ZZ.poly_ring('x','y'), gens=('y', 'z'))")
def test_Algebra__unify():
assert ZZ.unify(ZZ) == ZZ
assert QQ.unify(QQ) == QQ
assert ZZ.unify(QQ) == QQ
assert QQ.unify(ZZ) == QQ
assert EX.unify(EX) == EX
assert ZZ.unify(EX) == EX
assert QQ.unify(EX) == EX
assert EX.unify(ZZ) == EX
assert EX.unify(QQ) == EX
assert ZZ.poly_ring('x').unify(EX) == EX
assert ZZ.frac_field('x').unify(EX) == EX
assert EX.unify(ZZ.poly_ring('x')) == EX
assert EX.unify(ZZ.frac_field('x')) == EX
assert ZZ.poly_ring('x','y').unify(EX) == EX
assert ZZ.frac_field('x','y').unify(EX) == EX
assert EX.unify(ZZ.poly_ring('x','y')) == EX
assert EX.unify(ZZ.frac_field('x','y')) == EX
assert QQ.poly_ring('x').unify(EX) == EX
assert QQ.frac_field('x').unify(EX) == EX
assert EX.unify(QQ.poly_ring('x')) == EX
assert EX.unify(QQ.frac_field('x')) == EX
assert QQ.poly_ring('x','y').unify(EX) == EX
assert QQ.frac_field('x','y').unify(EX) == EX
assert EX.unify(QQ.poly_ring('x','y')) == EX
assert EX.unify(QQ.frac_field('x','y')) == EX
assert ZZ.poly_ring('x').unify(ZZ) == ZZ.poly_ring('x')
assert ZZ.poly_ring('x').unify(QQ) == QQ.poly_ring('x')
assert QQ.poly_ring('x').unify(ZZ) == QQ.poly_ring('x')
assert QQ.poly_ring('x').unify(QQ) == QQ.poly_ring('x')
assert ZZ.unify(ZZ.poly_ring('x')) == ZZ.poly_ring('x')
assert QQ.unify(ZZ.poly_ring('x')) == QQ.poly_ring('x')
assert ZZ.unify(QQ.poly_ring('x')) == QQ.poly_ring('x')
assert QQ.unify(QQ.poly_ring('x')) == QQ.poly_ring('x')
assert ZZ.poly_ring('x','y').unify(ZZ) == ZZ.poly_ring('x','y')
assert ZZ.poly_ring('x','y').unify(QQ) == QQ.poly_ring('x','y')
assert QQ.poly_ring('x','y').unify(ZZ) == QQ.poly_ring('x','y')
assert QQ.poly_ring('x','y').unify(QQ) == QQ.poly_ring('x','y')
assert ZZ.unify(ZZ.poly_ring('x','y')) == ZZ.poly_ring('x','y')
assert QQ.unify(ZZ.poly_ring('x','y')) == QQ.poly_ring('x','y')
assert ZZ.unify(QQ.poly_ring('x','y')) == QQ.poly_ring('x','y')
assert QQ.unify(QQ.poly_ring('x','y')) == QQ.poly_ring('x','y')
assert ZZ.frac_field('x').unify(ZZ) == ZZ.frac_field('x')
assert ZZ.frac_field('x').unify(QQ) == EX # QQ.frac_field('x')
assert QQ.frac_field('x').unify(ZZ) == EX # QQ.frac_field('x')
assert QQ.frac_field('x').unify(QQ) == QQ.frac_field('x')
assert ZZ.unify(ZZ.frac_field('x')) == ZZ.frac_field('x')
assert QQ.unify(ZZ.frac_field('x')) == EX # QQ.frac_field('x')
assert ZZ.unify(QQ.frac_field('x')) == EX # QQ.frac_field('x')
assert QQ.unify(QQ.frac_field('x')) == QQ.frac_field('x')
assert ZZ.frac_field('x','y').unify(ZZ) == ZZ.frac_field('x','y')
assert ZZ.frac_field('x','y').unify(QQ) == EX # QQ.frac_field('x','y')
assert QQ.frac_field('x','y').unify(ZZ) == EX # QQ.frac_field('x','y')
assert QQ.frac_field('x','y').unify(QQ) == QQ.frac_field('x','y')
assert ZZ.unify(ZZ.frac_field('x','y')) == ZZ.frac_field('x','y')
assert QQ.unify(ZZ.frac_field('x','y')) == EX # QQ.frac_field('x','y')
assert ZZ.unify(QQ.frac_field('x','y')) == EX # QQ.frac_field('x','y')
assert QQ.unify(QQ.frac_field('x','y')) == QQ.frac_field('x','y')
assert ZZ.poly_ring('x').unify(ZZ.poly_ring('x')) == ZZ.poly_ring('x')
assert ZZ.poly_ring('x').unify(QQ.poly_ring('x')) == QQ.poly_ring('x')
assert QQ.poly_ring('x').unify(ZZ.poly_ring('x')) == QQ.poly_ring('x')
assert QQ.poly_ring('x').unify(QQ.poly_ring('x')) == QQ.poly_ring('x')
assert ZZ.poly_ring('x','y').unify(ZZ.poly_ring('x')) == ZZ.poly_ring('x','y')
assert ZZ.poly_ring('x','y').unify(QQ.poly_ring('x')) == QQ.poly_ring('x','y')
assert QQ.poly_ring('x','y').unify(ZZ.poly_ring('x')) == QQ.poly_ring('x','y')
assert QQ.poly_ring('x','y').unify(QQ.poly_ring('x')) == QQ.poly_ring('x','y')
assert ZZ.poly_ring('x').unify(ZZ.poly_ring('x','y')) == ZZ.poly_ring('x','y')
assert ZZ.poly_ring('x').unify(QQ.poly_ring('x','y')) == QQ.poly_ring('x','y')
assert QQ.poly_ring('x').unify(ZZ.poly_ring('x','y')) == QQ.poly_ring('x','y')
assert QQ.poly_ring('x').unify(QQ.poly_ring('x','y')) == QQ.poly_ring('x','y')
assert ZZ.poly_ring('x','y').unify(ZZ.poly_ring('x','z')) == ZZ.poly_ring('x','y','z')
assert ZZ.poly_ring('x','y').unify(QQ.poly_ring('x','z')) == QQ.poly_ring('x','y','z')
assert QQ.poly_ring('x','y').unify(ZZ.poly_ring('x','z')) == QQ.poly_ring('x','y','z')
assert QQ.poly_ring('x','y').unify(QQ.poly_ring('x','z')) == QQ.poly_ring('x','y','z')
assert ZZ.frac_field('x').unify(ZZ.frac_field('x')) == ZZ.frac_field('x')
assert ZZ.frac_field('x').unify(QQ.frac_field('x')) == QQ.frac_field('x')
assert QQ.frac_field('x').unify(ZZ.frac_field('x')) == QQ.frac_field('x')
assert QQ.frac_field('x').unify(QQ.frac_field('x')) == QQ.frac_field('x')
assert ZZ.frac_field('x','y').unify(ZZ.frac_field('x')) == ZZ.frac_field('x','y')
assert ZZ.frac_field('x','y').unify(QQ.frac_field('x')) == QQ.frac_field('x','y')
assert QQ.frac_field('x','y').unify(ZZ.frac_field('x')) == QQ.frac_field('x','y')
assert QQ.frac_field('x','y').unify(QQ.frac_field('x')) == QQ.frac_field('x','y')
assert ZZ.frac_field('x').unify(ZZ.frac_field('x','y')) == ZZ.frac_field('x','y')
assert ZZ.frac_field('x').unify(QQ.frac_field('x','y')) == QQ.frac_field('x','y')
assert QQ.frac_field('x').unify(ZZ.frac_field('x','y')) == QQ.frac_field('x','y')
assert QQ.frac_field('x').unify(QQ.frac_field('x','y')) == QQ.frac_field('x','y')
assert ZZ.frac_field('x','y').unify(ZZ.frac_field('x','z')) == ZZ.frac_field('x','y','z')
assert ZZ.frac_field('x','y').unify(QQ.frac_field('x','z')) == QQ.frac_field('x','y','z')
assert QQ.frac_field('x','y').unify(ZZ.frac_field('x','z')) == QQ.frac_field('x','y','z')
assert QQ.frac_field('x','y').unify(QQ.frac_field('x','z')) == QQ.frac_field('x','y','z')
assert ZZ.poly_ring('x').unify(ZZ.frac_field('x')) == ZZ.frac_field('x')
assert ZZ.poly_ring('x').unify(QQ.frac_field('x')) == EX # QQ.frac_field('x')
assert QQ.poly_ring('x').unify(ZZ.frac_field('x')) == EX # QQ.frac_field('x')
assert QQ.poly_ring('x').unify(QQ.frac_field('x')) == QQ.frac_field('x')
assert ZZ.poly_ring('x','y').unify(ZZ.frac_field('x')) == ZZ.frac_field('x','y')
assert ZZ.poly_ring('x','y').unify(QQ.frac_field('x')) == EX # QQ.frac_field('x','y')
assert QQ.poly_ring('x','y').unify(ZZ.frac_field('x')) == EX # QQ.frac_field('x','y')
assert QQ.poly_ring('x','y').unify(QQ.frac_field('x')) == QQ.frac_field('x','y')
assert ZZ.poly_ring('x').unify(ZZ.frac_field('x','y')) == ZZ.frac_field('x','y')
assert ZZ.poly_ring('x').unify(QQ.frac_field('x','y')) == EX # QQ.frac_field('x','y')
assert QQ.poly_ring('x').unify(ZZ.frac_field('x','y')) == EX # QQ.frac_field('x','y')
assert QQ.poly_ring('x').unify(QQ.frac_field('x','y')) == QQ.frac_field('x','y')
assert ZZ.poly_ring('x','y').unify(ZZ.frac_field('x','z')) == ZZ.frac_field('x','y','z')
assert ZZ.poly_ring('x','y').unify(QQ.frac_field('x','z')) == EX # QQ.frac_field('x','y','z')
assert QQ.poly_ring('x','y').unify(ZZ.frac_field('x','z')) == EX # QQ.frac_field('x','y','z')
assert QQ.poly_ring('x','y').unify(QQ.frac_field('x','z')) == QQ.frac_field('x','y','z')
assert ZZ.frac_field('x').unify(ZZ.poly_ring('x')) == ZZ.frac_field('x')
assert ZZ.frac_field('x').unify(QQ.poly_ring('x')) == EX # QQ.frac_field('x')
assert QQ.frac_field('x').unify(ZZ.poly_ring('x')) == EX # QQ.frac_field('x')
assert QQ.frac_field('x').unify(QQ.poly_ring('x')) == QQ.frac_field('x')
assert ZZ.frac_field('x','y').unify(ZZ.poly_ring('x')) == ZZ.frac_field('x','y')
assert ZZ.frac_field('x','y').unify(QQ.poly_ring('x')) == EX # QQ.frac_field('x','y')
assert QQ.frac_field('x','y').unify(ZZ.poly_ring('x')) == EX # QQ.frac_field('x','y')
assert QQ.frac_field('x','y').unify(QQ.poly_ring('x')) == QQ.frac_field('x','y')
assert ZZ.frac_field('x').unify(ZZ.poly_ring('x','y')) == ZZ.frac_field('x','y')
assert ZZ.frac_field('x').unify(QQ.poly_ring('x','y')) == EX # QQ.frac_field('x','y')
assert QQ.frac_field('x').unify(ZZ.poly_ring('x','y')) == EX # QQ.frac_field('x','y')
assert QQ.frac_field('x').unify(QQ.poly_ring('x','y')) == QQ.frac_field('x','y')
assert ZZ.frac_field('x','y').unify(ZZ.poly_ring('x','z')) == ZZ.frac_field('x','y','z')
assert ZZ.frac_field('x','y').unify(QQ.poly_ring('x','z')) == EX # QQ.frac_field('x','y','z')
assert QQ.frac_field('x','y').unify(ZZ.poly_ring('x','z')) == EX # QQ.frac_field('x','y','z')
assert QQ.frac_field('x','y').unify(QQ.poly_ring('x','z')) == QQ.frac_field('x','y','z')
raises(UnificationFailed, "ZZ.poly_ring('x','y').unify(ZZ, gens=('y', 'z'))")
raises(UnificationFailed, "ZZ.unify(ZZ.poly_ring('x','y'), gens=('y', 'z'))")
