def test_EX_EXRAW():
assert EXRAW.zero is S.Zero
assert EXRAW.one is S.One
assert EX(1) == EX.Expression(1)
assert EX(1).ex is S.One
assert EXRAW(1) is S.One
# EX has cancelling but EXRAW does not
assert 2*EX((x + y*x)/x) == EX(2 + 2*y) != 2*((x + y*x)/x)
assert 2*EXRAW((x + y*x)/x) == 2*((x + y*x)/x) != (1 + y)
assert EXRAW.convert_from(EX(1), EX) is EXRAW.one
assert EX.convert_from(EXRAW(1), EXRAW) == EX.one
assert EXRAW.from_sympy(S.One) is S.One
assert EXRAW.to_sympy(EXRAW.one) is S.One
raises(CoercionFailed, lambda: EXRAW.from_sympy([]))
assert EXRAW.get_field() == EXRAW
assert EXRAW.unify(EX) == EXRAW
assert EX.unify(EXRAW) == EXRAW
def test_Domain__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')
alg = QQ.algebraic_field(sqrt(5))
assert alg.unify(alg['x', 'y']) == alg['x', 'y']
assert alg['x', 'y'].unify(alg) == alg['x', 'y']
assert alg.unify(alg.frac_field('x', 'y')) == alg.frac_field('x', 'y')
assert alg.frac_field('x', 'y').unify(alg) == alg.frac_field('x', 'y')
ext = QQ.algebraic_field(sqrt(7))
raises(NotImplementedError, "alg.unify(ext)")
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_Domain__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')
alg = QQ.algebraic_field(sqrt(5))
assert alg.unify(alg['x','y']) == alg['x','y']
assert alg['x','y'].unify(alg) == alg['x','y']
assert alg.unify(alg.frac_field('x','y')) == alg.frac_field('x','y')
assert alg.frac_field('x','y').unify(alg) == alg.frac_field('x','y')
ext = QQ.algebraic_field(sqrt(7))
raises(NotImplementedError, "alg.unify(ext)")
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_Domain__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)
alg = QQ.algebraic_field(sqrt(5))
assert alg.unify(alg[x, y]) == alg[x, y]
assert alg[x, y].unify(alg) == alg[x, y]
assert alg.unify(alg.frac_field(x, y)) == alg.frac_field(x, y)
assert alg.frac_field(x, y).unify(alg) == alg.frac_field(x, y)
ext = QQ.algebraic_field(sqrt(7))
raises(NotImplementedError, lambda: alg.unify(ext))
raises(UnificationFailed, lambda: ZZ.poly_ring(x, y).unify(ZZ, gens=(y, z)))
raises(UnificationFailed, lambda: ZZ.unify(ZZ.poly_ring(x, y), gens=(y, z)))
def test_Domain__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_Domain__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)
alg = QQ.algebraic_field(sqrt(5))
assert alg.unify(alg[x, y]) == alg[x, y]
assert alg[x, y].unify(alg) == alg[x, y]
assert alg.unify(alg.frac_field(x, y)) == alg.frac_field(x, y)
assert alg.frac_field(x, y).unify(alg) == alg.frac_field(x, y)
ext = QQ.algebraic_field(sqrt(7))
raises(NotImplementedError, lambda: alg.unify(ext))
raises(UnificationFailed,
lambda: ZZ.poly_ring(x, y).unify(ZZ, gens=(y, z)))
raises(UnificationFailed,
lambda: ZZ.unify(ZZ.poly_ring(x, y), gens=(y, z)))
