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# sympy.polys.QQ.old_poly_ring

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```Returns a polynomial ring, i.e. `K[X]`.
```

```def test_ideal_operations():
R = QQ.old_poly_ring(x, y)
I = R.ideal(x)
J = R.ideal(y)
S = R.ideal(x*y)
```
```def test_nontriv_global():
R = QQ.old_poly_ring(x, y, z)

def contains(I, f):
return R.ideal(*I).contains(f)
```
```def test_nontriv_local():
R = QQ.old_poly_ring(x, y, z, order=ilex)

def contains(I, f):
return R.ideal(*I).contains(f)
```
```def test_intersection():
R = QQ.old_poly_ring(x, y, z)
# SCA, example 1.8.11
assert R.ideal(x, y).intersect(R.ideal(y**2, z)) == R.ideal(y**2, y*z, x*z)

assert R.ideal(x, y).intersect(R.ideal()).is_zero()

R = QQ.old_poly_ring(x, y, z, order="ilex")
```

```
assert M.convert([x, x, x]) / QQ.old_poly_ring(x).convert(x) == [1, 1, 1]
R = QQ.old_poly_ring(x, order="ilex")
assert R.free_module(1).convert([x]) / R.convert(x) == [1]

def test_FreeModule():
M1 = FreeModule(QQ.old_poly_ring(x), 2)
assert M1 == FreeModule(QQ.old_poly_ring(x), 2)
assert M1 != FreeModule(QQ.old_poly_ring(y), 2)
```
```def test_FreeModule():
M1 = FreeModule(QQ.old_poly_ring(x), 2)
assert M1 == FreeModule(QQ.old_poly_ring(x), 2)
assert M1 != FreeModule(QQ.old_poly_ring(y), 2)
assert M1 != FreeModule(QQ.old_poly_ring(x), 3)
```