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)
M2 = FreeModule(QQ.old_poly_ring(x, order="ilex"), 2)
assert [x, 1] in M1
assert [x] not in M1
assert [2, y] not in M1
assert [1 / (x + 1), 2] not in M1
e = M1.convert([x, x**2 + 1])
X = QQ.old_poly_ring(x).convert(x)
assert e == [X, X**2 + 1]
assert e == [x, x**2 + 1]
assert 2 * e == [2 * x, 2 * x**2 + 2]
assert e * 2 == [2 * x, 2 * x**2 + 2]
assert e / 2 == [x / 2, (x**2 + 1) / 2]
assert x * e == [x**2, x**3 + x]
assert e * x == [x**2, x**3 + x]
assert X * e == [x**2, x**3 + x]
assert e * X == [x**2, x**3 + x]
assert [x, 1] in M2
assert [x] not in M2
assert [2, y] not in M2
assert [1 / (x + 1), 2] in M2
e = M2.convert([x, x**2 + 1])
X = QQ.old_poly_ring(x, order="ilex").convert(x)
assert e == [X, X**2 + 1]
assert e == [x, x**2 + 1]
assert 2 * e == [2 * x, 2 * x**2 + 2]
assert e * 2 == [2 * x, 2 * x**2 + 2]
assert e / 2 == [x / 2, (x**2 + 1) / 2]
assert x * e == [x**2, x**3 + x]
assert e * x == [x**2, x**3 + x]
assert e / (1 + x) == [x / (1 + x), (x**2 + 1) / (1 + x)]
assert X * e == [x**2, x**3 + x]
assert e * X == [x**2, x**3 + x]
M3 = FreeModule(QQ.old_poly_ring(x, y), 2)
assert M3.convert(e) == M3.convert([x, x**2 + 1])
assert not M3.is_submodule(0)
assert not M3.is_zero()
raises(NotImplementedError, lambda: ZZ.old_poly_ring(x).free_module(2))
raises(NotImplementedError, lambda: FreeModulePolyRing(ZZ, 2))
raises(
CoercionFailed,
lambda: M1.convert(
QQ.old_poly_ring(x).free_module(3).convert([1, 2, 3])),
)
raises(CoercionFailed, lambda: M3.convert(1))
def free_module(self, rank):
"""
Generate a free module of rank ``rank`` over ``self``.
>>> from sympy.abc import x
>>> from sympy import QQ
>>> QQ.old_poly_ring(x).free_module(2)
QQ[x]**2
"""
return FreeModulePolyRing(self, rank)