.coordinate_vector() for IntegerLattice does not respect the base ring (ZZ)

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The following code demonstrates that despite IntegerLattice being defined as a module over ZZ, its .component_vector() method fails to recognize that a given vector is not in self and proceeds with representing it as a linear combination with fractional coefficients.

from sage.modules.free_module_integer import IntegerLattice

L = IntegerLattice([2,2,2])
r = vector(ZZ,[1,1,1])

print(r in L)                             # this is False
print(L.coordinate_vector(r,check=True))  # check should fail, and exception should be raised but it's not

On a related note, it is unclear how L.coordinate_vector(r) behaves when r does belong to L. I'd expect it to return a vector with integer components, but given the above behavior it seems that it may return a vector with fractional components anyway. It should stick to the base ring, i.e. ZZ in this case, or at least have an option to enforce this.

CC: @yyyyx4

Component: linear algebra

Stopgaps: todo

Issue created by migration from https://trac.sagemath.org/ticket/33882

[maxale]

Stopgaps: todo