# subquotient of module

how can I take a quotient of a submodule? I was expecting the following to work:

```
sage: M = CombinatorialFreeModule(QQ, [1,2], prefix='x'); x = M.basis()
sage: A = M.submodule([x[2]])
sage: A.quotient_module(A)
Free module generated by {1} over Rational Field
```

Which is clearly taking the quotient over the ambient space of `A`

and not the image

```
sage: A.quotient_module(A) == M.quotient_module(A)
True
```

Replacing `A`

with `A.lift.image()`

is the same.

EDIT: well, reading now in `Modules.WithBasis.FiniteDimensional.ParentMethods.quotient_modules`

this is simply a call to `QuotientModuleWithBasis(A,category)`

which will infer the parent of `A`

.

As a side observation, I find it disturbing that there is not even a check that `submodule`

is indeed a submodule of `self`

in that call.