gh-40176: Trac #40167: Fix incorrect parent reuse in matrix-vector multiplication over GF(2)

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Fixes [#40167](#40167). This PR
fixes a bug in `Matrix_mod2_dense._matrix_times_vector_` revealed in
[#40167](#40167), where the
parent of the resulting vector was incorrectly reused from the input
vector.

The regression was introduced in [PR
#37375](#37375), which added an
optimization to speed up matrix-vector multiplication when the matrix is
square and matches the vector dimension. However, it failed to account
for edge cases where the input vector's parent is not the full ambient
vector space—for example, when working with subspaces. In this case, we
can no longer assume that the ambient space is the vector's ambient
space.

In such cases, reusing the parent leads to incorrect coercion or a
result vector with an invalid parent space. This patch introduces an
explicit check: if the vector's parent is the full space `GF(2)^n`, it
is reused; otherwise, a default parent is constructed to ensure
correctness.

### Example (correct behavior restored)

```python
sage: M = Matrix(GF(2), [[1, 1], [0, 1]])
sage: v = vector(GF(2), [0, 1])
sage: V = span([v])             # one-dimensional subspace of GF(2)^2
sage: image_basis = [M * b for b in V.basis()]
sage: image = span(image_basis)
sage: image.basis() == [(1, 1)]
True # now returns True
```

### 📝 Checklist

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- [ ] I have updated the documentation and checked the documentation
preview.

### ⌛ Dependencies

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URL: #40176
Reported by: Aolong Li
Reviewer(s): Travis Scrimshaw

Author: Release Manager

build/pkgs/configure/checksums.ini

@@ -1,3 +1,3 @@
 tarball=configure-VERSION.tar.gz
-sha1=2b82d3f61ce5242564303693ec5cf868bed70e67
-sha256=307a4306540a791edb795baad821ebc708a589960146c4a20d3d14aa730fc1ea
+sha1=11062cbee8ecac01543919cb9f8da3a38dbea65a
+sha256=80999cd87c7f1585cf63e873bd3a1725fa7630a4cbc1b96b2a1d35897cf77d39

build/pkgs/configure/package-version.txt

@@ -1 +1 @@
-731c1bad33aa2dc17ded3fb92e76203331ecd3f5
+987b4a607790c21641793798e19ef977df1f78e8

src/sage/matrix/matrix_mod2_dense.pyx

@@ -677,9 +677,23 @@ cdef class Matrix_mod2_dense(matrix_dense.Matrix_dense):   # dense or sparse
             sage: r1 = A*v1
             sage: r0.column(0) == r1
             True
+
+        Check that :issue:`40167` is fixed::
+
+            sage: M = matrix(GF(2), [[1,1],[0,1]])
+            sage: v = vector(GF(2), [0, 1])
+            sage: V = span([v])             # one-dimensional subspace of GF(2)^2
+            sage: image_basis = [M * b for b in V.basis()]
+            sage: image = span(image_basis)
+            sage: image_basis[0] in image.basis()
+            True
         """
         cdef mzd_t *tmp
-        if self._nrows == self._ncols and isinstance(v, Vector_mod2_dense):
+        if (
+            self._nrows == self._ncols and
+            isinstance(v, Vector_mod2_dense) and
+            v.parent().rank() == self._ncols # check if the parent of v is full rank
+            ):
             VS = v.parent()
         else:
             global VectorSpace