gh-37375: Speed up square matrix times vector over GF(2)
    
When doing a matrix-times-vector multiplication over F_2, there is some
inefficiency caused by calling `VectorSpace` to create a parent for the
result. This becomes noticeable when repeatedly multiplying small
matrices.

When the dimensions are all the same, this can be improved by using the
parent of the vector also as the parent for the result. Before:
```
sage: A = random_matrix(GF(2),10,10)
sage: v0 = vector(random_matrix(GF(2),10,1))
sage: %timeit A*v0
2.26 µs ± 4.57 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops
each)
```
After:
```
sage: A = random_matrix(GF(2),10,10)
sage: v0 = vector(random_matrix(GF(2),10,1))
sage: %timeit A*v0
981 ns ± 9.57 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops
each)
```
    
URL: #37375
Reported by: kedlaya
Reviewer(s): Lorenz Panny

Author: Release Manager

src/sage/matrix/matrix_mod2_dense.pyx

@@ -595,14 +595,27 @@ cdef class Matrix_mod2_dense(matrix_dense.Matrix_dense):   # dense or sparse
             sage: v = vector(GF(2), 0)
             sage: m * v
             (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
+
+        Add a test involving a nonsquare matrix::
+
+            sage: A = random_matrix(GF(2),10^4,10^3)
+            sage: v0 = random_matrix(GF(2),10^3,1)
+            sage: v1 = v0.column(0)
+            sage: r0 = A*v0
+            sage: r1 = A*v1
+            sage: r0.column(0) == r1
+            True
         """
         cdef mzd_t *tmp
-        global VectorSpace
-        if VectorSpace is None:
-            from sage.modules.free_module import VectorSpace
-        VS = VectorSpace(self._base_ring, self._nrows)
-        if not isinstance(v, Vector_mod2_dense):
-            v = VS(v)
+        if self._nrows == self._ncols and isinstance(v, Vector_mod2_dense):
+            VS = v.parent()
+        else:
+            global VectorSpace
+            if VectorSpace is None:
+                from sage.modules.free_module import VectorSpace
+            VS = VectorSpace(self._base_ring, self._nrows)
+            if not isinstance(v, Vector_mod2_dense):
+                v = VS(v)
         if self.ncols() != v.degree():
             raise ArithmeticError("number of columns of matrix must equal degree of vector")