gh-38453: Enhance augment method in Matrix_gf2e

    
This pull request modified `augment()` method defined in
`matrix_gf2e_dense` to allow vectors to be augmented.
See issue: #36761

Earlier it accepted only matrix of type `matrix_gf2e_dense`.
I removed that dependency.
Added check for vector.
If vector then try to change the base ring of vector to self.base_ring
and create matrix of type `matrix_gf2e_dense` from that vector
Rest of the flow remains same.

The parent class Matrix1 defined generic augment() method which allowed
vectors to be augmented but `matrix_gf2e_dense` provides new definition
of augment() and do not provide support for vectors.
For consistency it would be good to have vector augmentation in this
class too.

Fixes #36761



### 📝 Checklist

<!-- Put an `x` in all the boxes that apply. -->

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [x] I have linked a relevant issue or discussion.
- [x] I have created tests covering the changes.
- [ ] I have updated the documentation and checked the documentation
preview.

### ⌛ Dependencies

<!-- List all open PRs that this PR logically depends on. For example,
-->
<!-- - #12345: short description why this is a dependency -->
<!-- - #34567: ... -->
    
URL: #38453
Reported by: Animesh Shree
Reviewer(s): Travis Scrimshaw

src/sage/matrix/matrix_gf2e_dense.pyx

@@ -1125,7 +1125,7 @@ cdef class Matrix_gf2e_dense(matrix_dense.Matrix_dense):
         """
         mzed_col_swap(self._entries, col1, col2)
 
-    def augment(self, Matrix_gf2e_dense right):
+    def augment(self, right):
         """
         Augments ``self`` with ``right``.
 
@@ -1167,21 +1167,50 @@ cdef class Matrix_gf2e_dense(matrix_dense.Matrix_dense):
             sage: N = Matrix(K, 0, 1, 0)
             sage: M.augment(N)
             []
+
+            sage: A = matrix(K, 3, range(12))
+            sage: B = vector(QQ, [2,5/7,1.2]) # see issue: 38448
+            sage: A.augment(B).ncols()
+            5
+
+            sage: B = vector([])
+            sage: A.augment(B) == A
+            True
         """
+        cdef Matrix_gf2e_dense _right
         cdef Matrix_gf2e_dense A
 
-        if self._nrows != right._nrows:
+        if not isinstance(right, Matrix_gf2e_dense):
+            # See issue: #36761 - Allow Vectors to be augmented
+            if hasattr(right, '_vector_'):
+                rsize = len(right)
+                if rsize==0:
+                    return self.__copy__()
+                if self._nrows != rsize:
+                    raise TypeError("Both numbers of rows must match.")
+                if self.base_ring() is not right.base_ring():
+                    right = right.change_ring(self.base_ring())
+                from sage.matrix.matrix_space import MatrixSpace
+                M = MatrixSpace(self.base_ring(), nrows=rsize, ncols=1)
+                _right = <Matrix_gf2e_dense>(M(right))
+            else:
+                raise TypeError("a matrix must be augmented with another matrix, "
+                    "or a vector")
+        else:
+            _right = <Matrix_gf2e_dense>right
+
+        if self._nrows != _right._nrows:
             raise TypeError("Both numbers of rows must match.")
 
         if self._ncols == 0:
-            return right.__copy__()
-        if right._ncols == 0:
+            return _right.__copy__()
+        if _right._ncols == 0:
             return self.__copy__()
 
-        A = self.new_matrix(ncols = self._ncols + right._ncols)
+        A = self.new_matrix(ncols = self._ncols + _right._ncols)
         if self._nrows == 0:
             return A
-        A._entries = mzed_concat(A._entries, self._entries, right._entries)
+        A._entries = mzed_concat(A._entries, self._entries, _right._entries)
         return A
 
     cdef _stack_impl(self, bottom):