Faster implementation of is_invertible() by checking full rank

src/sage/matrix/matrix_gf2e_dense.pyx

@@ -963,6 +963,22 @@
                 break
         return pivots
 
+    def is_invertible(self):
+        """
+        Return if invertible by checking full rank.
+
+        EXAMPLES::
+
+            sage: m = Matrix(GL(2^8, GF(2^8)).random_element())
+            sage: m.is_invertible()
+            True
+        """
+        if self._ncols != self._nrows:
+            return False
+        if self._nrows != self.rank():
+            return False
+        return True
+
     def __invert__(self):
         """
         EXAMPLES::
@@ -980,13 +996,12 @@
         cdef Matrix_gf2e_dense A
         A = Matrix_gf2e_dense.__new__(Matrix_gf2e_dense, self._parent, 0, 0, 0)
 
-        if self.rank() != self._nrows:
+        if not self.is_invertible():
             raise ZeroDivisionError("Matrix does not have full rank.")
 
-        if self._nrows:
-            sig_on()
-            mzed_invert_newton_john(A._entries, self._entries)
-            sig_off()
+        sig_on()
+        mzed_invert_newton_john(A._entries, self._entries)
+        sig_off()
 
         return A