From 5e7e19afded220ad7e88b6362e7f98448a46df04 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?= <chapoton@unistra.fr>
Date: Wed, 19 Aug 2020 10:08:36 +0200
Subject: [PATCH] tentative fix, move inversion to monoids

---
 src/sage/categories/magmas.py           | 30 -------------------------
 src/sage/categories/monoids.py          | 30 +++++++++++++++++++++++++
 src/sage/monoids/free_monoid_element.py |  7 ++++--
 3 files changed, 35 insertions(+), 32 deletions(-)

diff --git a/src/sage/categories/magmas.py b/src/sage/categories/magmas.py
index ba6a5b7135f..89af2269084 100644
--- a/src/sage/categories/magmas.py
+++ b/src/sage/categories/magmas.py
@@ -589,36 +589,6 @@ def _div_(left, right):
                 """
                 return left * ~right
 
-            def __invert__(self):
-                r"""
-                Return the inverse of ``self``.
-
-                The default implementation is to divide ``self.one()``.
-
-                EXAMPLES::
-
-                    sage: A = Matrix([[1, 0], [1, 1]])
-                    sage: ~A
-                    [ 1 0]
-                    [-1 1]
-                """
-                return self.parent().one()._div_(self)
-
-            def inverse(self):
-                """
-                Return the inverse of ``self``.
-
-                This an alias for inversion, defined in ``__invert__``.
-
-                Element classes should implement ``__invert__`` only.
-
-                EXAMPLES::
-
-                    sage: AA(sqrt(~2)).inverse()
-                    1.414213562373095?
-                """
-                return self.__invert__()
-
         class SubcategoryMethods:
 
             @cached_method
diff --git a/src/sage/categories/monoids.py b/src/sage/categories/monoids.py
index 42b55b8dda4..d598a6cecb3 100644
--- a/src/sage/categories/monoids.py
+++ b/src/sage/categories/monoids.py
@@ -313,6 +313,36 @@ def powers(self, n):
                 l.append(x)
             return l
 
+        def __invert__(self):
+            r"""
+            Return the inverse of ``self``.
+
+            The default implementation is to divide ``self.one()``.
+
+            EXAMPLES::
+
+                sage: A = Matrix([[1, 0], [1, 1]])
+                sage: ~A
+                [ 1 0]
+                [-1 1]
+            """
+            return self.parent().one()._div_(self)
+
+        def inverse(self):
+            """
+            Return the inverse of ``self``.
+
+            This an alias for inversion, defined in ``__invert__``.
+
+            Element classes should implement ``__invert__`` only.
+
+            EXAMPLES::
+
+                sage: AA(sqrt(~2)).inverse()
+                1.414213562373095?
+            """
+            return self.__invert__()
+
     class Commutative(CategoryWithAxiom):
         r"""
         Category of commutative (abelian) monoids.
diff --git a/src/sage/monoids/free_monoid_element.py b/src/sage/monoids/free_monoid_element.py
index 549f9381e94..0da37bb9adf 100644
--- a/src/sage/monoids/free_monoid_element.py
+++ b/src/sage/monoids/free_monoid_element.py
@@ -21,7 +21,7 @@
 #  See the GNU General Public License for more details; the full text
 #  is available at:
 #
-#                  http://www.gnu.org/licenses/
+#                  https://www.gnu.org/licenses/
 #*****************************************************************************
 
 from sage.rings.integer import Integer
@@ -102,7 +102,7 @@ def __hash__(self):
 
     def __iter__(self):
         """
-        Returns an iterator which yields tuples of variable and exponent.
+        Return an iterator which yields tuples of variable and exponent.
 
         EXAMPLES::
 
@@ -257,6 +257,9 @@ def _mul_(self, y):
                 z._element_list = x_elt[:k] + [ m ] + y_elt[1:]
         return z
 
+    def __invert__(self):
+        raise NotImplementedError
+
     def __len__(self):
         """
         Return the degree of the monoid element ``self``, where each