correct handling of parent in __invert__

src/sage/rings/asymptotic/asymptotic_ring.py

@@ -910,18 +910,21 @@ def __invert__(self):
 
             sage: A.<a> = AsymptoticRing(growth_group='a^ZZ', coefficient_ring=ZZ)
             sage: (1 / a).parent()
-            Asymptotic Ring <a^ZZ> over Integer Ring
+            Asymptotic Ring <a^ZZ> over Rational Field
             sage: (a / 2).parent()
             Asymptotic Ring <a^ZZ> over Rational Field
         """
         if len(self.summands) == 0:
             raise ZeroDivisionError('Division by zero in %s.' % (self,))
 
         elif len(self.summands) == 1:
-            new_element = ~next(self.summands.elements())
-            try:
+            element = next(self.summands.elements())
+            new_element = ~element
+            if new_element.parent() is element.parent():
                 return self.parent()(new_element)
-            except (ValueError, TypeError):
+            else:
+                # Insert an 'if' here once terms can have different
+                # coefficient rings, as this will be for L-terms.
                 new_parent = self.parent().change_parameter(
                     growth_group=new_element.parent().growth_group,
                     coefficient_ring=new_element.parent().coefficient_ring)
@@ -931,11 +934,21 @@ def __invert__(self):
         if len(max_elem) != 1:
             raise ValueError('Expression %s cannot be inverted, since there '
                              'are several maximal elements: %s.' % (self, max_elem))
-
         max_elem = max_elem[0]
+
         imax_elem = ~max_elem
-        one = self.parent().one()
-        geom = one - self._mul_term_(imax_elem)
+        if imax_elem.parent() is max_elem.parent():
+            new_self = self
+        else:
+            # Insert an 'if' here once terms can have different
+            # coefficient rings, as this will be for L-terms.
+            new_parent = self.parent().change_parameter(
+                growth_group=imax_elem.parent().growth_group,
+                coefficient_ring=imax_elem.parent().coefficient_ring)
+            new_self = new_parent(self)
+
+        one = new_self.parent().one()
+        geom = one - new_self._mul_term_(imax_elem)
 
         expanding = True
         result = one

src/sage/rings/asymptotic/growth_group.py

@@ -2078,9 +2078,9 @@ def __invert__(self):
             True
         """
         new_element = -self.exponent
-        try:
+        if new_element.parent() is self.exponent.parent():
             return self.parent()(raw_element=new_element)
-        except (ValueError, TypeError):
+        else:
             new_parent = self.parent().__class__(new_element.parent(),
                                                  self.parent()._var_)
             return new_parent(raw_element=new_element)
@@ -2627,11 +2627,16 @@ def __invert__(self):
             True
             sage: e2.parent()
             Growth Group QQ^x
+
+        ::
+
+            sage: (~P(raw_element=1)).parent()
+            Growth Group QQ^x
         """
         new_element = 1 / self.base
-        try:
+        if new_element.parent() is self.base.parent():
             return self.parent()(raw_element=new_element)
-        except (ValueError, TypeError):
+        else:
             new_parent = self.parent().__class__(new_element.parent(),
                                                  self.parent()._var_)
             return new_parent(raw_element=new_element)

src/sage/rings/asymptotic/growth_group_cartesian.py

@@ -878,9 +878,10 @@ def __invert__(self):
                  Growth Group QQ^x * x^ZZ
             """
             new_element = tuple(~x for x in self.cartesian_factors())
-            try:
+            if all(n.parent() is x.parent()
+                   for n, x in zip(new_element, self.cartesian_factors())):
                 return self.parent()(new_element)
-            except (ValueError, TypeError):
+            else:
                 from sage.categories.cartesian_product import cartesian_product
                 new_parent = cartesian_product(
                     tuple(x.parent() for x in new_element))

src/sage/rings/asymptotic/term_monoid.py

@@ -2285,9 +2285,9 @@ def __invert__(self):
             raise ZeroDivisionError('Cannot invert %s since its coefficient %s '
                                     'cannot be inverted.' % (self, self.coefficient))
         g = ~self.growth
-        try:
+        if c.parent() is self.coefficient.parent() and g.parent() is self.growth.parent():
             return self.parent()(g, c)
-        except (ValueError, TypeError):
+        else:
             new_parent = self.parent().__class__(g.parent(), c.parent())
             return new_parent(g, c)