creation of element via parent method for ring

src/sage/rings/asymptotic/asymptotic_ring.py

@@ -1482,6 +1482,40 @@ def _create_empty_summands_():
                             merge=absorption)
 
 
+    def _create_element_via_parent_(self, term, old_parent=None):
+        r"""
+        Create an element with a possibly other parent.
+
+        INPUT:
+
+        - ``term`` -- the element data.
+
+        - ``old_parent`` -- the parent of ``term`` is compared to this parent.
+
+        OUTPUT:
+
+        An element.
+
+            sage: from sage.rings.asymptotic.term_monoid import TermMonoid
+            sage: from sage.rings.asymptotic.growth_group import GrowthGroup
+            sage: G = GrowthGroup('z^ZZ')
+            sage: T = TermMonoid('exact', G, ZZ)
+            sage: T._create_element_via_parent_(G.an_element(), 3, G, ZZ)
+            3*z
+            sage: T._create_element_via_parent_(G.an_element(), 3/2, G, ZZ).parent()
+            Exact Term Monoid z^ZZ with coefficients in Rational Field
+        """
+        if old_parent is None or term.parent() is old_parent:
+            parent = self
+        else:
+            # Insert an 'if' here once terms can have different
+            # coefficient rings, as this will be for L-terms.
+            parent = self.change_parameter(
+                growth_group=term.parent().growth_group,
+                coefficient_ring=term.parent().coefficient_ring)
+        return parent(term, simplify=False, convert=False)
+
+
     def _element_constructor_(self, data, simplify=True, convert=True):
         r"""
         Convert a given object to this asymptotic ring.

src/sage/rings/asymptotic/growth_group.py

@@ -1401,7 +1401,8 @@ def _create_element_via_parent_(self, raw_element, old_parent=None):
 
         - ``raw_element`` -- the element data.
 
-        - ``old_parent`` -- the parent of ``raw_element`` is compared to ``old_parent``.
+        - ``old_parent`` -- the parent of ``raw_element`` is compared
+          to this parent.
 
         OUTPUT:
 

src/sage/rings/asymptotic/term_monoid.py

@@ -1423,9 +1423,11 @@ def _create_element_via_parent_(self, growth, coefficient,
 
         INPUT:
 
-        - ``raw_element`` -- the element data.
+        - ``growth`` and ``coefficient`` -- the element data.
 
-        - ``old_parent`` -- the parent of ``raw_element`` is compared to ``old_parent``.
+        - ``old_parent_growth`` and ``old_parent_coefficient`` -- the
+          parents of ``growth`` and ``coefficient`` are compared to
+          these parents.
 
         OUTPUT: