diff --git a/src/sage/rings/asymptotic/asymptotic_ring.py b/src/sage/rings/asymptotic/asymptotic_ring.py
index f86bc8afcf2..76acf2e8d43 100644
--- a/src/sage/rings/asymptotic/asymptotic_ring.py
+++ b/src/sage/rings/asymptotic/asymptotic_ring.py
@@ -604,7 +604,7 @@ def __init__(self, parent, summands, simplify=True, convert=True):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: G = GrowthGroup('x^ZZ'); x = G.gen()
             sage: OT = TermMonoid('O', G, ZZ); ET = TermMonoid('exact', G, ZZ)
             sage: R = AsymptoticRing(G, ZZ)
@@ -976,7 +976,7 @@ def _simplify_(self):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: G = GrowthGroup('x^ZZ')
             sage: OT = TermMonoid('O', G, ZZ); ET = TermMonoid('exact', G, ZZ)
             sage: R = AsymptoticRing(G, ZZ)
@@ -1239,7 +1239,7 @@ def _mul_term_(self, term):
 
             sage: from sage.rings.asymptotic.term_monoid import OTermMonoid
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: R.<x> = AsymptoticRing(growth_group='x^ZZ', coefficient_ring=ZZ)
             sage: T = OTermMonoid(TermMonoid, R.growth_group, ZZ)
@@ -3608,7 +3608,7 @@ def term_monoid_factory(self):
 
             sage: AR = AsymptoticRing(growth_group='x^ZZ', coefficient_ring=ZZ)
             sage: AR.term_monoid_factory
-            Term Monoid Factory 'DefaultTermMonoidFactory'
+            Term Monoid Factory 'sage.rings.asymptotic.term_monoid.DefaultTermMonoidFactory'
 
         .. SEEALSO::
 
diff --git a/src/sage/rings/asymptotic/term_monoid.py b/src/sage/rings/asymptotic/term_monoid.py
index be8bee78b63..80c79199da2 100644
--- a/src/sage/rings/asymptotic/term_monoid.py
+++ b/src/sage/rings/asymptotic/term_monoid.py
@@ -56,7 +56,7 @@
 
     sage: from sage.rings.asymptotic.term_monoid import OTermMonoid, ExactTermMonoid
     sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-    sage: TermMonoid = TermMonoidFactory('TermMonoid')
+    sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
     sage: from sage.rings.asymptotic.growth_group import GrowthGroup
     sage: G = GrowthGroup('x^ZZ'); x = G.gen()
     sage: OT = OTermMonoid(TermMonoid, growth_group=G, coefficient_ring=QQ)
@@ -242,7 +242,7 @@ def absorption(left, right):
 
         sage: from sage.rings.asymptotic.growth_group import GrowthGroup
         sage: from sage.rings.asymptotic.term_monoid import (TermMonoidFactory, absorption)
-        sage: TermMonoid = TermMonoidFactory('TermMonoid')
+        sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
         sage: T = TermMonoid('O', GrowthGroup('x^ZZ'), ZZ)
         sage: absorption(T(x^2), T(x^3))
         O(x^3)
@@ -293,7 +293,7 @@ def can_absorb(left, right):
 
         sage: from sage.rings.asymptotic.growth_group import GrowthGroup
         sage: from sage.rings.asymptotic.term_monoid import (TermMonoidFactory, can_absorb)
-        sage: TermMonoid = TermMonoidFactory('TermMonoid')
+        sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
         sage: T = TermMonoid('O', GrowthGroup('x^ZZ'), ZZ)
         sage: can_absorb(T(x^2), T(x^3))
         True
@@ -319,7 +319,7 @@ class GenericTerm(MultiplicativeGroupElement):
         sage: from sage.rings.asymptotic.growth_group import GrowthGroup
         sage: from sage.rings.asymptotic.term_monoid import GenericTermMonoid
         sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-        sage: TermMonoid = TermMonoidFactory('TermMonoid')
+        sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
         sage: G = GrowthGroup('x^ZZ'); x = G.gen()
         sage: T = GenericTermMonoid(TermMonoid, G, QQ)
@@ -346,7 +346,7 @@ def __init__(self, parent, growth):
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import GenericTermMonoid
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: G = GrowthGroup('x^ZZ'); x = G.gen()
             sage: T = GenericTermMonoid(TermMonoid, G, ZZ)
@@ -397,7 +397,7 @@ def _mul_(self, other):
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import GenericTermMonoid
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: G = GrowthGroup('x^ZZ'); x = G.gen()
             sage: T = GenericTermMonoid(TermMonoid, G, ZZ)
@@ -422,7 +422,7 @@ def __invert__(self):
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import GenericTermMonoid
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: G = GrowthGroup('x^ZZ'); x = G.gen()
             sage: T = GenericTermMonoid(TermMonoid, G, QQ)
@@ -462,7 +462,7 @@ def __pow__(self, exponent):
             sage: from sage.rings.asymptotic.term_monoid import GenericTermMonoid
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: G = GrowthGroup('z^ZZ')
             sage: t = GenericTermMonoid(TermMonoid, G, ZZ).an_element(); t
@@ -494,7 +494,7 @@ def _calculate_pow_test_zero_(self, exponent):
             sage: from sage.rings.asymptotic.term_monoid import GenericTermMonoid
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: G = GrowthGroup('z^ZZ')
             sage: t = GenericTermMonoid(TermMonoid, G, ZZ).an_element(); t
@@ -552,7 +552,7 @@ def _calculate_pow_(self, exponent, new_coefficient=None):
             sage: from sage.rings.asymptotic.term_monoid import GenericTermMonoid
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: G = GrowthGroup('z^ZZ')
             sage: t = GenericTermMonoid(TermMonoid, G, ZZ).an_element(); t
@@ -606,7 +606,7 @@ def can_absorb(self, other):
             sage: from sage.rings.asymptotic.growth_group import GenericGrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import GenericTermMonoid
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: G = GenericGrowthGroup(ZZ)
             sage: T = GenericTermMonoid(TermMonoid, G, QQ)
@@ -656,7 +656,7 @@ def absorb(self, other, check=True):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: G_QQ = GrowthGroup('x^QQ'); x = G_QQ.gen()
             sage: OT = TermMonoid('O', G_QQ, coefficient_ring=ZZ)
             sage: ET = TermMonoid('exact', G_QQ, coefficient_ring=QQ)
@@ -744,7 +744,7 @@ def _absorb_(self, other):
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import GenericTermMonoid
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: G = GrowthGroup('x^ZZ'); x = G.gen()
             sage: T = GenericTermMonoid(TermMonoid, G, QQ)
@@ -795,7 +795,7 @@ def log_term(self, base=None):
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import GenericTermMonoid
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: T = GenericTermMonoid(TermMonoid, GrowthGroup('x^ZZ'), QQ)
             sage: T.an_element().log_term()
@@ -839,7 +839,7 @@ def _log_growth_(self, base=None):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: T = TermMonoid('O', GrowthGroup('x^ZZ * log(x)^ZZ'), QQ)
             sage: T(x^2)._log_growth_()
             (O(log(x)),)
@@ -883,7 +883,7 @@ def _lt_(self, other):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import (GenericTermMonoid, TermMonoidFactory)
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: G = GrowthGroup('x^ZZ'); x = G.gen()
             sage: GT = GenericTermMonoid(TermMonoid, G, QQ)
             sage: OT = TermMonoid('O', G, QQ)
@@ -930,7 +930,7 @@ def _lt_(self, other):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: G = GrowthGroup('x^ZZ'); x = G.gen()
             sage: ET = TermMonoid('exact', G, QQ)
             sage: t1 = ET(x, 5); t2 = ET(x^2, 3); t3 = ET(x^2, 42)
@@ -987,7 +987,7 @@ def _eq_(self, other):
             sage: from sage.rings.asymptotic.term_monoid import (GenericTermMonoid,
             ....:      ExactTermMonoid, OTermMonoid)
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: GT = GenericTermMonoid(TermMonoid, GrowthGroup('x^ZZ'), QQ)
             sage: ET = ExactTermMonoid(TermMonoid, GrowthGroup('x^ZZ'), ZZ)
@@ -1042,7 +1042,7 @@ def is_constant(self):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import (GenericTermMonoid, TermMonoidFactory)
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: T = GenericTermMonoid(TermMonoid, GrowthGroup('x^ZZ * log(x)^ZZ'), QQ)
             sage: t = T.an_element(); t
             Generic Term with growth x*log(x)
@@ -1072,7 +1072,7 @@ def is_exact(self):
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import GenericTermMonoid
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: T = GenericTermMonoid(TermMonoid, GrowthGroup('x^ZZ * log(x)^ZZ'), QQ)
             sage: T.an_element().is_exact()
             False
@@ -1097,7 +1097,7 @@ def is_little_o_of_one(self):
             sage: from sage.rings.asymptotic.term_monoid import (GenericTermMonoid,
             ....:                                                TermWithCoefficientMonoid)
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: T = GenericTermMonoid(TermMonoid, GrowthGroup('x^ZZ'), QQ)
             sage: T.an_element().is_little_o_of_one()
@@ -1134,7 +1134,7 @@ def rpow(self, base):
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import GenericTermMonoid
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: T = GenericTermMonoid(TermMonoid, GrowthGroup('x^ZZ * log(x)^ZZ'), QQ)
             sage: T.an_element().rpow('e')
@@ -1164,7 +1164,7 @@ def _repr_(self):
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import GenericTermMonoid
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: G = GrowthGroup('x^ZZ'); x = G.gen()
             sage: T = GenericTermMonoid(TermMonoid, G, QQ)
@@ -1188,7 +1188,7 @@ def _latex_(self):
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import GenericTermMonoid
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: G = GrowthGroup('x^ZZ'); x = G.gen()
             sage: T = GenericTermMonoid(TermMonoid, G, QQ)
@@ -1218,7 +1218,7 @@ def _substitute_(self, rules):
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import GenericTermMonoid
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: t = GenericTermMonoid(TermMonoid, GrowthGroup('x^ZZ'), ZZ).an_element()
             sage: t._substitute_({})
@@ -1245,7 +1245,7 @@ def variable_names(self):
         EXAMPLES::
 
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: T = TermMonoid('exact', 'QQ^m * m^QQ * log(n)^ZZ', QQ)
             sage: T('4 * 2^m * m^4 * log(n)').variable_names()
             ('m', 'n')
@@ -1273,7 +1273,7 @@ def _factorial_(self):
             sage: from sage.rings.asymptotic.term_monoid import GenericTermMonoid
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: T = GenericTermMonoid(TermMonoid, GrowthGroup('x^QQ'), QQ)
             sage: T.an_element()._factorial_()
@@ -1309,7 +1309,7 @@ def _singularity_analysis_(self, var, zeta, precision):
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import GenericTermMonoid
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: t = GenericTermMonoid(TermMonoid, GrowthGroup('x^ZZ'), ZZ).an_element()
             sage: t._singularity_analysis_('n', 2, precision=3)
@@ -1354,7 +1354,7 @@ class GenericTermMonoid(UniqueRepresentation, Parent):
         sage: from sage.rings.asymptotic.growth_group import GrowthGroup
         sage: from sage.rings.asymptotic.term_monoid import GenericTermMonoid
         sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-        sage: TermMonoid = TermMonoidFactory('TermMonoid')
+        sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
         sage: G_x = GrowthGroup('x^ZZ'); x = G_x.gen()
         sage: G_y = GrowthGroup('y^QQ'); y = G_y.gen()
@@ -1382,7 +1382,7 @@ def __classcall__(cls, term_monoid_factory,
             sage: from sage.rings.asymptotic.term_monoid import GenericTermMonoid
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: G = GrowthGroup('x^ZZ')
             sage: T = GenericTermMonoid(TermMonoid, G, QQ)
@@ -1440,7 +1440,7 @@ def __init__(self, term_monoid_factory, growth_group, coefficient_ring, category
             sage: from sage.rings.asymptotic.term_monoid import GenericTermMonoid, TermWithCoefficientMonoid
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: G_x = GrowthGroup('x^ZZ')
             sage: T_x = GenericTermMonoid(TermMonoid, G_x, QQ); T_x
@@ -1484,7 +1484,7 @@ def term_monoid_factory(self):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: TermMonoid('exact', GrowthGroup('x^ZZ'), ZZ).term_monoid_factory
             Term Monoid Factory 'TermMonoid'
         """
@@ -1499,7 +1499,7 @@ def growth_group(self):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: TermMonoid('exact', GrowthGroup('x^ZZ'), ZZ).growth_group
             Growth Group x^ZZ
         """
@@ -1516,7 +1516,7 @@ def coefficient_ring(self):
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import GenericTermMonoid
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: GenericTermMonoid(TermMonoid, GrowthGroup('x^ZZ'), ZZ).coefficient_ring
             Integer Ring
@@ -1542,7 +1542,7 @@ def change_parameter(self, growth_group=None, coefficient_ring=None):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: E = TermMonoid('exact', GrowthGroup('n^ZZ'), ZZ)
             sage: E.change_parameter(coefficient_ring=QQ)
             Exact Term Monoid n^ZZ with coefficients in Rational Field
@@ -1586,7 +1586,7 @@ def _repr_(self):
             sage: from sage.rings.asymptotic.growth_group import (GenericGrowthGroup, GrowthGroup)
             sage: from sage.rings.asymptotic.term_monoid import GenericTermMonoid
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: GenericTermMonoid(TermMonoid, GenericGrowthGroup(ZZ), QQ)._repr_()
             'Generic Term Monoid Generic(ZZ) with (implicit) coefficients in Rational Field'
@@ -1621,7 +1621,7 @@ def _coerce_map_from_(self, S):
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import GenericTermMonoid
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: G_ZZ = GrowthGroup('x^ZZ')
             sage: T_ZZ = GenericTermMonoid(TermMonoid, G_ZZ, QQ); T_ZZ
@@ -1676,7 +1676,7 @@ def _element_constructor_(self, data, coefficient=None):
             sage: from sage.rings.asymptotic.term_monoid import GenericTermMonoid
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: G_ZZ = GrowthGroup('x^ZZ')
             sage: G_QQ = GrowthGroup('x^QQ')
@@ -1802,7 +1802,7 @@ def _create_element_(self, growth, coefficient):
             sage: from sage.rings.asymptotic.term_monoid import GenericTermMonoid
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: G_ZZ = GrowthGroup('x^ZZ')
             sage: T_ZZ = GenericTermMonoid(TermMonoid, G_ZZ, QQ)
@@ -1830,7 +1830,7 @@ def _create_element_in_extension_(self, growth, coefficient):
         EXAMPLES::
 
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: G = GrowthGroup('z^ZZ')
             sage: T = TermMonoid('exact', G, ZZ)
@@ -1866,7 +1866,7 @@ def _split_growth_and_coefficient_(self, data):
         TESTS::
 
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: G = GrowthGroup('x^ZZ')
             sage: T = TermMonoid('exact', G, QQ)
@@ -1948,7 +1948,7 @@ def _get_factors_(self, data):
         TESTS::
 
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: G_ZZ = GrowthGroup('x^ZZ')
             sage: T_ZZ = TermMonoid('exact', G_ZZ, QQ)
@@ -1988,7 +1988,7 @@ def _an_element_(self):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import (GenericTermMonoid, TermMonoidFactory)
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: G = GrowthGroup('x^ZZ')
             sage: TermMonoid('O', G, QQ).an_element()  # indirect doctest
             O(x)
@@ -2015,7 +2015,7 @@ def some_elements(self):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: G = GrowthGroup('x^ZZ')
             sage: tuple(TermMonoid('O', G, QQ).some_elements())
             (O(1), O(x), O(x^(-1)), O(x^2), O(x^(-2)), O(x^3), ...)
@@ -2042,7 +2042,7 @@ def le(self, left, right):
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import GenericTermMonoid
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: G = GrowthGroup('x^ZZ'); x = G.gen()
             sage: T = GenericTermMonoid(TermMonoid, G, QQ)
@@ -2072,7 +2072,7 @@ class OTerm(GenericTerm):
         sage: from sage.rings.asymptotic.growth_group import GrowthGroup
         sage: from sage.rings.asymptotic.term_monoid import OTermMonoid
         sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-        sage: TermMonoid = TermMonoidFactory('TermMonoid')
+        sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
         sage: G = GrowthGroup('x^ZZ'); x = G.gen()
         sage: OT = OTermMonoid(TermMonoid, G, QQ)
@@ -2116,7 +2116,7 @@ def _repr_(self, latex=False):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: G = GrowthGroup('x^ZZ'); x = G.gen()
             sage: OT = TermMonoid('O', G, QQ)
             sage: OT(x)._repr_()
@@ -2150,7 +2150,7 @@ def _latex_(self):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: G = GrowthGroup('x^ZZ'); x = G.gen()
             sage: OT = TermMonoid('O', G, QQ)
             sage: latex(OT(x))
@@ -2174,7 +2174,7 @@ def __invert__(self):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: G = GrowthGroup('x^ZZ'); x = G.gen()
             sage: T = TermMonoid('O', G, QQ)
             sage: ~T(x) # indirect doctest
@@ -2199,7 +2199,7 @@ def __pow__(self, exponent):
         TESTS::
 
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: G = GrowthGroup('z^ZZ')
             sage: t = TermMonoid('O', G, ZZ).an_element(); t
@@ -2240,7 +2240,7 @@ def can_absorb(self, other):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: OT = TermMonoid('O', GrowthGroup('x^ZZ'), QQ)
             sage: t1 = OT(x^21); t2 = OT(x^42)
             sage: t1.can_absorb(t2)
@@ -2279,7 +2279,7 @@ def _absorb_(self, other):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: G = GrowthGroup('x^ZZ'); x = G.gen()
             sage: OT = TermMonoid('O', G, QQ)
             sage: ot1 = OT(x); ot2 = OT(x^2)
@@ -2316,7 +2316,7 @@ def log_term(self, base=None):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: T = TermMonoid('O', GrowthGroup('x^ZZ * log(x)^ZZ'), QQ)
             sage: T(x^2).log_term()
             (O(log(x)),)
@@ -2352,7 +2352,7 @@ def is_little_o_of_one(self):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: T = TermMonoid('O', GrowthGroup('x^ZZ'), QQ)
             sage: T(x).is_little_o_of_one()
             False
@@ -2406,7 +2406,7 @@ def rpow(self, base):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: T = TermMonoid('O', GrowthGroup('x^ZZ * log(x)^ZZ'), QQ)
             sage: T(1).rpow('e')
             O(1)
@@ -2459,7 +2459,7 @@ def _substitute_(self, rules):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: T = TermMonoid('O', GrowthGroup('x^ZZ'), ZZ)
             sage: t = T.an_element(); t
             O(x)
@@ -2531,7 +2531,7 @@ def _factorial_(self):
         TESTS::
 
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: T = TermMonoid('O', 'z^QQ', QQ)
             sage: T(1)._factorial_()
             O(1)
@@ -2571,7 +2571,7 @@ def _singularity_analysis_(self, var, zeta, precision):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: T = TermMonoid('O', GrowthGroup('x^ZZ'), ZZ)
             sage: T('x^1')._singularity_analysis_('n', 2, precision=3)
             O((1/2)^n)
@@ -2600,7 +2600,7 @@ class OTermMonoid(GenericTermMonoid):
         sage: from sage.rings.asymptotic.growth_group import GrowthGroup
         sage: from sage.rings.asymptotic.term_monoid import OTermMonoid
         sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-        sage: TermMonoid = TermMonoidFactory('TermMonoid')
+        sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
         sage: G_x_ZZ = GrowthGroup('x^ZZ')
         sage: G_y_QQ = GrowthGroup('y^QQ')
         sage: OT_x_ZZ = OTermMonoid(TermMonoid, G_x_ZZ, QQ); OT_x_ZZ
@@ -2638,7 +2638,7 @@ def _create_element_(self, growth, coefficient):
         TESTS::
 
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: G = GrowthGroup('x^ZZ')
             sage: T = TermMonoid('O', G, QQ)
@@ -2691,7 +2691,7 @@ def _coerce_map_from_(self, S):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: G_ZZ = GrowthGroup('x^ZZ'); x_ZZ = G_ZZ.gen()
             sage: G_QQ = GrowthGroup('x^QQ'); x_QQ = G_QQ.gen()
             sage: OT_ZZ = TermMonoid('O', G_ZZ, QQ)
@@ -2733,7 +2733,7 @@ def _repr_(self):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: G = GrowthGroup('x^ZZ'); x = G.gen()
             sage: TermMonoid('O', G, QQ)._repr_()
             'O-Term Monoid x^ZZ with implicit coefficients in Rational Field'
@@ -2761,7 +2761,7 @@ class TermWithCoefficient(GenericTerm):
         sage: from sage.rings.asymptotic.growth_group import GrowthGroup
         sage: from sage.rings.asymptotic.term_monoid import TermWithCoefficientMonoid
         sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-        sage: TermMonoid = TermMonoidFactory('TermMonoid')
+        sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
         sage: G = GrowthGroup('x^ZZ'); x = G.gen()
         sage: CT_ZZ = TermWithCoefficientMonoid(TermMonoid, G, ZZ)
@@ -2783,7 +2783,7 @@ def __init__(self, parent, growth, coefficient):
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermWithCoefficientMonoid
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: G = GrowthGroup('x^ZZ'); x = G.gen()
             sage: CT_ZZ = TermWithCoefficientMonoid(TermMonoid, G, ZZ)
@@ -2845,7 +2845,7 @@ def _repr_(self):
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermWithCoefficientMonoid
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: G = GrowthGroup('x^ZZ'); x = G.gen()
             sage: T = TermWithCoefficientMonoid(TermMonoid, G, ZZ)
@@ -2878,7 +2878,7 @@ def _mul_(self, other):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import (TermWithCoefficientMonoid, TermMonoidFactory)
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: G = GrowthGroup('x^ZZ'); x = G.gen()
             sage: CT = TermWithCoefficientMonoid(TermMonoid, G, ZZ)
             sage: ET = TermMonoid('exact', G, ZZ)
@@ -2919,7 +2919,7 @@ def _calculate_pow_(self, exponent):
             sage: from sage.rings.asymptotic.term_monoid import TermWithCoefficientMonoid
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: G = GrowthGroup('z^ZZ')
             sage: T = TermWithCoefficientMonoid(TermMonoid, G, ZZ)
@@ -2971,7 +2971,7 @@ def _log_coefficient_(self, base=None):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: T = TermMonoid('exact', GrowthGroup('x^ZZ * log(x)^ZZ'), QQ)
             sage: T(3*x^2)._log_coefficient_()
             (log(3),)
@@ -3013,7 +3013,7 @@ def _eq_(self, other):
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermWithCoefficientMonoid
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: T = TermWithCoefficientMonoid(TermMonoid, GrowthGroup('x^ZZ'), ZZ)
             sage: t = T.an_element(); t
@@ -3053,7 +3053,7 @@ class TermWithCoefficientMonoid(GenericTermMonoid):
         sage: from sage.rings.asymptotic.growth_group import GrowthGroup
         sage: from sage.rings.asymptotic.term_monoid import TermWithCoefficientMonoid
         sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-        sage: TermMonoid = TermMonoidFactory('TermMonoid')
+        sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
         sage: G_ZZ = GrowthGroup('x^ZZ'); x_ZZ = G_ZZ.gen()
         sage: G_QQ = GrowthGroup('x^QQ'); x_QQ = G_QQ.gen()
@@ -3089,7 +3089,7 @@ def _create_element_(self, growth, coefficient):
         TESTS::
 
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: G_ZZ = GrowthGroup('x^ZZ')
             sage: T_ZZ = TermMonoid('exact', G_ZZ, QQ)
@@ -3114,7 +3114,7 @@ def _an_element_(self):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import (TermWithCoefficientMonoid, TermMonoidFactory)
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: G = GrowthGroup('x^ZZ')
             sage: TermWithCoefficientMonoid(TermMonoid, G, ZZ).an_element()  # indirect doctest
             Term with coefficient 1 and growth x
@@ -3144,7 +3144,7 @@ def some_elements(self):
 
             sage: from itertools import islice
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: G = GrowthGroup('z^QQ')
             sage: T = TermMonoid('exact', G, ZZ)
@@ -3177,7 +3177,7 @@ class ExactTerm(TermWithCoefficient):
 
         sage: from sage.rings.asymptotic.growth_group import GrowthGroup
         sage: from sage.rings.asymptotic.term_monoid import (ExactTermMonoid, TermMonoidFactory)
-        sage: TermMonoid = TermMonoidFactory('TermMonoid')
+        sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
         sage: G = GrowthGroup('x^ZZ'); x = G.gen()
         sage: ET = ExactTermMonoid(TermMonoid, G, QQ)
 
@@ -3241,7 +3241,7 @@ def _repr_(self, latex=False):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: G = GrowthGroup('x^ZZ'); x = G.gen()
             sage: ET = TermMonoid('exact', G, ZZ)
             sage: ET(x^2, 2)
@@ -3307,7 +3307,7 @@ def _latex_(self):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: G = GrowthGroup('x^ZZ'); x = G.gen()
             sage: ET = TermMonoid('exact', G, ZZ)
             sage: latex(ET(x^2, 2))
@@ -3352,7 +3352,7 @@ def __invert__(self):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: G = GrowthGroup('x^ZZ'); x = G.gen()
             sage: T = TermMonoid('exact', G, ZZ)
             sage: ~T(x, 2)  # indirect doctest
@@ -3383,7 +3383,7 @@ def __pow__(self, exponent):
         TESTS::
 
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: G = GrowthGroup('z^ZZ')
             sage: T = TermMonoid('exact', G, ZZ)
@@ -3421,7 +3421,7 @@ def can_absorb(self, other):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: ET = TermMonoid('exact', GrowthGroup('x^ZZ'), ZZ)
             sage: t1 = ET(x^21, 1); t2 = ET(x^21, 2); t3 = ET(x^42, 1)
             sage: t1.can_absorb(t2)
@@ -3458,7 +3458,7 @@ def _absorb_(self, other):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: G = GrowthGroup('x^ZZ'); x = G.gen()
             sage: ET = TermMonoid('exact', G, QQ)
 
@@ -3506,7 +3506,7 @@ def log_term(self, base=None):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: T = TermMonoid('exact', GrowthGroup('x^ZZ * log(x)^ZZ'), SR)
             sage: T(3*x^2).log_term()
             (log(3), 2*log(x))
@@ -3550,7 +3550,7 @@ def is_constant(self):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: T = TermMonoid('exact', GrowthGroup('x^ZZ * log(x)^ZZ'), QQ)
             sage: T('x * log(x)').is_constant()
             False
@@ -3579,7 +3579,7 @@ def is_little_o_of_one(self):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: T = TermMonoid('exact', GrowthGroup('x^ZZ'), QQ)
             sage: T(x).is_little_o_of_one()
             False
@@ -3624,7 +3624,7 @@ def is_exact(self):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: T = TermMonoid('exact', GrowthGroup('x^ZZ * log(x)^ZZ'), QQ)
             sage: T('x * log(x)').is_exact()
             True
@@ -3655,7 +3655,7 @@ def rpow(self, base):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: T = TermMonoid('exact', GrowthGroup('QQ^x * x^ZZ * log(x)^ZZ'), QQ)
             sage: T('x').rpow(2)
             2^x
@@ -3730,7 +3730,7 @@ def _substitute_(self, rules):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: E = TermMonoid('exact', GrowthGroup('x^ZZ'), ZZ)
             sage: e = E.an_element(); e
             x
@@ -3778,7 +3778,7 @@ def _factorial_(self):
         TESTS::
 
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: T = TermMonoid('exact', 'z^QQ', QQ)
             sage: T('4')._factorial_()
             24
@@ -3822,7 +3822,7 @@ def _singularity_analysis_(self, var, zeta, precision):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: T = TermMonoid('exact', GrowthGroup('x^QQ'), ZZ)
             sage: T('5*x^(1/2)')._singularity_analysis_('n', 2, precision=2)
             5/sqrt(pi)*(1/2)^n*n^(-1/2)
@@ -3860,7 +3860,7 @@ class ExactTermMonoid(TermWithCoefficientMonoid):
         sage: from sage.rings.asymptotic.growth_group import GrowthGroup
         sage: from sage.rings.asymptotic.term_monoid import ExactTermMonoid
         sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-        sage: TermMonoid = TermMonoidFactory('TermMonoid')
+        sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
         sage: G_ZZ = GrowthGroup('x^ZZ'); x_ZZ = G_ZZ.gen()
         sage: G_QQ = GrowthGroup('x^QQ'); x_QQ = G_QQ.gen()
@@ -3901,7 +3901,7 @@ def _repr_(self):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: G = GrowthGroup('x^ZZ'); x = G.gen()
             sage: TermMonoid('exact', G, QQ)._repr_()
             'Exact Term Monoid x^ZZ with coefficients in Rational Field'
@@ -3945,7 +3945,7 @@ class TermMonoidFactory(UniqueRepresentation, UniqueFactory):
 
         sage: from sage.rings.asymptotic.growth_group import GrowthGroup
         sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-        sage: TermMonoid = TermMonoidFactory('TermMonoid')
+        sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
         sage: G = GrowthGroup('x^ZZ')
         sage: TermMonoid('O', G, QQ)
         O-Term Monoid x^ZZ with implicit coefficients in Rational Field
@@ -4041,7 +4041,7 @@ def __init__(self, name,
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import ExactTermMonoid, OTermMonoid
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
 
             sage: class MyExactTermMonoid(ExactTermMonoid):
             ....:     pass
@@ -4078,7 +4078,7 @@ def create_key_and_extra_args(self, term_monoid,
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: G = GrowthGroup('x^ZZ')
             sage: TermMonoid.create_key_and_extra_args('O', G, QQ)
             ((<class 'sage.rings.asymptotic.term_monoid.OTermMonoid'>,
@@ -4147,7 +4147,7 @@ def create_object(self, version, key, **kwds):
 
             sage: from sage.rings.asymptotic.growth_group import GrowthGroup
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: G = GrowthGroup('x^ZZ')
             sage: TermMonoid('O', G, QQ)  # indirect doctest
             O-Term Monoid x^ZZ with implicit coefficients in Rational Field
@@ -4176,7 +4176,7 @@ def _cache_key(self):
         TESTS::
 
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: TermMonoid._cache_key()
             (<class 'sage.rings.asymptotic.term_monoid.TermMonoidFactory'>,
              'TermMonoid',
@@ -4195,7 +4195,7 @@ def __hash__(self):
         TESTS::
 
             sage: from sage.rings.asymptotic.term_monoid import TermMonoidFactory
-            sage: TermMonoid = TermMonoidFactory('TermMonoid')
+            sage: TermMonoid = TermMonoidFactory('__main__.TermMonoid')
             sage: hash(TermMonoid)  # random
             42
         """