doctest parameter log_function

src/sage/rings/asymptotic/asymptotic_ring.py

@@ -1929,8 +1929,32 @@ def log(self, base=None, precision=None, log_function=None):
             sage: log(x-1)
             log(x) - x^(-1) - 1/2*x^(-2) - 1/3*x^(-3) - ... + O(x^(-21))
 
+        The coefficient ring aus automatically extended if needed::
+
+            sage: R.<x> = AsymptoticRing(growth_group='x^ZZ * log(x)^ZZ', coefficient_ring=ZZ, default_prec=3)
+            sage: (49*x^3-1).log()
+            3*log(x) + log(49) - 1/49*x^(-3) - 1/4802*x^(-6) ... + O(x^(-12))
+            sage: _.parent()
+            Asymptotic Ring <x^ZZ * log(x)^ZZ> over Symbolic Ring
+
+        If one wants to avoid this extending to the Symbolic Ring, then
+        the following helps::
+
+            sage: L.<log7> = ZZ[]
+            sage: def log_function(z, base=None):
+            ....:     try:
+            ....:         if ZZ(z).is_power_of(7):
+            ....:             return log(ZZ(z), 7) * log7
+            ....:     except TypeError, ValueError:
+            ....:         pass
+            ....:     return log(z, base)
+            sage: R.<x> = AsymptoticRing(growth_group='x^ZZ * log(x)^ZZ', coefficient_ring=L, default_prec=3)
+            sage: (49*x^3-1).log(log_function=log_function)
+            3*log(x) + 2*log7 - 1/49*x^(-3) - 1/4802*x^(-6) ... + O(x^(-12))
+
         TESTS::
 
+            sage: R.<x> = AsymptoticRing(growth_group='x^ZZ * log(x)^ZZ', coefficient_ring=QQ)
             sage: log(R(1))
             0
             sage: log(R(0))

src/sage/rings/asymptotic/growth_group.py

@@ -2818,6 +2818,17 @@ def _log_factor_(self, base=None, log_function=None):
             ArithmeticError: When calculating log(exp(x), base=2) a factor
             1/log(2) != 1 appeared, which is not contained in
             Growth Group exp(x)^ZZ * x^ZZ.
+
+        ::
+
+            sage: from sage.rings.asymptotic.growth_group import MonomialGrowthGroup
+            sage: L.<log2> = ZZ[]
+            sage: G = MonomialGrowthGroup(L, 'x')
+            sage: G(raw_element=log2)._log_factor_(base=2)
+            (('log(x)', log2/log(2)),)
+            sage: G(raw_element=log2)._log_factor_(base=2,
+            ....:       log_function=lambda z: log2 if z == 2 else log(z))
+            (('log(x)', 1),)
         """
         if self.is_one():
             return tuple()
@@ -3723,6 +3734,17 @@ def _log_factor_(self, base=None, log_function=None):
             ...
             ArithmeticError: Cannot build log(4^x, base=2) since x is not in
             Growth Group QQ^x.
+
+        ::
+
+            sage: from sage.rings.asymptotic.growth_group import ExponentialGrowthGroup
+            sage: L.<log2> = ZZ[]
+            sage: G = ExponentialGrowthGroup(L, 'x')
+            sage: G(raw_element=2)._log_factor_()
+            (('x', log(2)),)
+            sage: G(raw_element=2)._log_factor_(
+            ....:       log_function=lambda z, base: log2 if z == 2 else log(z))
+            (('x', log2),)
         """
         if self.is_one():
             return tuple()

src/sage/rings/asymptotic/term_monoid.py

@@ -2965,6 +2965,20 @@ def _log_coefficient_(self, base=None, log_function=None):
 
             :meth:`ExactTerm.log_term`,
             :meth:`OTerm.log_term`.
+
+        TESTS::
+
+            sage: L.<log3> = QQ[]
+            sage: T = TermMonoid('exact', GrowthGroup('x^ZZ * log(x)^ZZ'), L)
+            sage: T(3*x^2)._log_coefficient_()
+            (log(3),)
+            sage: log_function=lambda z, base: log3 if z == 3 else log(z)
+            sage: T(3*x^2)._log_coefficient_(log_function=log_function)
+            (log3,)
+            sage: T(3*x^2).log_term()  # indirect doctest
+            (log(3), 2*log(x))
+            sage: T(3*x^2).log_term(log_function=log_function)  # indirect doctest
+            (log3, 2*log(x))
         """
         if self.coefficient.is_one():
             return tuple()