Merge branch 'asy/map_coefficients' into asy/generators-binomial

* asy/map_coefficients:
  write map_coefficients
  correct a bug in change_parameter
  term monoid: write change_parameter
  mutable poset map: remove elements ``None``

src/sage/data_structures/mutable_poset.py

@@ -3451,6 +3451,11 @@ def map(self, function, topological=False, reverse=False):
             Since this method works inplace, it is not allowed that
             ``function`` alters the key of an element.
 
+        .. NOTE::
+
+            If ``function`` returns ``None``, then the element is
+            removed after the mapping.
+
         EXAMPLES::
 
             sage: from sage.data_structures.mutable_poset import MutablePoset as MP
@@ -3464,15 +3469,25 @@ def map(self, function, topological=False, reverse=False):
             sage: P
             poset((1, 2, 3), (1, 3, 4), (2, 1, 3), (2, 2, 4), (4, 4, 8))
 
+        TESTS::
+
+            sage: P.map(lambda e: e if e[2] != 4 else None); P
+            poset((1, 2, 3), (2, 1, 3), (4, 4, 8))
+
         .. SEEALSO::
 
             :meth:`copy`,
             :meth:`mapped`.
         """
         shells = self.shells_topological(reverse=reverse) \
             if topological else self.shells()
+        remove = []
         for shell in shells:
             shell._element_ = function(shell._element_)
+            if shell._element_ is None:
+                remove.append(shell.key)
+        for key in remove:
+            self.remove(key)
 
 
     def mapped(self, function):

src/sage/rings/asymptotic/asymptotic_ring.py

@@ -2119,6 +2119,59 @@ def symbolic_expression(self, R=None):
     _symbolic_ = symbolic_expression  # will be used by SR._element_constructor_
 
 
+    def map_coefficients(self, f, new_coefficient_ring=None):
+        r"""
+        Return the asymptotic expansion obtained by applying ``f`` to
+        each coefficient of this asymptotic expansion.
+
+        INPUT:
+
+        - ``f`` -- a callable. A coefficient `c` will be mapped to `f(c)`.
+
+        - ``new_coefficient_ring`` -- (default: ``None``) a ring.
+
+        OUTPUT:
+
+        An asymptotic expansion.
+
+        EXAMPLES::
+
+            sage: A.<n> = AsymptoticRing(growth_group='n^ZZ', coefficient_ring=ZZ)
+            sage: a = n^4 + 2*n^3 + 3*n^2 + O(n)
+            sage: a.map_coefficients(lambda c: c+1)
+            2*n^4 + 3*n^3 + 4*n^2 + O(n)
+            sage: a.map_coefficients(lambda c: c-2)
+            -n^4 + n^2 + O(n)
+
+        TESTS::
+
+            sage: a.map_coefficients(lambda c: 1/c, new_coefficient_ring=QQ)
+            n^4 + 1/2*n^3 + 1/3*n^2 + O(n)
+            sage: _.parent()
+            Asymptotic Ring <n^ZZ> over Rational Field
+            sage: a.map_coefficients(lambda c: 1/c)
+            Traceback (most recent call last):
+            ...
+            ValueError: ... is not a coefficient in
+            Exact Term Monoid n^ZZ with coefficients in Integer Ring.
+        """
+        def mapping(term):
+            T = term.parent().change_parameter(
+                coefficient_ring=new_coefficient_ring)
+            if hasattr(term, 'coefficient'):
+                c = f(term.coefficient)
+                if c == 0:
+                    return None
+                return T(term.growth, c)
+            else:
+                return T(term.growth)
+
+        P = self.parent().change_parameter(coefficient_ring=new_coefficient_ring)
+        S = self.summands.copy()
+        S.map(mapping)
+        return P(S, simplify=False, convert=False)
+
+
 class AsymptoticRing(Algebra, UniqueRepresentation):
     r"""
     A ring consisting of :class:`asymptotic expansions <AsymptoticExpansion>`.
@@ -2453,11 +2506,16 @@ def change_parameter(self, **kwds):
 
             sage: A.change_parameter(coefficient_ring=ZZ) is A
             True
+            sage: A.change_parameter(coefficient_ring=None) is A
+            True
         """
         parameters = ('growth_group', 'coefficient_ring', 'default_prec')
         values = dict()
         for parameter in parameters:
-            values[parameter] = kwds.get(parameter, getattr(self, parameter))
+            default = getattr(self, parameter)
+            values[parameter] = kwds.get(parameter, default)
+            if values[parameter] is None:
+                values[parameter] = default
         values['category'] = self.category()
         if isinstance(values['growth_group'], str):
             from growth_group import GrowthGroup

src/sage/rings/asymptotic/term_monoid.py

@@ -1456,6 +1456,52 @@ def coefficient_ring(self):
         return self._coefficient_ring_
 
 
+    def change_parameter(self, growth_group=None, coefficient_ring=None):
+        r"""
+        Return a term monoid with a change in one or more of the
+        given parameters.
+
+        INPUT:
+
+        - ``growth_group`` -- (default: ``None``) the new growth group.
+
+        - ``coefficient_ring`` -- (default: ``None``) the new coefficient ring.
+
+        OUTPUT:
+
+        A term monoid.
+
+        EXAMPLES::
+
+            sage: from sage.rings.asymptotic.growth_group import GrowthGroup
+            sage: from sage.rings.asymptotic.term_monoid import 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
+            sage: E.change_parameter(growth_group=GrowthGroup('n^QQ'))
+            Exact Term Monoid n^QQ with coefficients in Integer Ring
+
+        TESTS::
+
+            sage: E.change_parameter() is E
+            True
+            sage: E.change_parameter(growth_group=None) is E
+            True
+            sage: E.change_parameter(coefficient_ring=None) is E
+            True
+            sage: E.change_parameter(growth_group=None, coefficient_ring=None) is E
+            True
+        """
+        if growth_group is None:
+            growth_group = self.growth_group
+        if coefficient_ring is None:
+            coefficient_ring = self.coefficient_ring
+        if self.growth_group is growth_group and \
+                self.coefficient_ring is coefficient_ring:
+            return self
+        return TermMonoid(self, growth_group, coefficient_ring)
+
+
     def _repr_(self):
         r"""
         A representation string for this generic term monoid.