Trac #19540: variable_names for growth elements

src/sage/rings/asymptotic/growth_group.py

@@ -1397,6 +1397,24 @@ def _substitute_(self, rules):
             'base class %s.' % (self.parent(),)))
 
 
+    def variable_names(self):
+        r"""
+        Return the names of the variables of this generic growth element.
+
+        OUTPUT:
+
+        A tuple of strings.
+
+        EXAMPLES::
+
+            sage: from sage.rings.asymptotic.growth_group import GenericGrowthGroup
+            sage: G = GenericGrowthGroup(QQ)
+            sage: G(raw_element=2).variable_names()
+            ()
+        """
+        return self.parent()._var_.variable_names()
+
+
 class GenericGrowthGroup(
         sage.structure.unique_representation.UniqueRepresentation,
         sage.structure.parent.Parent):
@@ -2814,6 +2832,29 @@ def _substitute_(self, rules):
             substitute_raise_exception(self, e)
 
 
+    def variable_names(self):
+        r"""
+        Return the names of the variables of this monomial growth element.
+
+        OUTPUT:
+
+        A tuple of strings.
+
+        EXAMPLES::
+
+            sage: from sage.rings.asymptotic.growth_group import GrowthGroup
+            sage: G = GrowthGroup('m^QQ')
+            sage: G('m^2').variable_names()
+            ('m',)
+            sage: G('m^0').variable_names()
+            ()
+        """
+        if self.is_one():
+            return tuple()
+        else:
+            return self.parent()._var_.variable_names()
+
+
 class MonomialGrowthGroup(GenericGrowthGroup):
     r"""
     A growth group dealing with powers of a fixed object/symbol.
@@ -3480,6 +3521,29 @@ def _substitute_(self, rules):
             substitute_raise_exception(self, e)
 
 
+    def variable_names(self):
+        r"""
+        Return the names of the variables of this exponential growth element.
+
+        OUTPUT:
+
+        A tuple of strings.
+
+        EXAMPLES::
+
+            sage: from sage.rings.asymptotic.growth_group import GrowthGroup
+            sage: G = GrowthGroup('QQ^m')
+            sage: G('2^m').variable_names()
+            ('m',)
+            sage: G('1^m').variable_names()
+            ()
+        """
+        if self.is_one():
+            return tuple()
+        else:
+            return self.parent()._var_.variable_names()
+
+
 class ExponentialGrowthGroup(GenericGrowthGroup):
     r"""
     A growth group dealing with expressions involving a fixed

src/sage/rings/asymptotic/growth_group_cartesian.py

@@ -1191,6 +1191,36 @@ def _substitute_(self, rules):
                 substitute_raise_exception(self, e)
 
 
+        def variable_names(self):
+            r"""
+            Return the names of the variables of this growth element.
+
+            OUTPUT:
+
+            A tuple of strings.
+
+            EXAMPLES::
+
+                sage: from sage.rings.asymptotic.growth_group import GrowthGroup
+                sage: G = GrowthGroup('QQ^m * m^QQ * log(n)^ZZ')
+                sage: G('2^m * m^4 * log(n)').variable_names()
+                ('m', 'n')
+                sage: G('2^m * m^4').variable_names()
+                ('m',)
+                sage: G('log(n)').variable_names()
+                ('n',)
+                sage: G('m^3').variable_names()
+                ('m',)
+                sage: G('m^0').variable_names()
+                ()
+            """
+            vars = sum(iter(factor.variable_names()
+                            for factor in self.factors()),
+                       tuple())
+            from itertools import groupby
+            return tuple(v for v, _ in groupby(vars))
+
+
     CartesianProduct = CartesianProductGrowthGroups