variable_names

src/sage/rings/asymptotic/growth_group.py

@@ -1213,6 +1213,23 @@ def gens_monomial(self):
                                   " implementations.")
 
 
+    def variable_names(self):
+        r"""
+        Return the names of the variables.
+
+        OUTPUT:
+
+        A tuple of strings.
+
+        EXAMPLES::
+
+            sage: import sage.rings.asymptotic.growth_group as agg
+            sage: agg.GenericGrowthGroup(ZZ).variable_names()
+            ()
+        """
+        return tuple()
+
+
     CartesianProduct = CartesianProductGrowthGroups
 
 
@@ -1870,6 +1887,25 @@ def ngens(self):
         return len(self.gens())
 
 
+    def variable_names(self):
+        r"""
+        Return the names of the variables.
+
+        OUTPUT:
+
+        A tuple of strings.
+
+        EXAMPLES::
+
+            sage: from sage.rings.asymptotic.growth_group import GrowthGroup
+            sage: GrowthGroup('x^ZZ').variable_names()
+            ('x',)
+            sage: GrowthGroup('log(x)^ZZ').variable_names()
+            ('x',)
+        """
+        return self._var_.variable_names()
+
+
 class GrowthGroupFactory(sage.structure.factory.UniqueFactory):
     r"""
     A factory creating asymptotic growth groups.

src/sage/rings/asymptotic/growth_group_cartesian.py

@@ -66,7 +66,7 @@ def create_object(self, version, growth_groups, **kwds):
 
         # check if multivariate and all have distinct single variables
         vg = tuple((g.variable_names(), g) for g in growth_groups)
-        vars = add(iter(v for v, _ in vg), tuple())
+        vars = sum(iter(v for v, _ in vg), tuple())
         if len(vars) != len(set(vars)):
             raise ValueError('Growth groups %s do not have distinct variables.' %
                              growth_groups)
@@ -313,6 +313,27 @@ def gens_monomial(self):
         return t
 
 
+    def variable_names(self):
+        r"""
+        Return the names of the variables.
+
+        OUTPUT:
+
+        A tuple of strings.
+
+        EXAMPLES::
+
+            sage: from sage.rings.asymptotic.growth_group import GrowthGroup
+            sage: GrowthGroup('x^ZZ * log(x)^ZZ * y^QQ * log(z)^ZZ').variable_names()
+            ('x', 'y', 'z')
+        """
+        vars = sum(iter(factor.variable_names()
+                        for factor in self.cartesian_factors()),
+                   tuple())
+        from itertools import groupby
+        return tuple(v for v, _ in groupby(vars))
+
+
     class Element(CartesianProductPosets.Element):
         def _repr_(self):
             r"""