Trac #34493: Make TrivialFamily.map return a TrivialFamily

calling the `map` method of a `TrivialFamily` should give a
`TrivialFamily` again.

URL: https://trac.sagemath.org/34493
Reported by: mkoeppe
Ticket author(s): Matthias Koeppe
Reviewer(s): Travis Scrimshaw

Author: Release Manager

src/sage/categories/additive_magmas.py

@@ -519,7 +519,7 @@ def algebra_generators(self):
                     An example of a commutative semigroup: the free commutative semigroup generated by ('a', 'b', 'c', 'd')
                     sage: A = S.algebra(QQ)
                     sage: A.algebra_generators()
-                    Finite family {0: B[a], 1: B[b], 2: B[c], 3: B[d]}
+                    Family (B[a], B[b], B[c], B[d])
 
                 .. TODO::
 

src/sage/categories/additive_semigroups.py

@@ -153,7 +153,7 @@ def algebra_generators(self):
                     An example of a commutative semigroup: the free commutative semigroup generated by ('a', 'b', 'c', 'd')
                     sage: A = S.algebra(QQ)
                     sage: A.algebra_generators()
-                    Finite family {0: B[a], 1: B[b], 2: B[c], 3: B[d]}
+                    Family (B[a], B[b], B[c], B[d])
                 """
                 return self.basis().keys().additive_semigroup_generators().map(self.monomial)
 

src/sage/categories/monoids.py

@@ -556,18 +556,17 @@ def algebra_generators(self):
                     sage: Z12.semigroup_generators()
                     Family (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11)
                     sage: Z12.algebra(QQ).algebra_generators()
-                    Finite family {0: B[0], 1: B[1], 2: B[2], 3: B[3],  4: B[4],   5: B[5],
-                                   6: B[6], 7: B[7], 8: B[8], 9: B[9], 10: B[10], 11: B[11]}
+                    Family (B[0], B[1], B[2], B[3], B[4], B[5], B[6], B[7], B[8], B[9], B[10], B[11])
 
 
                     sage: GroupAlgebras(QQ).example(AlternatingGroup(10)).algebra_generators()
-                    Finite family {0: (8,9,10), 1: (1,2,3,4,5,6,7,8,9)}
+                    Family ((8,9,10), (1,2,3,4,5,6,7,8,9))
 
                     sage: A = DihedralGroup(3).algebra(QQ); A
                     Algebra of Dihedral group of order 6 as a permutation group
                      over Rational Field
                     sage: A.algebra_generators()
-                    Finite family {0: (1,2,3), 1: (1,3)}
+                    Family ((1,2,3), (1,3))
                 """
                 monoid = self.basis().keys()
                 try:

src/sage/categories/semigroups.py

@@ -882,7 +882,7 @@ def algebra_generators(self):
                     sage: M.semigroup_generators()
                     Family ('a', 'b', 'c', 'd')
                     sage: M.algebra(ZZ).algebra_generators()
-                    Finite family {0: B['a'], 1: B['b'], 2: B['c'], 3: B['d']}
+                    Family (B['a'], B['b'], B['c'], B['d'])
                 """
                 return self.basis().keys().semigroup_generators().map(self.monomial)
 

src/sage/sets/family.py

@@ -1380,6 +1380,23 @@ def __setstate__(self, state):
         """
         self.__init__(state['_enumeration'])
 
+    def map(self, f, name=None):
+        r"""
+        Return the family `( f(\mathtt{self}[i]) )_{i \in I}`,
+        where `I` is the index set of ``self``.
+
+        The result is again a :class:`TrivialFamily`.
+
+        EXAMPLES::
+
+            sage: from sage.sets.family import TrivialFamily
+            sage: f = TrivialFamily(['a', 'b', 'd'])
+            sage: g = f.map(lambda x: x + '1'); g
+            Family ('a1', 'b1', 'd1')
+        """
+        # tuple([... for ...]) is faster than tuple(... for ...)
+        return Family(tuple([f(x) for x in self._enumeration]), name=name)
+
 
 from sage.sets.non_negative_integers import NonNegativeIntegers
 from sage.rings.infinity import Infinity