Trac #33824: make gens and orbits of PermutationGroup immutable

We don't want the following to happen:
{{{
sage: G = PermutationGroup([ [(3,4)], [(1,3)] ])
sage: O = G.orbits(); O
[[1, 3, 4], [2]]
sage: O[0] = 1
sage: G.orbits()
[1, [2]]

sage: G = PermutationGroup([[2,1]]); G
Permutation Group with generators [(1,2)]
sage: g = G.gens()
sage: g[0] = 1
sage: G.gens()
[1]
}}}
Therefore, we change the return type of `gens` and `orbits` to be a
tuple of tuples.  We keep the `_repr_` of `PermutationGroup_generic`,
because the output is more compact.

Note that `gens` returns a tuple for all other groups I checked.

URL: https://trac.sagemath.org/33824
Reported by: mantepse
Ticket author(s): Martin Rubey
Reviewer(s): Travis Scrimshaw

src/sage/categories/pushout.py

@@ -3522,7 +3522,7 @@ def __init__(self, gens, domain):
             PermutationGroupFunctor[(1,2)]
         """
         Functor.__init__(self, Groups(), Groups())
-        self._gens = gens
+        self._gens = tuple(gens)
         self._domain = domain
 
     def _repr_(self):
@@ -3534,7 +3534,7 @@ def _repr_(self):
             sage: PF
             PermutationGroupFunctor[(1,2)]
         """
-        return "PermutationGroupFunctor%s" % self.gens()
+        return "PermutationGroupFunctor%s" % list(self.gens())
 
     def __call__(self, R):
         """
@@ -3556,7 +3556,7 @@ def gens(self):
             sage: P1 = PermutationGroup([[(1,2)]])
             sage: PF, P = P1.construction()
             sage: PF.gens()
-            [(1,2)]
+            ((1,2),)
         """
         return self._gens
 

src/sage/coding/codecan/autgroup_can_label.pyx

@@ -73,10 +73,10 @@ columns do share the same coloring::
     sage: A = [a.get_perm() for a in P.get_autom_gens()]
     sage: H = SymmetricGroup(21).subgroup(A)
     sage: H.orbits()
-    [[1],
-     [2],
-     [3, 5, 4],
-     [6, 19, 16, 9, 21, 10, 8, 15, 14, 11, 20, 13, 12, 7, 17, 18]]
+    ((1,),
+     (2,),
+     (3, 5, 4),
+     (6, 19, 16, 9, 21, 10, 8, 15, 14, 11, 20, 13, 12, 7, 17, 18))
 
 We can also restrict the group action to linear isometries::
 

src/sage/graphs/generic_graph.py

@@ -22419,17 +22419,17 @@ def automorphism_group(self, partition=None, verbosity=0,
             sage: for g in L:
             ....:     G = g.automorphism_group()
             ....:     G.order(), G.gens()
-            (24, [(2,3), (1,2), (0,1)])
-            (4, [(2,3), (0,1)])
-            (2, [(1,2)])
-            (6, [(1,2), (0,1)])
-            (6, [(2,3), (1,2)])
-            (8, [(1,2), (0,1)(2,3)])
-            (2, [(0,1)(2,3)])
-            (2, [(1,2)])
-            (8, [(2,3), (0,1), (0,2)(1,3)])
-            (4, [(2,3), (0,1)])
-            (24, [(2,3), (1,2), (0,1)])
+            (24, ((2,3), (1,2), (0,1)))
+            (4, ((2,3), (0,1)))
+            (2, ((1,2),))
+            (6, ((1,2), (0,1)))
+            (6, ((2,3), (1,2)))
+            (8, ((1,2), (0,1)(2,3)))
+            (2, ((0,1)(2,3),))
+            (2, ((1,2),))
+            (8, ((2,3), (0,1), (0,2)(1,3)))
+            (4, ((2,3), (0,1)))
+            (24, ((2,3), (1,2), (0,1)))
             sage: C = graphs.CubeGraph(4)
             sage: G = C.automorphism_group()
             sage: M = G.character_table() # random order of rows, thus abs() below