make PermutationGroup_generic.gens return a tuple, to ensure immutabi…

…lity

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

@@ -22250,17 +22250,17 @@ 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

src/sage/groups/perm_gps/permgroup.py

@@ -292,7 +292,7 @@ def PermutationGroup(gens=None, *args, **kwds):
         sage: H = PermutationGroup(G); H
         Transitive group number 3 of degree 4
         sage: H.gens()
-        [(1,2,3,4), (1,3)]
+        ((1,2,3,4), (1,3))
 
     We can also create permutation groups whose generators are Gap
     permutation objects::
@@ -486,9 +486,9 @@ def __init__(self, gens=None, gap_group=None, canonicalize=True,
 
         if not gens:  # length 0
             gens = [()]
-        gens = [self.element_class(x, self, check=False) for x in gens]
+        gens = tuple(self.element_class(x, self, check=False) for x in gens)
         if canonicalize:
-            gens = sorted(set(gens))
+            gens = tuple(sorted(set(gens)))
         self._gens = gens
 
     _libgap = None
@@ -1181,14 +1181,14 @@ def gens(self):
 
             sage: G = PermutationGroup([[(1,2,3)], [(1,2)]])
             sage: G.gens()
-            [(1,2), (1,2,3)]
+            ((1,2), (1,2,3))
 
         Note that the generators need not be minimal, though duplicates are
         removed::
 
             sage: G = PermutationGroup([[(1,2)], [(1,3)], [(2,3)], [(1,2)]])
             sage: G.gens()
-            [(2,3), (1,2), (1,3)]
+            ((2,3), (1,2), (1,3))
 
         We can use index notation to access the generators returned by
         ``self.gens``::
@@ -1258,7 +1258,7 @@ def gen(self, i=None):
             sage: A4 = PermutationGroup([[(1,2,3)],[(2,3,4)]]); A4
             Permutation Group with generators [(2,3,4), (1,2,3)]
             sage: A4.gens()
-            [(2,3,4), (1,2,3)]
+            ((2,3,4), (1,2,3))
             sage: A4.gen(0)
             (2,3,4)
             sage: A4.gen(1)
@@ -1998,7 +1998,7 @@ def _repr_(self):
             sage: AlternatingGroup(4)._repr_()
             'Alternating group of order 4!/2 as a permutation group'
         """
-        return "Permutation Group with generators %s"%self.gens()
+        return "Permutation Group with generators %s" % list(self.gens())
 
     def _latex_(self):
         r"""
@@ -2645,7 +2645,7 @@ def semidirect_product(self, N, mapping, check=True):
             sage: S.is_isomorphic(DihedralGroup(8))
             True
             sage: S.gens()
-            [(3,4,5,6,7,8,9,10), (1,2)(4,10)(5,9)(6,8)]
+            ((3,4,5,6,7,8,9,10), (1,2)(4,10)(5,9)(6,8))
 
         A more complicated example can be drawn from [TW1980]_.
         It is there given that a semidirect product of $D_4$ and $C_3$
@@ -2745,7 +2745,7 @@ def semidirect_product(self, N, mapping, check=True):
                 raise ValueError(msg)
 
         # create a parallel list of the automorphisms of N in GAP
-        libgap.eval('N := Group({})'.format(N.gens()))
+        libgap.eval('N := Group({})'.format(list(N.gens())))
         gens_string = ",".join(str(x) for x in N.gens())
         homomorphism_cmd = 'alpha := GroupHomomorphismByImages(N, N, [{0}],[{1}])'
         libgap.eval('morphisms := []')
@@ -2799,7 +2799,7 @@ def holomorph(self):
             sage: D4 = DihedralGroup(4)
             sage: H = D4.holomorph()
             sage: H.gens()
-            [(3,8)(4,7), (2,3,5,8), (2,5)(3,8), (1,4,6,7)(2,3,5,8), (1,8)(2,7)(3,6)(4,5)]
+            ((3,8)(4,7), (2,3,5,8), (2,5)(3,8), (1,4,6,7)(2,3,5,8), (1,8)(2,7)(3,6)(4,5))
             sage: G = H.subgroup([H.gens()[0],H.gens()[1],H.gens()[2]])
             sage: N = H.subgroup([H.gens()[3],H.gens()[4]])
             sage: N.is_normal(H)
@@ -2820,7 +2820,7 @@ def holomorph(self):
         - Kevin Halasz (2012-08-14)
         """
 
-        libgap.eval('G := Group({})'.format(self.gens()))
+        libgap.eval('G := Group({})'.format(list(self.gens())))
         libgap.eval('aut := AutomorphismGroup(G)')
         libgap.eval('alpha := InverseGeneralMapping(NiceMonomorphism(aut))')
         libgap.eval('product := SemidirectProduct(NiceObject(aut),alpha,G)')
@@ -4777,7 +4777,7 @@ class PermutationGroup_subgroup(PermutationGroup_generic):
         sage: K.ambient_group()
         Dihedral group of order 8 as a permutation group
         sage: K.gens()
-        [(1,2,3,4)]
+        ((1,2,3,4),)
     """
     def __init__(self, ambient, gens=None, gap_group=None, domain=None,
                  category=None, canonicalize=True, check=True):
@@ -4809,7 +4809,7 @@ def __init__(self, ambient, gens=None, gap_group=None, domain=None,
             sage: G = DihedralGroup(4)
             sage: H = CyclicPermutationGroup(4)
             sage: gens = H.gens(); gens
-            [(1,2,3,4)]
+            ((1,2,3,4),)
             sage: S = G.subgroup(gens)
             sage: S
             Subgroup generated by [(1,2,3,4)] of (Dihedral group of order 8 as a permutation group)
@@ -4947,7 +4947,7 @@ def _repr_(self):
             sage: S._repr_()
             'Subgroup generated by [(1,2,3,4)] of (Dihedral group of order 8 as a permutation group)'
         """
-        return "Subgroup generated by %s of (%s)" % (self.gens(), self.ambient_group())
+        return "Subgroup generated by %s of (%s)" % (list(self.gens()), self.ambient_group())
 
     def _latex_(self):
         r"""

src/sage/groups/perm_gps/permgroup_morphism.py

@@ -281,7 +281,7 @@ def _repr_defn(self):
             sage: phi._repr_defn()
             '[(1,2,3,4)] -> [(1,2,3,4)]'
         """
-        return "%s -> %s"%(self.domain().gens(), self._images)
+        return "%s -> %s"%(list(self.domain().gens()), self._images)
 
     def _gap_(self):
         """

src/sage/groups/perm_gps/permgroup_named.py

@@ -1191,7 +1191,7 @@ class GeneralDihedralGroup(PermutationGroup_generic):
         sage: G.order()
         18
         sage: G.gens()
-        [(4,5,6), (2,3)(5,6), (1,2,3)]
+        ((4,5,6), (2,3)(5,6), (1,2,3))
         sage: a = G.gens()[2]; b = G.gens()[0]; c = G.gens()[1]
         sage: a.order() == 3, b.order() == 3, c.order() == 2
         (True, True, True)
@@ -1212,7 +1212,7 @@ class GeneralDihedralGroup(PermutationGroup_generic):
         sage: G.order()
         16
         sage: G.gens()
-        [(7,8), (5,6), (3,4), (1,2)]
+        ((7,8), (5,6), (3,4), (1,2))
         sage: G.is_abelian()
         True
         sage: H = KleinFourGroup()
@@ -1385,10 +1385,10 @@ def __init__(self, n):
             sage: DihedralGroup(2)
             Dihedral group of order 4 as a permutation group
             sage: DihedralGroup(2).gens()
-            [(3,4), (1,2)]
+            ((3,4), (1,2))
 
             sage: DihedralGroup(5).gens()
-            [(1,2,3,4,5), (1,5)(2,4)]
+            ((1,2,3,4,5), (1,5)(2,4))
             sage: sorted(DihedralGroup(5))
             [(), (2,5)(3,4), (1,2)(3,5), (1,2,3,4,5), (1,3)(4,5), (1,3,5,2,4), (1,4)(2,3), (1,4,2,5,3), (1,5,4,3,2), (1,5)(2,4)]
 
@@ -1401,7 +1401,7 @@ def __init__(self, n):
             sage: G
             Dihedral group of order 10 as a permutation group
             sage: G.gens()
-            [(1,2,3,4,5), (1,5)(2,4)]
+            ((1,2,3,4,5), (1,5)(2,4))
 
             sage: DihedralGroup(0)
             Traceback (most recent call last):
@@ -1644,7 +1644,7 @@ def __init__(self,m):
             sage: len([H for H in G.subgroups() if H.is_cyclic() and H.order() == 8])
             1
             sage: G.gens()
-            [(2,4)(3,7)(6,8), (1,2,3,4,5,6,7,8)]
+            ((2,4)(3,7)(6,8), (1,2,3,4,5,6,7,8))
             sage: x = G.gens()[1]; y = G.gens()[0]
             sage: x.order() == 2^3; y.order() == 2
             True
@@ -1783,7 +1783,7 @@ def __init__(self, d, n):
             sage: G = TransitiveGroup(5, 2); G
             Transitive group number 2 of degree 5
             sage: G.gens()
-            [(1,2,3,4,5), (1,4)(2,3)]
+            ((1,2,3,4,5), (1,4)(2,3))
 
             sage: G.category()
             Category of finite enumerated permutation groups
@@ -2170,7 +2170,7 @@ class PrimitiveGroup(PermutationGroup_unique):
         sage: G = PrimitiveGroup(5, 2); G
         D(2*5)
         sage: G.gens()
-        [(2,4)(3,5), (1,2,3,5,4)]
+        ((2,4)(3,5), (1,2,3,5,4))
         sage: G.category()
         Category of finite enumerated permutation groups
 

src/sage/rings/polynomial/polynomial_rational_flint.pyx

@@ -2107,7 +2107,7 @@ cdef class Polynomial_rational_flint(Polynomial):
             sage: G = f.galois_group(); G
             Transitive group number 5 of degree 4
             sage: G.gens()
-            [(1,2), (1,2,3,4)]
+            ((1,2), (1,2,3,4))
             sage: G.order()
             24
 

src/sage/tests/books/judson-abstract-algebra/actions-sage.py

@@ -152,7 +152,7 @@
 ~~~~~~~~~~~~~~~~~~~~~~ ::
 
     sage: A.orbits()
-    [[0, 10], [1, 9], [2, 8], [3, 7], [4, 6], [5]]
+    ((0, 10), (1, 9), (2, 8), (3, 7), (4, 6), (5,))
 
 ~~~~~~~~~~~~~~~~~~~~~~ ::
 
@@ -169,6 +169,6 @@
     sage: G = SymmetricGroup(4)
     sage: S = G.stabilizer(4)
     sage: S.orbits()
-    [[1, 2, 3], [4]]
+    ((1, 2, 3), (4,))
 
 """

src/sage/tests/books/judson-abstract-algebra/galois-sage.py

@@ -265,16 +265,16 @@
 
     sage: sg = P.subgroups()
     sage: [H.gens() for H in sg]
-    [[()],
-     [(1,4)(2,3)],
-     [(2,3)],
-     [(1,4)],
-     [(1,2)(3,4)],
-     [(1,3)(2,4)],
-     [(2,3), (1,4)(2,3)],
-     [(1,2,4,3), (1,4)(2,3)],
-     [(1,2)(3,4), (1,4)(2,3)],
-     [(2,3), (1,2,4,3), (1,4)(2,3)]]
+    [((),),
+     ((1,4)(2,3),),
+     ((2,3),),
+     ((1,4),),
+     ((1,2)(3,4),),
+     ((1,3)(2,4),),
+     ((2,3), (1,4)(2,3)),
+     ((1,2,4,3), (1,4)(2,3)),
+     ((1,2)(3,4), (1,4)(2,3)),
+     ((2,3), (1,2,4,3), (1,4)(2,3))]
 
 ~~~~~~~~~~~~~~~~~~~~~~ ::
 

src/sage/tests/books/judson-abstract-algebra/homomorph-sage-exercises.py

@@ -45,7 +45,7 @@
     sage: results = G.direct_product(H)
     sage: phi = results[2]
     sage: H.gens()
-    [(1,2,3,4), (1,4)(2,3)]
+    ((1,2,3,4), (1,4)(2,3))
 
 ~~~~~~~~~~~~~~~~~~~~~~ ::
 

src/sage/tests/books/judson-abstract-algebra/homomorph-sage.py

@@ -104,13 +104,13 @@
     sage: G = DihedralGroup(5)
     sage: H = DihedralGroup(20)
     sage: G.gens()
-    [(1,2,3,4,5), (1,5)(2,4)]
+    ((1,2,3,4,5), (1,5)(2,4))
 
 ~~~~~~~~~~~~~~~~~~~~~~ ::
 
     sage: H.gens()
-    [(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20),
-     (1,20)(2,19)(3,18)(4,17)(5,16)(6,15)(7,14)(8,13)(9,12)(10,11)]
+    ((1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20),
+     (1,20)(2,19)(3,18)(4,17)(5,16)(6,15)(7,14)(8,13)(9,12)(10,11))
 
 ~~~~~~~~~~~~~~~~~~~~~~ ::