From 65e1d7be9f84a1a7dbd49e963cef3ea2fb2c2c9a Mon Sep 17 00:00:00 2001 From: Martin Rubey Date: Wed, 13 Dec 2023 08:39:17 +0100 Subject: [PATCH] add is_trivial method --- src/sage/groups/perm_gps/permgroup.py | 23 +++++++++++++++++++++++ 1 file changed, 23 insertions(+) diff --git a/src/sage/groups/perm_gps/permgroup.py b/src/sage/groups/perm_gps/permgroup.py index b0083394cb0..585071fdb8c 100644 --- a/src/sage/groups/perm_gps/permgroup.py +++ b/src/sage/groups/perm_gps/permgroup.py @@ -1365,6 +1365,29 @@ def ngens(self): """ return len(self.gens()) + def is_trivial(self): + r""" + Return ``True`` if this group is the trivial group. + + A permutation group is trivial, if it consists only of the + identity element, that is, if it has no generators. + + EXAMPLES:: + + sage: G = PermutationGroup([], domain=["a", "b", "c"]) + sage: G.is_trivial() + True + sage: SymmetricGroup(0).is_trivial() + True + sage: SymmetricGroup(1).is_trivial() + True + sage: SymmetricGroup(2).is_trivial() + False + sage: DihedralGroup(1).is_trivial() + False + """ + return not self._gens or (len(self._gens) == 1 and self._gens[0].is_one()) + @cached_method def one(self): """