Methods for permutation group elements

[nthiery]

Add the following features to permutation group elements:

    def support(self):
        """
        Return the support of ``self`` that is the points that are not fixed.
        """

    def fixed_points(self): ?
        ...

    def cycle_type(self):
        """
        Return the cycle type of ``self``.
        """

Besides, for concistency with the cycle_tuples method, the cycles method could accept the option singleton. It's questionable whether we want to have those two very similar methods in the first place.

See also the discussion in #14319.

CC: @sagetrac-sage-combinat @tscrim

Component: group theory

Issue created by migration from https://trac.sagemath.org/ticket/15357

[nthiery]

Description changed:

--- 
+++ 
@@ -8,6 +8,14 @@

     def fixed_points(self): ?
         ...
+
+    def cycle_type(self):
+        """
+        Return the cycle type of ``self``.
+        """
+

+Besides, for concistency with the cycle_tuples method, the cycles method could accept the option singleton. It's questionable whether we want to have those two very similar methods in the first place. + See also the discussion in #14319.