group multiplication seems to depend on order sometimes

[kcrisman]

See this ask.sagemath.org question. This doesn't always happen, but usually happens pretty soon.

sage: G.random_element()*H.random_element()
(1,3,2)
sage: H.random_element()*G.random_element()
()
sage: H.random_element()*G.random_element()
(1,2,3)
sage: H.random_element()*G.random_element()
(1,2,3)
sage: H.random_element()*G.random_element()
(1,3,2)
sage: H.random_element()*G.random_element()
ERROR: An unexpected error occurred while tokenizing input

TypeError: unsupported operand parent(s) for '*': 'Alternating group of order 3!/2 as a permutation group' and 'Symmetric group of order 3! as a permutation group'

Component: group theory

Issue created by migration from https://trac.sagemath.org/ticket/13569

[mezzarobba]

comment:3

sage: G = SymmetricGroup(3)
sage: H = AlternatingGroup(3)
sage: for g in G:
    for h in H:
        try:
            print h, "*", g, "=", h*g
        except TypeError:
            print "???"
....:             
() * () = ()
(1,2,3) * () = (1,2,3)
(1,3,2) * () = (1,3,2)
() * (2,3) = ???
(1,2,3) * (2,3) = ???
(1,3,2) * (2,3) = ???
() * (1,2) = ???
(1,2,3) * (1,2) = ???
(1,3,2) * (1,2) = ???
() * (1,2,3) = (1,2,3)
(1,2,3) * (1,2,3) = (1,3,2)
(1,3,2) * (1,2,3) = ()
() * (1,3,2) = (1,3,2)
(1,2,3) * (1,3,2) = ()
(1,3,2) * (1,3,2) = (1,2,3)
() * (1,3) = ???
(1,2,3) * (1,3) = ???
(1,3,2) * (1,3) = ???