Is there a way to multiply arbitrary permutations?
sage: P=Permutations(var('x y z'));P
Permutations of the set [x, y, z]
sage: P[1];P[2]
[x, z, y]
[y, x, z]
But now
sage: P[1]*P[2]
gives an error:
TypeError: unsupported operand parent(s) for *: 'Permutations of the set [x, y, z]' and 'Permutations of the set [x, y, z]'
I can't even evaluate such a permutation at an element.
sage: P[1](x)
results in
TypeError: 'Permutations_set_with_category.element_class' object is not callable
