Am Freitag, 19. Juni 2020 18:40:34 UTC+2 schrieb Nils Bruin:
>
> All this disappears once we are happy using functions with two parameters
> as "action operation":
>
> left = G.acting_on_the_left_on(M) # or left = M.left_action_by(G)
>
> left(g,m)
>
> left = G.acting_on_the_right_on(M) # or left = M.right_action_by(G)
>
> right(m,g)
>
This functionality is already available for actions that are actually
implemented via Action:
sage: G = SymmetricGroup(3)
sage: M = MatrixSpace(QQ, 3)
sage: right = coercion_model.get_action(M, G)
sage: right(M.diagonal_matrix([1,2,3]), G('(2,3)')) # with #29808
⎛1 0 0⎞
⎜0 0 2⎟
⎝0 3 0⎠
For cases where this is not implemented, it is possible to construct and
register custom actions (a factory function for this might be useful). For
example, the right action of the symmetric group on the integers via
exponentiation:
sage: class CallAction(sage.categories.action.Action):
....: def _act_(self, g, a):
....: return g(a)
sage: G = SymmetricGroup(3); g, h = G('(1,2,3)'), G('(2,3)')
sage: right = CallAction(G, ZZ, is_left=False, op=operator.pow)
sage: right(right(1, g), h)
3
sage: ZZ._unset_coercions_used()
sage: ZZ.register_action(right)
sage: (1 ^ g) ^ h
3
sage: 1 ^ (g * h)
3
It is not currently possible to use shift operators for this, as they are
not implemented in sage.structure.element. Also, it might not be easily
possible to support the operator syntax for actions on non-Sage types such
as Python lists.
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