Hi David,
On 2013-07-16, David Kohel <drko...@gmail.com> wrote:
> Defining the (left or right) action by * would probably be a
> nightmare with the coercion model, since it is handled as
> a symmetric operator.
Is this really so?
There is stuff in sage.structure.coerce, for example methods
R.get_action(S,operator.mul),
which can be overloaded using R._get_action_, where you can also decide on the
side from which S acts.
Hence, if you want to let S act on R from the left by multiplication, you could
simply let S._get_action_(R, operator.mul, True) return an action, and
if you want to let S act on R from the right by multiplication, you
could let S._get_action_(R, operator.mul, False) return an action.
Here, "action" means something like the stuff in
sage.structure.coerce_acitons.
Let's try an example:
sage: from sage.structure.coerce_actions import GenericAction
sage: class MyAction(GenericAction):
....: def _call_(self, x, y):
....: if self.is_left():
....: return x.left_action(y)
....: return y.right_action(x)
....:
sage: from sage.structure.element import Element
sage: class MyElement(Element):
....: def __init__(self, s, parent=None):
....: self.s = s
....: Element.__init__(self, parent)
....: def left_action(self, n):
....: return self.__class__(self.s+repr(n), self.parent())
....: def right_action(self, n):
....: return self.__class__(self.s*n, self.parent())
....:
sage: class MyParent(Parent):
....: Element = MyElement
....: def _get_action_(self, S, op, self_is_left):
....: if op is operator.mul:
....: return MyAction(self, S, self_is_left, check=False)
....: def _element_constructor_(self, s):
....: return self.element_class(s, self)
....:
sage: P = MyParent(category=Objects())
sage: a = P('hi')
sage: a.s
'hi'
sage: b = a*5
sage: b.s
'hi5'
sage: c = 3*a
sage: c.s
'hihihi'
So, this should show how to implement left and right actions.
Of course, the mathematical property of being an action must be ensured
by a correct implementation of the action.
In particular, note that technically I have implemented an action of
MyParent on ZZ, but in fact I did so in order to get two different
actions of ZZ on MyParent.
Best regards,
Simon
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