On Tue, May 10, 2011 at 05:00:29AM -0700, Bruce wrote:
> My main problem now is that I don't know how to implement a new parent.
> Specifically a new monoid. I have looked at FreeMonoid and all I really
> got out of this was how to call the function.
Note:
sage: M = Monoids().example()
has nothing to do with FreeMonoid. The former is a basic
implementation meant as an example to implement new monoids. The
latter is a more full featured implementation (which by the way is not
yet refactored to use categories) .
Please use introspection to find the sources for M:
sage: M??
This will actually point you to sage/categories/examples/monoids.py
> I am still unclear about parents and categories. As I understand it these
> must be implemented using classes
> (including abstract classes and/or metaclasses which are still classes).
Yup. In principle you should not have to worry about metaclasses
(there is one behind the scene, but for a fairly localized technical
detail).
> Looking in FreeMonoid I find FreeMonoid_class and FreeMonoidFactory. I
> don't know what a factory is so I have to guess.
> My guess is that it is a function that returns a class. This would then
> give a construction of classes depending on parameters
> (for FreeMonoid the parameters are the set of generators).
Yes. See http://en.wikipedia.org/wiki/Factory_method_pattern.
The Monoids().example() implementation does not need it though.
> To construct a single monoid I would expect to define a class
> whose parent is Monoid and then to write the class methods (in
> this case one, returning the unit and mul, returning the
> product). There are several things Monoid or Monoids and I don't
> know what their roles are.
>
> However I would really want to construct monoids depending on
> parameters (which I would have thought was typical) and I don't
> know where to start with this.
Please have a look at sage/categories/examples/monoids.py, and get
back to us for things that will still need clarification.
> I am amazed that posets is immutable. How is that done?
The covering relations are computed, and this is used as a key to a
caching function when constructing a poset.
> I have not yet discovered how labelled posets are constructed.
> Have I missed something?
The current Poset implementation does not support labels indeed. If
you need thouse, you will need to use a DiGraph instead.
> Thank you for your patience with me.
You are welcome.
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <[email protected]>
http://Nicolas.Thiery.name/
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