Parents with a natural action on a space
Nicolas M. Thiery
Dan Bump recently raised the issue that the `lattice` method for Weyl
groups is badly named. I agree, but the issue is more general. Hence,
here is a call for good names.
Let P be a parent endowed with a natural action (or representation) on
a space `E`. For example:
- P is a group of permutations of E = {2,4,9,7}
- P is an algebra of matrices, acting on a vector space E
- P is a monoid of functions from E = {a,b,c} to itself
- P = End(E)
What should be the name of the method of P returning E ?
- P.domain() ?
- P.natural_representation() ?
- P.natural_representation_space() ?
- P.natural_module() ?
- P.action_set() ?
- something else?
My question goes in particular to the GAP experts like Dima: what
convention is used there?
Thanks for your feedback and votes!
Cheers,
Nicolas
--
Nicolas M. Thi�ry "Isil" <nth...@users.sf.net>
http://Nicolas.Thiery.name/
Alec Mihailovs
wrote:
> Dear Dima, dear Sage devs,
>
> Dan Bump recently raised the issue that the `lattice` method for Weyl
> groups is badly named. I agree, but the issue is more general. Hence,
> here is a call for good names.
>
> Let P be a parent endowed with a natural action (or representation) on
> a space `E`. For example:
>
> - P is a group of permutations of E = {2,4,9,7}
> - P is an algebra of matrices, acting on a vector space E
> - P is a monoid of functions from E = {a,b,c} to itself
> - P = End(E)
>
> What should be the name of the method of P returning E ?
>
> - P.domain() ?
> - P.natural_representation() ?
> - P.natural_representation_space() ?
> - P.natural_module() ?
> - P.action_set() ?
> - something else?
Maybe, P.over ? It could be a property, perhaps, rather than a method.
Alec Mihailovs
Nicolas M. Thiery
> > Dan Bump recently raised the issue that the `lattice` method for Weyl
> > groups is badly named. I agree, but the issue is more general. Hence,
> > here is a call for good names.
> >
> > Let P be a parent endowed with a natural action (or representation) on
> > a space `E`. For example:
> >
> > �- P is a group of permutations of E = {2,4,9,7}
> > �- P is an algebra of matrices, acting on a vector space E
> > �- P is a monoid of functions from E = {a,b,c} to itself
> > �- P = End(E)
> >
> > What should be the name of the method of P returning E ?
> >
> > �- P.domain() ?
> > �- P.natural_representation() ?
> > �- P.natural_representation_space() ?
> > �- P.natural_module() ?
> > �- P.action_set() ?
> > �- something else?
>
> Maybe, P.over ?
Thanks for the feedback.
> It could be a property, perhaps, rather than a method.
For good and bad, it's one of Sage's policy not to use properties in
the user interface.
I browsed the GAP documentation, and for a group action, they call
*domain* the space on which the group act:
http://www.gap-system.org/Manuals/doc/htm/ref/CHAP039.htm
which by chance is consistent with the `domain` method of Sage's homsets:
sage: V = FreeModule(QQ,3)
sage: End(V).domain()
Vector space of dimension 3 over Rational Field
So I vote for domain, even though it is a bit unspecific.
Anyone unhappy with this choice?
Georg S. Weber
On 23 Mrz., 00:08, "Nicolas M. Thiery" <Nicolas.Thi...@u-psud.fr>
wrote:
+1 for domain
Cheers,
Georg
> Anyone unhappy with this choice?
>
> Cheers,
> Nicolas
> --
> Nicolas M. Thi ry "Isil" <nthi...@users.sf.net>http://Nicolas.Thiery.name/
Robert Bradshaw
I like that too. This is what we use for actions in the coercion model.
sage: cm = sage.structure.element.get_coercion_model()
sage: cm.get_action(QQ, ZZ['x'], operator.mul)
Left scalar multiplication by Rational Field on Univariate Polynomial
Ring in x over Integer Ring
sage: A = cm.get_action(QQ, ZZ['x'], operator.mul); A
Left scalar multiplication by Rational Field on Univariate Polynomial
Ring in x over Integer Ring
sage: A.domain()
Univariate Polynomial Ring in x over Integer Ring
- Robert