Thanks, FiniteSetMaps might be what I want, but I'll keep both approaches
in mind.
John
On Monday, April 18, 2016 at 3:51:27 PM UTC-7, vdelecroix wrote:
>
> I read the end of your mail too late. The following works with lambda
> functions.
>
> sage: S = FiniteEnumeratedSet([1,2,3])
> sage: T = FiniteEnumeratedSet([4,5,6,7])
> sage: d = {1:5, 2:7, 3:5}
> sage: f = S.hom(lambda x: d[x], T)
> sage: f(1)
> 5
> sage: f(2)
> 7
> sage: f(3)
> 5
>
> Otherwise you should have a look at FiniteSetMaps.
>
> On 18/04/16 19:48, Vincent Delecroix wrote:
> > It should... but Sage does not recognize that 2 belongs to S. Note that
> > the following works
> >
> > sage: S = FiniteEnumeratedSet([1,2,3])
> > sage: T = FiniteEnumeratedSet([4,5,6,7])
> > sage: f = S.hom(lambda x: 3+x, T)
> > sage: f(1)
> > 4
> >
> > Vincent
> >
> > On 18/04/16 15:02, John H Palmieri wrote:
> >> How do I define a function between finite sets within the category
> >> framework? Should the following work?
> >>
> >> sage: S = Set([1,2,3])
> >> sage: T = Set([4,5,6,7])
> >> sage: f = S.hom(lambda x: 3+x, T)
> >> sage: f
> >> Generic morphism:
> >> From: {1, 2, 3}
> >> To: {4, 5, 6, 7}
> >> sage: f(2)
> >>
> >>
> ---------------------------------------------------------------------------
> >>
> >> TypeError Traceback (most recent
> >> call
> >> last)
> >> ....
> >> TypeError: 2 fails to convert into the map's domain {1, 2, 3}, but
> a
> >> `pushforward` method is not properly implemented
> >>
> >> I see that it works if I define S and T using FiniteEnumeratedSet
> >> instead.
> >> Is that the best solution?
> >>
> >> Or suppose I want to define a map sending 1 to 5, 2 to 7, 3 to 5. I
> can't
> >> see how to use the dictionary {1:5, 2:7, 3:5} (for example) to define a
> >> function.
> >>
> >> In general, I would like fully functional, callable, composable
> morphisms
> >> of sets, and finite sets are good enough for now. Any advice? Also of
> >> other
> >> categories, in particular finite abelian groups, but maybe those work
> >> better already?
> >>
>
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