[sage-support] How do I define a morphism/function/map of sets?
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?
--
John
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Re: [sage-support] How do I define a morphism/function/map of sets?
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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Re: [sage-support] How do I define a morphism/function/map of sets?
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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Re: [sage-support] How do I define a morphism/function/map of sets?
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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