formal sets

[Ralf Stephan]

Hello,

The set of integers can be formally represented as

sage: Set(ZZ)
Set of elements of Integer Ring

A bit more tricky are the reals:

sage: Set(RealSet(-oo,oo))
Set of elements of (-oo, +oo)

How could one represent the complexes? Is it a cartesian product?

Regards,

[Dima Pasechnik]

sure - if you are willing to sacrifice the field structure.

sage: RealSet(-oo,oo).cartesian_product(RealSet(-oo,oo))

The Cartesian product of ((-oo, +oo), (-oo, +oo))

[Eric Gourgoulhon]

Hi,

Le dimanche 5 novembre 2017 15:14:16 UTC+1, Ralf Stephan a écrit :

A bit more tricky are the reals:

sage: Set(RealSet(-oo,oo))
Set of elements of (-oo, +oo)

Well, this one is maybe too tricky:

sage: R = Set(RealSet(-oo,oo))
sage: R.an_element()
(-oo, +oo)

???

In passing, we may also note that

sage: RealSet(-oo,+oo).an_element()
...
SignError: cannot add infinity to minus infinity

Eric.

[Ralf Stephan]

On Sunday, November 5, 2017 at 8:56:44 PM UTC+1, Eric Gourgoulhon wrote:

sage: R = Set(RealSet(-oo,oo))
sage: R.an_element()
(-oo, +oo)

I see, R is a set with one element, so there is a difference to Set(ZZ)

In passing, we may also note that

sage: RealSet(-oo,+oo).an_element()
...
SignError: cannot add infinity to minus infinity

Thanks. I think this needs to be fixed. 

[Ralf Stephan]

Please review

https://trac.sagemath.org/ticket/24162

[Ralf Stephan]

On another note, while there is support for sets with maps from ZZ in EnumeratedSetFromIterator. How can for example the set under a function from the positive reals be formally represented? I'm looking for an equivalent of SymPy's ImageSet.

Regards,