Hi Simon,
On 26/12/2017 17:45, Simon King wrote:
Hi Vincent,
On 2017-12-26, Vincent Delecroix <20100.delecr...@gmail.com> wrote:
While working on Puiseux series [1] I wanted to introduce a
construction functor for them. When the base ring is algebraically
closed then it is an algebraic closure functor (from power series).
But when it is not, it is an infinite algebraic extension (ie
adding all x^(1/n)). I think that it would make sense for such a
functor since the same construction is in action from QQ to the
universal cyclotomic field.
Any suggestion on what should be done here?
I am not sure if I understand what you're asking. Let's try:
Is the construction a functor? If yes: What categories are domain
and range of the functor?
> It is of course possible that domain/range depend on parameters.
In my situation, the (mathematical) specifications are
INPUT: a field K and an element x of K
OUTPUT: K[x^(1/2), x^(1/3), x^(1/4), ...]
> SNIP (explanation on implementation)
thanks!
A canonical name of Construction X would be "ConstructionXFunctor".
So, I guess PuiseuxSeriesFunctor seems fine. If you are unhappy with
how the functor is printed, you can of course override _repr_.
I came up with the above specifications because I thought about two
different cases at hand
- if input is S = QQ and x = -1 then output shoud be UCF (universal
cyclotomic field)
- if input is S = "Laurent polynomials in t over QQ" and x = t then
output should be "Puiseux series in t"
As a consequence of having different sources I had no idea about a name!
Best
Vincent
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