[GAP Forum] ring theory

[Igor Korepanov]

Dear Alexander,

Thank you for addressing me by name (and not just "Dear Forum"). In return, I will refrain from attributing ironical epithets to your excellent work.

> Thus again my request for any concrete need of such an element test (the use itself can be trivial, but the context shouldn't be) for rings.

I was just showing GAP to a student and saying "see how beautiful it is! Let's see how it works with this and that...". Being partly of Ukrainian ancestry, I was of course wondering what Ukrainian comrades write, e.g. on page http://ukrgap.exponenta.ru/Examples/rings.htm . Aha, I said, they write:

gap> M:=Ring(5,7);
Integers

And what if 

gap> r:=Ring(10,12);

?
So, I typed that in the presence of my student, hoping that GAP understands me. And - oops!

So, the first reason why GAP should know such things is simply for students - not to scare them away from GAP by such hardly explainable to them things. And we know that in order to win, we have the young generation on our side!

The second reason is: if experts see no interest in some problem, then this problem is probably in reality the most interesting one. It always happens like this in pure art. So, perhaps, in some near future, the element test for rings will gain much popularity :)

Remark: as for myself, I have just delivered a course in Finite Fields, using GAP, for engineering students this last semester which by no means makes me an expert in ring theory.

I am also using GAP in my research, since last summer (see one of my previous posts).

I would like to end this letter with expressing my pretty sincere gratitude to you and all GAP authors - you are doing a great job.

Igor



23.01.2011, 06:51, "Alexander Hulpke" <ahulpke at gmail.com>:
> Dear Igor,
>
>>  I think you must agree that, even in such trivial cases, there must be no such epic bugs as this one with rings.
>
> I would not consider this as a bug (and would be careful with the `epic' attribute in any case). Of course this is not a ``hard'' problem, but simply one for which the computer is not well suited.
>
> I am not aware of an element test for infinite rings that will always terminate. As I wrote, I can imagine special methods for subrings of polynomial rings or subrings of the integers (or for element test of the generators), but at this point I see minimal gain in implementing this and am rather doubtful of the merits of devoting time on such particular features. Thus again my request for any concrete need of such an element test (the use itself can be trivial, but the context shouldn't be) for rings.
>
> Best,
>
>   Alexander Hulpke
>