Re: [Axiom-developer] Question concerning types...

[Ralf Hemmecke]

Good that you join,

> a very interesting discussion! Perhaps you might enjoy reading 'The
> Skeleton Key' by Dudley E. Littlewood, where the nature of indeterminates
> is nicely contemplated.

Well, this "indefinite" (not indeterminate) is not my invention. I was 
just elaborating on what I believe I could be.

If you use "indeterminate" as the x in a univariate polynomial ring R[x] 
then (as I understand it) this is not the "indefinite" thing we are 
talking about. This x lives in R[x] but not in R.

Whoever wanted "indefinite things" should speak for himself, I only try 
to explain what I think they could be.

Of course it is possible to model indefinites by indeterminates, but you 
see that your domain now gets bigger. Indefinite integers are integers 
in every respect but the don't have a value (yet). In that sense the 
diagram is OK in my eyes.

But maybe the whole thing needs more elaboration.

> > From my point of view, could you please explain, why an indeterminate
> should behave like the original ring it was abstracted from. This is
> uncategorical.

If I understand the whole business correctly, then it is NOT an 
indeterminate.

> Would you agree that one should try to have say a Ring (integers) and
> another algebraic structure (indeterminates) which might have several
> attirbutes (associative, power associative, alternative, commutative,
> ring, group,....) and that one builds up a new algebra from the
> (semi/direct) product of the two algebraic structures at hand.

I think, I said something like that here.

http://lists.nongnu.org/archive/html/axiom-developer/2006-09/msg00548.html

Ralf