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

From: Ralf Hemmecke
Subject: Re: [Axiom-developer] Question concerning types...
Date: Mon, 18 Sep 2006 15:07:29 +0200
User-agent: Thunderbird (X11/20060719)

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

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.


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