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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 1.5.0.5 (X11/20060719)

```Good that you join,

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```a very interesting discussion! Perhaps you might enjoy reading 'The
Skeleton Key' by Dudley E. Littlewood, where the nature of indeterminates
is nicely contemplated.
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Well, this "indefinite" (not indeterminate) is not my invention. I was just elaborating on what I believe I could be.
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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.
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Whoever wanted "indefinite things" should speak for himself, I only try to explain what I think they could be.
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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.
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But maybe the whole thing needs more elaboration.

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```From my point of view, could you please explain, why an indeterminate
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```should behave like the original ring it was abstracted from. This is
uncategorical.
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If I understand the whole business correctly, then it is NOT an indeterminate.
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```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.
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I think, I said something like that here.

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

Ralf

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