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## Re: [Axiom-developer] about Expression Integer

 From: Ralf Hemmecke Subject: Re: [Axiom-developer] about Expression Integer Date: Tue, 21 Feb 2006 22:53:02 +0100 User-agent: Thunderbird 1.5 (X11/20051201)

```(4) -> differentiate(ex1,x)\$S
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```This function seems to come from 'DifferentialExtension'
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No. I rather think it comes from 'PartialDifferentialRing(Symbol)'.
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Look at Hyperdoc. Browse SUP and view Operations->Origins (Filter "differentiate").
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```So I am confused as to why
'differentiate(univariate(p,v))' does not seem to yield this
same result. Can you help?
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Not really. I think there is a bug here, since x is sometimes treated as the indeterminate of SUP and sometimes not.
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```It seems to me that the interrelationship between all of these
polynomial categories, domains and packages is remarkably
convoluted.
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I don't really think so. The problematic thing is to take
"Expression Integer" as an argument in the construction of SUP.

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Could you explain in which sense SUP(Expression Integer) should be semantically different from Expression(Integer)?
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Isn't an element of SUP(Expression Integer) also an expression?
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It is obvious that Axiom can construct SUP(Expression Integer), but does this make sense?
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I do not fully understand the "Expression" constructor, but I somehow consider it as a domain that contains every expression. Therefore, I think constructing higher domains that are built on Expression should not yield a bigger class than Expression itself.
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What would be the relation between
SUP(Expression Integer) and Expression(Integer) on a semantic level?
Equality, subset, superset?

Ralf

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