Re: [Axiom-developer] about Expression Integer

[Ralf Hemmecke]

> (4) -> differentiate(ex1,x)$S

> This function seems to come from 'DifferentialExtension'

No. I rather think it comes from 'PartialDifferentialRing(Symbol)'.
Look at Hyperdoc. Browse SUP and view Operations->Origins (Filter 
"differentiate").

> So I am confused as to why
> 'differentiate(univariate(p,v))' does not seem to yield this
> same result. Can you help?

Not really. I think there is a bug here, since x is sometimes treated as 
the indeterminate of SUP and sometimes not.

> It seems to me that the interrelationship between all of these
> polynomial categories, domains and packages is remarkably
> convoluted.

I don't really think so. The problematic thing is to take
"Expression Integer" as an argument in the construction of SUP.

Could you explain in which sense SUP(Expression Integer) should be 
semantically different from Expression(Integer)?

Isn't an element of SUP(Expression Integer) also an expression?
It is obvious that Axiom can construct SUP(Expression Integer), but does 
this make sense?

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.

What would be the relation between
SUP(Expression Integer) and Expression(Integer) on a semantic level?
Equality, subset, superset?

Ralf