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

 From: Bill Page Subject: RE: [Axiom-developer] about Expression Integer Date: Tue, 21 Feb 2006 12:21:53 -0500

```On February 21, 2006 12:01 PM I wrote:

On February 21, 2006 10:13 AM you wrote:
>
>
> >>        differentiate(p: %,v: OV) ==
> >>              multivariate(differentiate(univariate(p,v)),v)
> >>
>
> ...
> I am looking at:
>
>
> and
>
>
> but I am confused by this result:
>
> (1) -> S:=SUP EXPR INT
>
>    (1)  SparseUnivariatePolynomial Expression Integer
>    Type: Domain
>
> (2) -> ex1:=(x^2+1)\$S
>
>          2
>    (2)  x  + 1
>    Type: SparseUnivariatePolynomial Expression Integer
>
> (3) -> differentiate(ex1)\$S
>
>    (3)  0
>    Type: SparseUnivariatePolynomial Expression Integer
>
> Ok, so 'differentiate\$SUP' treated 'x^2+1' as being in the
> coefficient domain, right? But:
>
> (4) -> differentiate(ex1,x)\$S
>
>    (4)  2x
>    Type: SparseUnivariatePolynomial Expression Integer
>
> ')set message bottomup on' shows that 'differentiate' with
> signature '(SUP EXPR INT,SYMBOL) -> SUP EXPR INT' is called
> from SUP.
>
> (4) -> differentiate(ex1,x)\$S
>
>  Function Selection for differentiate
>       Arguments: (SUP EXPR INT,VARIABLE x)
>       Target type: SUP EXPR INT
>       From:      SUP EXPR INT
>    -> no appropriate x found in Expression Integer
>    -> no appropriate x found in Integer
>    -> no appropriate x found in Expression Integer
>    -> no appropriate x found in Integer
>
>  [1]  signature:   (SUP EXPR INT,SYMBOL) -> SUP EXPR INT
>       implemented: slot \$\$(Symbol) from SUP EXPR INT
>
> This function seems to come from 'DifferentialExtension' in
>
>
> and this seems correct to me. So I am confused as to why
> 'differentiate(univariate(p,v))' does not seem to yield this
> same result. Can you help?
>

Oh! Re-reading this I just noticed something.

Shouldn't this differentiation be written
'differentiate(univariate(p,v),v)' in SUP:

differentiate(p: %,v: OV) ==
multivariate(differentiate(univariate(p,v),v),v)

-------

That should allow the differentiation of any expressions occuring
in the underlying Ring.

Regards,
Bill Page.

```

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