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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:
>
> http://wiki.axiom-developer.org/axiom--test--1/src/algebra/PolySpad
>
> and
>
> http://wiki.axiom-developer.org/axiom--test--1/src/algebra/PolycatSpad
>
> 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
>
> http://wiki.axiom-developer.org/axiom--test--1/src/algebra/CatdefSpad
>
> 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.
- RE: [Axiom-developer] about Expression Integer, (continued)
- RE: [Axiom-developer] about Expression Integer, Bill Page, 2006/02/21
- Re: [Axiom-developer] about Expression Integer, Ralf Hemmecke, 2006/02/21
- RE: [Axiom-developer] about Expression Integer, Bill Page, 2006/02/21
- Re: [Axiom-developer] about Expression Integer, Doug Stewart, 2006/02/20
- RE: [Axiom-developer] about Expression Integer, Bill Page, 2006/02/21
- Re: [Axiom-developer] about Expression Integer, Francois Maltey, 2006/02/19
- RE: [Axiom-developer] about Expression Integer, Bill Page, 2006/02/19
- Re: [Axiom-developer] about Expression Integer, Ralf Hemmecke, 2006/02/19
- Re: [Axiom-developer] about Expression Integer, William Sit, 2006/02/21
- RE: [Axiom-developer] about Expression Integer,
Bill Page <=
- RE: [Axiom-developer] about Expression Integer, Page, Bill, 2006/02/24
- RE: [Axiom-developer] about Expression Integer, Page, Bill, 2006/02/24
- RE: [Axiom-developer] about Expression Integer, Page, Bill, 2006/02/24