# [om] Re: library

Mike Dewar miked at nag.co.uk
Mon Jun 4 12:09:40 CEST 2001

```James Davenport is the main author of the polynomial CDs, but here are
some non-definitive responses to the points you raise.

> Bye the way, is there any page where all (small or little) projects that
> use OpenMath  are listed? That would be very helpful to avoid double
> inventions and learn from another.
of the website.  I'd be overjoyed to add some more :-)

> > As for the polynomial CD, the group CD, the algebra (rings and algebras) CD,
> > etc., I have no clue as to who is active on this area right now.
James Davenport is doing polynomials, and Andrew Solomon volunteered to look
after the algebraic stuff, most of which I think he wrote in the first place.

> I'm using the 'factor' symbol in the 'poly.cd' at the moment because I
> offer the polynomial factorization of CoCoA as an abstract mathematical
> service for mathematical reasoning agents.
>
> Two remarks on the poly.cd:
>
> 1) A matter of personal taste: I don't like the functional writing:
>                 <OMA>
>                   <OMS name="eq" cd="relation1"/>
>                   <OMA>
>                     <OMS name="factor" cd="poly"/>
>                         POLY
>    		    <OMS name="factored" cd="poly"/>
> 		        FACTORS
>
> Since I come from the 'logic' side of computer science I would really
> appreciate to use factor as a predicate without the 'eq':
>                   <OMA>
>                     <OMS name="factor" cd="poly"/>
>                        POLY
>    		       <OMS name="factored" cd="poly"/
> 		           FACTORS
>                      ....
>
> But I'm sure there are some good reasons for the functional view. As far as
> I can see, factor and factored are still not used in any other polyXY.cd.
The current arrangement allows you to represent factor(P) without knowing the
factors explictly, and also factored(F) without knowing the original
polynomial.  You could have a different predicate `factorisation(P,F)' to do
what you want, but it looks a bit redundant to me.  The polynomial CD is
designed by people who want to compute with polynomials, while it looks to me
as if you want to make statements about polynomials.

> 2) I don't understand the reason why to use 'factored' when it is nothing
>    else than a list of factors...
Actually it is more, the semantics of `factored' says that each factor, a
formal power of a polynomial, is irreducible.  A list of formal powers does
not have that property.

>    As said before, factored is not used in any other poly.cd.
>    Bye the way, I guess the example for the 'expand' symbol in cd 'poly' is not
>    very meaningful because there is no 'expand' in it...
>
>    eq(factored(power(x,2),power(plus(x,2),1),power(minus(x,2),1)),
>       plus(power(x,4),times(-4,power(x,2))))
I think you're right, and there should be an `expand' wrapped around the
`factored'.

Cheers, Mike.

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