> > On September 18, 2006 1:50 PM C Y wrote: > > > > Sorry in advance if this question is a bit daft... > > > On September 18, 2006 2:16 PM I wrote: > Not at all. There is not such thing as a daft question - > however always keep in mind that the same is not true of > answers. :-) >
I am afraid that what I wrote below might be a good example of a "daft answer" - even if it is in the right spirit... :( This idea needs more work. On 2nd thought what I wrote below does not make good sense as it stands. Maybe this is better: (2) -> a1:MPOLY([a1,a2],INT) Type: Void (3) -> a2:MPOLY([a1,a2],INT) Type: Void (4) -> a1+a2 (4) a1 + a2 Type: MultivariatePolynomial([a1,a2],Integer) This way it is clear that there are no indeterminants that are not integers. Regards, Bill Page. > > --- Earlier I wrote: > ... > My proposal is that to define this in algebraic terms what we > need is a domain like Polynomial which consists of some symbols > and expressions (of a specific kind) over these symobls. So it > is clear, right? that the type > > Polynomial Integer > > consists of a large clase of expressiions of that type. And saying > > a1:Polynomial Integer > > is just a way of saying that the variable a1 will take values from > this domain. > > But because the coefficients of the polynomial must come from the > domain Integer we know that these Integers are embedded in this class > of expressions as polynomials of degree 0, so we have no problem > specifying that a certain variable suchs as 'a1' is exact such an > integer (polynomial of degree 0). > > In general both Integer and Polynomial Integer has Ring so, yes > it is true that Polynomial Integer can be used in (most) places > where would like to use Integer (but were no specific value is > required). > > The only concern I have is whether or not Polynomial Integer is > "big enough" to model everything that we would want to mean by > "indefinite integer". > > Regards, > Bill Page. > > > > > _______________________________________________ > Axiom-developer mailing list > Axiom-developer@nongnu.org > http://lists.nongnu.org/mailman/listinfo/axiom-developer > > _______________________________________________ Axiom-developer mailing list Axiom-developer@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-developer