Ralf Hemmecke wrote:
>
> On 7/3/19 11:27 AM, Waldek Hebisch wrote:
> > Ralf Hemmecke wrote:
>
> >> In fact, I would like to show \omega * 2 as the output of \omega +
> >> \omega (ordinal addition), not 2*\omega.
> >
> > I think that this goes into user control of output. More precisely
> > standard notation is 2*\omega, and this agrees with other domains.
> > User may wish different output and it is resonable to provide
> > some means for customization. And that is much more general
> > problem: users should not be forced to change types to get
> > y*x as output for polynomials. Sometimes x*2 may be better
> > than 2*x...
>
> Maybe, but since with a domain where coefficients commute with
> variables, that shouldn't be much of a problem.
> However, for SmallOrd, how do I interpret the * in the output 2*omega?
> It can only be the "natural product, right?
Yes. "natural" product is commutative.
> Coming back to "semiring" operations. Aren't you lying when you claim
> that SmallOrdinal is a SeminRing? Or do the ordinals form indeed a group
> with respect to "natural" addition?
SemiRing means commutative monoid with respect to addition and we
have this.
>
> In fact, I wonder how the compiler actually creates code for
>
> 0 == 0$Rep
>
> , since the representation is PolynomialRing(NNI, %).
>
> I guess that can only work, because the representation of the 0 of
> PolynomialRing is the empty list. Would it fail, if it were not the
> empty list?
Yes, that is tricky. It works because we can compute 0 without
looking at the type.
--
Waldek Hebisch
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