Martin Rubey wrote:
>
> Waldek Hebisch <[EMAIL PROTECTED]> writes:
>
> > We have:
> >
> > ++ \spadtype{PowerSeriesCategory} is the most general power series
> > ++ category with exponents in an ordered abelian monoid.
> > PowerSeriesCategory(Coef,Expon,Var): Category == Definition where
> > ...
> > leadingMonomial: % -> %
> > ++ leadingMonomial(f) returns the monomial of \spad{f} of lowest
> > order.
> > leadingCoefficient: % -> Coef
> > ++ leadingCoefficient(f) returns the coefficient of the lowest order
> > ++ term of \spad{f}
> >
> > the "lowest order" can be only the order in Expon (since we have
> > no other order at our disposal).
>
> That's the only part where I don't follow. I'd interpret "lowest order" as
> "element of lowest degree in %". I don't see why the order in % has to be the
> one from Expon. I know that we inherit from AMR(Coef, Expon), but does this
> imply that the order of monomials has to be the same?
>
Note:
degree : % -> Expon
++ degree(f) returns the exponent of the lowest order term of \spad{f}.
which means that
degree(f) < degree(g)
has to be computed using comparison form Expon. Using different
order in other places would be insane.
> If so, would it make sense to change the order in IndexedExponents?
>
IndexedExponents are used by polynomial domains so I feel that the
impact would be too big (and not always positive). In principle
we could create a new domain, say HomogeneousIndexedExponents
with new order and use it as Expon. We still would have to
handle problems with coercions between power series and
polynomials, but it should be managable. OTOH for polynomials
we allow various orders -- lexicografic order makes sense as
default here. Similarly, for power series we may wish various
orders. Lexicographic order is less atractive for power series,
but is not too bad as default if we could use different order
when needed.
--
Waldek Hebisch
[EMAIL PROTECTED]
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