Martin Rubey wrote:
>
> Waldek Hebisch <[EMAIL PROTECTED]> writes:
>
> > > 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.
>
> Do you happen to know why it's OK for polynomials to allow various orders, but
> not so for powerseries? The design should be fairly parallel, shouldn't it?
>
Other orders simply are unimplemented. Different orders are very
important for Groebner bases, so there was enough motivation to
implement them. For power series having different orders is
useful but not critical, so motivation was smaller. Also, note
that DMP and SMP give separate implementations for many functions.
Similarly, new power series domain would have to provide separate
implementation.
One more remark: for polynomials just having linear order is enough
to give implementation (SMP may be treated as performance improvement).
Generalising this generic implementation (as a stream of pairs
(coefficient, exponent)) to powers series will work only if order is
isomorphic to natural numbers. One can generalize
SparseMultivariateTaylorSeries, but then there is still problem
with leadingCoefficient and friends -- they will work only if
order is isomorphic to natural numbers.
BTW: Certainly giving different weights (degrees) to variables is
useful. OTOH I am not sure how useful are general orders (ones
which are not isomorphic to natural numbers).
--
Waldek Hebisch
[EMAIL PROTECTED]
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