Re: [Axiom-math] repeated series expansion

[Ralf Hemmecke]

> That's interesting.  How does "MultivariateTaylorSeriesCategory()" from
> bookvol 10.2 page 1026  fall short?

It's a category, not a domain. And if you look into the source code then 
we find even.

TaylorSeries(Coef): Exports == Implementation where
  Coef  : Ring
  L   ==> List
  NNI ==> NonNegativeInteger
  SMP ==> Polynomial Coef
  StS ==> Stream SMP

  Exports ==> MultivariateTaylorSeriesCategory(Coef,Symbol) with
    ...

  Implementation ==> SparseMultivariateTaylorSeries(Coef,Symbol,SMP) add
    Rep := StS -- Below we use the fact that Rep of PS is Stream SMP.
    ...

The domain SparseMultivariateTaylorSeries is relatively general. It 
allows to specify the type of polynomials that serve as coefficients of 
a (univariate) power series. That's a bit of an implementation detail, 
but quite flexible.

Ralf