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Re: [Axiom-developer] series for sums

 From: Martin Rubey Subject: Re: [Axiom-developer] series for sums Date: Sun, 9 Oct 2005 18:09:18 +0200

```Dear all,

(still hoping for some response)

given a series from some domain in UPSCAT, it is possible to create a new one
by using

map(function, series)

which applies function (lazily) to every coefficient.

However, for the problem of expanding products in Puiseux series, to obtain a
certain coefficient, I need to know *all* previous coefficients.

Is there some operation similar to map which I could use for this purpose?

Martin

Martin Rubey writes:
> Dear all,
>
> I'm just trying to do the same for products, however, I came across a little
> mathematical difficulty. It seems to obtain the coefficient of x^k I need to
>
> * generate all compositions of k
>
> * for each composition (i1,i2,..,il), generate a multiple sum of the form
>
>   sum(a(i1,j1)*a(i2,j2)*...*a(il,jl),j1<j2<...<jl)
>
> Of course this is doable (although I will have to use ugly newsymbols for the
> j's), but I wonder whether somebody can think of a better alternative.
>
> Martin
>
> Martin Rubey writes:
>  > Well, here is a stupid alternative, which works better on the surface:
>  >
>  >       if FE has CombinatorialOpsCategory then
>  >         is?(ker,"%defsum" :: Symbol) =>
>  >           (summand := exprToUPS(first args,posCheck?,atanFlag)) case
> %problem =>
>  >             summand
>  > --          op := operator("%defsum"::Symbol)\$CommonOperators
>  > --          mp:FE->FE:=op cons(#1, rest args)
>  >           eq := equation(retract(third args)@Symbol,
> args.4..args.5)\$SegmentBinding(FE)
>  >           mp:FE->FE:=summation(eval(#1, retract(second args)@K, third
> args), eq)
>  >           [map(mp, summand.%series)\$UPS]
>  >
>  > now Axiom displays beautiful sums, but they won't be evaluated because of
> a bug
>  > equivalent to issue #212.
>  >
>  > The summation design is seriously broken, I'd say.
>  >
>  > Martin

```