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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