Re: [Axiom-developer] series for sums

[Martin Rubey]

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