Re: [Axiom-developer] series for sums

[Martin Rubey]

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