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## Re: [Axiom-developer] series for sums

**From**: |
Martin Rubey |

**Subject**: |
Re: [Axiom-developer] series for sums |

**Date**: |
Fri, 7 Oct 2005 17:57:22 +0200 |

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*