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Re: "Accumulate" in Mathematica 6

  • To: mathgroup at smc.vnet.net
  • Subject: [mg82790] Re: [mg82776] "Accumulate" in Mathematica 6
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Wed, 31 Oct 2007 06:08:35 -0500 (EST)
  • References: <200710301049.FAA20459@smc.vnet.net>

On 30 Oct 2007, at 19:49, Oskar Itzinger wrote:

> Very sadly, Mathematica 6 is not supported under Irix - so I can't  
> play with
> it practically - but I noticed in the online
>
> documentation that there is a new function "Accumulate[list]",  
> defined to be
> equivalent to "Rest[FoldList[Plus, 0, list]]",
>
> giving a list of the successive accumulated totals of the elements in
> <list>.
>
> Funny. While it was considered obsolete and superseded by  
> "FoldList" in
> Mathematica 2, Mathematica 1 (!) already did
>
> have a function "Accumulate", defined as
>
> Accumulate[f, g[e1, e2, e3, ...]] <==> g[e1, f[e1, e2], f[f[e1,  
> e2], e3],
> ...]
>
> so that
>
> Accumulate[Plus, Range[5]] <==> {1, 3, 6, 10, 15}
>
> However, "Accumulate" in Mathematica 1 clearly was not restricted  
> to "Plus"
> but rather specifically intended for dealing
>
> with functions that take exactly two arguments - so, I believe that
> "Accumulate" in Mathematica 6 is much less usable
>
> than the former in Mathematica 1.
>
> Maybe I'm missing something here - but what was the rationale behind
> re-implementing "Accumulate" in such a restricted
>
> version now?
>
> Thanks.
>
> /oskar
>
>
>
>

You are missing just one thing - performance. Accumulate in this  
restricted sense is incredibly fast - and extremly useful.

Andrzej Kozlowski


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