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MathGroup Archive 2003

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Re: nth differences

  • To: mathgroup at smc.vnet.net
  • Subject: [mg39860] Re: [mg39852] nth differences
  • From: Ken Levasseur <klevasseur at mac.com>
  • Date: Sun, 9 Mar 2003 05:26:46 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

These definitions generate the lists you want in "traditional form" for
differences:


Differences[input_] := Partition[input, 2, 1] /.
    {{a_, b_} -> b - a};


DifferencesTable[input_] := DT[FixedPointList[Differences,
    input, Length[input] - 1, SameTest ->
     (Length[Union[#2]] == 1 & )]]

DT[e_] := TableForm[Transpose[
      (MapThread[Prepend[#1, \[CapitalDelta]^StringJoin["(",
             ToString[#2 - 1], ")"]] & ,
         {#1, Range[Length[#1]]}] & )[
       (PadRight[#1, Length[e[[1]]], " "] & ) /@ e]]]


Ken Levasseur
Math. Sci.
UMass Lowell


> From: "Zachary Turner" <_NOzturnerSPAM_ at cyberonic.com>
To: mathgroup at smc.vnet.net
> Date: Sat, 8 Mar 2003 02:52:13 -0500 (EST)
> To: mathgroup at smc.vnet.net
> Subject: [mg39860] [mg39852] nth differences
> 
> Say I have a list of k integers and I want to produce a list containing the
> first differences?  For example, given {1, 2, 5, 7, 8, 9} the first
> differences are {1, 3, 2, 1, 1}, and the second differences are {2, -1, -1,
> 0}, the third are {-3, 0, 1}, etc
> 
> 
> 



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