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[
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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