Re: nth differences

• To: mathgroup at smc.vnet.net
• Subject: [mg39865] Re: [mg39852] nth differences
• From: BobHanlon at aol.com
• Date: Sun, 9 Mar 2003 05:28:39 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

In a message dated 3/8/03 3:35:44 AM, _NOzturnerSPAM_ at cyberonic.com writes:

> 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
>
v = {1, 2, 5, 7, 8, 9};

Rest[v-RotateRight[v]]

{1,3,2,1,1}

nthDifference[v_List, n_Integer] :=

Nest[Rest[#-RotateRight[#]]&,v,n] /;

0   <= n <= Length[v];

nthDifferenceList[v_List, n_:Length[v]] :=

NestList[Rest[#-RotateRight[#]]&,v,n] /;

0 <= n <= Length[v] && IntegerQ[n];

nthDifference[v,3]

{-3,0,1}

nthDifferenceList[v,3]

{{1,2,5,7,8,9},{1,3,2,1,1},{2,-1,-1,0},{-3,0,1}}

nthDifferenceList[v]

{{1,2,5,7,8,9},{1,3,2,1,1},{2,-1,-1,0},{-3,0,1},{3,1},{-2},{}}

Bob Hanlon

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