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Re: How to feed a list of xy pairs into Solve to output xyz triplets

  • To: mathgroup at smc.vnet.net
  • Subject: [mg101178] Re: [mg101149] How to feed a list of xy pairs into Solve to output xyz triplets
  • From: Sseziwa Mukasa <mukasa at jeol.com>
  • Date: Fri, 26 Jun 2009 06:48:44 -0400 (EDT)
  • References: <200906251113.HAA10623@smc.vnet.net>

On Jun 25, 2009, at 7:13 AM, Bill wrote:

> Hi:
>
> Let's say that I have a list of xy coordinate pairs:
>
> list= {{1,2}},{3,1},{5,4},{6,3},{2,5}}.
>
> Now I'd like to find xyz triplets using Solve for the equation 6*x  
> + 4*y + z == 1.
>
> xyz results:  {{1,2,-13}},{3,1,-21},{5,4,-45},{6,3,-47},{2,5,-31}}.  
> (I used Solve 5 times.)
>
>
> Question: How do I code that into Mathematica for a "one shot  
> output?" (Use Solve once.)

One approach is to solve for z, then map the solution over the list:

Block[{sol=Solve[6*x+4*y+z==1,z][[1]]},Append[#,z/.sol/.{x->#[[1]],y- 
 >#[[2]]}]&/@list]

If your equation is linear you can avoid using Solve altogether and  
just do the matrix arithmetic to get a  matrix of z values which you  
can append to list:

Block[{z = Table[1, {Length[list]}] - Flatten[list.{{6}, {4}}]},
  ArrayFlatten[{{list, Transpose[{z}]}}]]


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