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

*To*: mathgroup at smc.vnet.net*Subject*: [mg101179] Re: How to feed a list of xy pairs into Solve to output xyz triplets*From*: computer algebra <mike.honeychurch at gmail.com>*Date*: Fri, 26 Jun 2009 06:48:57 -0400 (EDT)*References*: <h1vm3r$aad$1@smc.vnet.net>

On Jun 25, 6:12 am, Bill <WDWNORW... at aol.com> 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.) > > Thanks, > > Bill > > Mathematica 6.0.1 using Win XP on a pc. Solve[6*x + 4*y + z == 1, z] /. {x -> list[[All, 1]], y -> list[[All, 2]]} gets you a one shot list of z. Mapping list onto the structure you want gets you a one shot x,y,z {#[[1]], #[[2]], Solve[6*#[[1]] + 4*#[[2]] + z == 1, z][[1, 1, 2]]} & / @ list Mike