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Can Mathematica construct a set of equations?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg119317] Can Mathematica construct a set of equations?
  • From: Ralph Dratman <ralph.dratman at gmail.com>
  • Date: Mon, 30 May 2011 06:35:29 -0400 (EDT)
  • References: <BANLkTimOrU4wUBXU7p-8G_GeUZGV+0L5Fg@mail.gmail.com>

Given a set of N points Pn in the real plane, all within a distance d
of each other,

In vector notation,

   || Pj - Pk || <= d,   1 <= j,k <= N

or written out, say for N=3,

|| P1 - P2 || <= d,
|| P2 - P3 || <= d,
|| P3 - P1 || <= d.

That is fine for 3 points, but suppose I have 10. Then the long
version is Choose[10,2] = 45 equations, and I don't particularly want
to write them out by hand. Can Mathematica do that for me, and give me
the equations in a notebook?

I'm not even sure how to represent the position vectors so I can refer
to xj or yk later on. How do I set up vector-sub-j and its components
x-sub-j and y-sub-j ?   Would that be a list of N lists of length 2?
Or is there a more specific vector notation?

Sorry to be so clueless. Thank you.

Ralph


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