Groups > comp.soft-sys.math.mathematica > #2794

Can Mathematica construct a set of equations?

From	Ralph Dratman <ralph.dratman@gmail.com>
Newsgroups	comp.soft-sys.math.mathematica
Subject	Can Mathematica construct a set of equations?
Date	2011-05-30 10:35 +0000
Organization	Steven M. Christensen and Associates, Inc and MathTensor, Inc.
Message-ID	<irvrtb$8jo$1@smc.vnet.net> (permalink)
References	<BANLkTimOrU4wUBXU7p-8G_GeUZGV+0L5Fg@mail.gmail.com>

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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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Can Mathematica construct a set of equations? Ralph Dratman <ralph.dratman@gmail.com> - 2011-05-30 10:35 +0000
  Re: Can Mathematica construct a set of equations? "Dr. Wolfgang Hintze" <weh@snafu.de> - 2011-05-31 11:45 +0000

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