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MathGroup Archive 2007

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FindInstance puzzler

  • To: mathgroup at smc.vnet.net
  • Subject: [mg83633] FindInstance puzzler
  • From: Mark Fisher <particlefilter at gmail.com>
  • Date: Mon, 26 Nov 2007 03:49:26 -0500 (EST)

Hi all,

I'm puzzled by the results of FindInstance which seems to restrict its
results to a subregion of the valid space.

conds = And @@
  Append[Thread[(Abs[L] /. Solve[1 - z1 L - z2 L^2 == 0, L]) >= 1],
   z1 + z2 >= 0];

RegionPlot[conds, {z1, -.75, 2.25}, {z2, -1.25, 1.25}, PlotPoints ->
90,
 Epilog ->  Point[{z1, z2} /. FindInstance[conds, {z1, z2}, Reals,
10^3]]]

I suppose this isn't a bug, because the results of FindInstance are
all valid, but nevertheless I find it unpleasing (to say the least)
that part of the valid space seems to get no representation. It means
that FindInstance is of limited use for exploring such spaces.

--Mark



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