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(amusement) surprising result from PossibleZeroQ

  • To: mathgroup at smc.vnet.net
  • Subject: [mg130709] (amusement) surprising result from PossibleZeroQ
  • From: Peter Pein <petsie at dordos.net>
  • Date: Sat, 4 May 2013 03:19:01 -0400 (EDT)
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Dear group,

 playing around with distributions, I experienced one of these "that's
strange!"-moments.

 Take the quantile of a Pareto distribution

test = Quantile[ParetoDistribution[k, a], q];
InputForm@test

ConditionalExpression[Piecewise[{{k/(1 - q)^a^(-1), q < 1}}, Infinity],
 0 <= q <= 1]

I thought the nesting of ConditionalExpression and Piecewise could
simplify and tried every possible combination of 4 functions; to no avail:

Block[{f = {Refine, Simplify, FullSimplify, PiecewiseExpand}},
 Length[funcs =
   Composition @@@ Flatten[Tuples[f, #] & /@ Range[Length@f], 1]]
 ]
340

DeleteCases[Through[funcs[test]], test]
{}

My expectation has been sth. like

test2 = Piecewise[{{k/(1 - q)^(1/a), 0 <= q < 1},
                   {Infinity, q == 1}},
                  Indeterminate];

and

FullSimplify[test2 - test] // InputForm
ConditionalExpression[0, 0 <= q <= 1]

looks good. But compare this to

PossibleZeroQ[test2 - test] // InputForm
ConditionalExpression[False, 0 <= q <= 1]

I decided to classify that as "funny" :)

MemberQ[Attributes@PossibleZeroQ, Listable]
True


Have fun with or without Mathematica!

  Peter



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