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(amusement) surprising result from PossibleZeroQ
Posted:
May 4, 2013 3:17 AM


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



