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MathGroup Archive 1997

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Re: Re: Q: Union and precision.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg8594] Re: [mg8544] Re: Q: Union and precision.
  • From: David Withoff <withoff>
  • Date: Sun, 7 Sep 1997 22:13:13 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

> > Hello again,
> >
> > How can I force Union to consider numbers equal in the current
> > precision as equal? Explanation:
> >
> > In:=    a=SetPrecision[1.234567,2]
> > Out:=   1.2
> >
> > In:=    b=SetPrecision[1.234561,2]  (* Notice difference *)
> > Out:=   1.2
> >
> > In:=    a==b
> > Out:=   True
> >
> > In:=    Union[{a,b}]
> > Out:=   {1.2,1.2} (* !!! *)
> >
> > How does Union evaluates equalities? How can I force it to do it the right
> > way??
>
> Hmmm.  Interesting.  And, perhaps, a little bizarre.
>
> When you do FullForm[a] you get 1.234567`2, whereas FullForm[b] returns
> 1.234561`2.  So Mathematica is storing the approximate real with precision
> information.  And asking whether "a==b" is different from asking whether
> "a===b" (since you're asking for equality rather than identity).
 
You should be able to get what you want using the SameTest option
(I think that this has already been suggested.)

The default value of the SameTest option in Union is equivalent to
the test used in OrderedQ or in Order, and makes distinctions between
any expressions that are not completely identical.  This test includes
consideration of the digits that are exposed by FullForm.  Such strict
comparison is needed because, for logical consistency, the comparison
test must be transitive.  In many cases you can use SameTest->Equal
or SameTest->SameQ if you only need to look for numerically significant
differences, but those comparisons are not transitive.  The Union
function, like OrderedQ and Order, makes distinctions that are
beyond the resolution of SameQ or Equal.

Dave Withoff
Wolfram Research


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