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Re: SetPrecision causes logical comparisons to fail in Mathematica 5.1 on Mac OS X?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg64173] Re: SetPrecision causes logical comparisons to fail in Mathematica 5.1 on Mac OS X?
*From*: Paul Abbott <paul at physics.uwa.edu.au>
*Date*: Fri, 3 Feb 2006 01:58:20 -0500 (EST)
*Organization*: The University of Western Australia
*References*: <200601251345.IAA25867@smc.vnet.net> <dra3g3$m55$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
In article <dra3g3$m55$1 at smc.vnet.net>,
Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote:
> A partial explanation is given in the documentation for Equal:
>
> "Approximate numbers are considered equal if they differ in at most
> their last eight binary digits (roughly their last two decimal digits)."
There is a subtlety here: clearly
RealDigits[1.101`2, 2]
and
RealDigits[1`2, 2]
do differ in their "last eight" binary digits (actually, in both cases
there are only seven binary digits). The sublety is that all following
(suppressed) binary digits are 0.
> The workaround is never to set anything to have so few digits of
> precision; there is no reason at all to do so. Mathematica's
> "significance" arithmetic is an approximation to true interval
> arithmetic that works well only at high precision.
But if the application is fixed precision arithmetic then one could use
RealDigits (in base 2 or 10). For example,
RealDigits[1.101`2, 2] == RealDigits[1`2, 2]
RealDigits[1.101`2] == RealDigits[1`2]
> If you only wanted to reduce the number of digits displayed you
> should use
>
> NumberForm[1.101, 2]
Or set the PrintPrecision options using the Option Inspector.
Cheers,
Paul
_______________________________________________________________________
Paul Abbott Phone: 61 8 6488 2734
School of Physics, M013 Fax: +61 8 6488 1014
The University of Western Australia (CRICOS Provider No 00126G)
AUSTRALIA http://physics.uwa.edu.au/~paul
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