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Re: Bad Precision output for SphericaBesselY and BesselY

• To: mathgroup at smc.vnet.net
• Subject: [mg123191] Re: Bad Precision output for SphericaBesselY and BesselY
• From: "Oleksandr Rasputinov" <oleksandr_rasputinov at hmamail.com>
• Date: Fri, 25 Nov 2011 04:59:45 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <jafud8$rrr$1@smc.vnet.net> <jalcav$snk$1@smc.vnet.net>

On Thu, 24 Nov 2011 12:12:15 -0000, Antonio Alvaro Ranha Neves  
<aneves at gmail.com> wrote:

> @Oleksander
> Why is Rationalize[120.3] better than SetPrecision[120.3, Infinity]?
> Each command gives me a rational output,
> 1203/10
> And
> 8465359924572979/70368744177664
> Respectivaly.
> I used 120.3 as an example, but my actual number is an irrational number  
> with a high precision (output of a findroot)
>

Simply because, when representing 120.3 as a rational number, in most  
cases one probably prefers a value that reproduces the number actually  
entered rather than one corresponding to the machine-precision real number  
closest to it. In this case the result of SetPrecision[120.3, Infinity] is  
equal to 1203/10 + 1/351843720888320, i.e. slightly more than 120.3. If  
the number is only known to finite precision to start with rather than  
being entered as something that could conceivably represent an exact  
rational value, it most likely makes little difference whether Rationalize  
or SetPrecision is used.

Of course, in your example, it will probably be better to use the  
PrecisionGoal option to get a number having sufficient precision from  
FindRoot, rather than accepting the default precision and then using a  
rational representation of that output in further calculations.