Re: Re: LegendreP error (bug?) in Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg81230] Re: [mg81214] Re: LegendreP error (bug?) in Mathematica
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Mon, 17 Sep 2007 03:29:44 -0400 (EDT)
• References: <200709160802.EAA29974@smc.vnet.net>

```On 16 Sep 2007, at 17:02, Bill Rowe wrote:

> On 9/15/07 at 4:15 AM, rschmied at gmail.com (Roman) wrote:
>
>> But, instead of telling you that you are getting garbage, the
>> algorithm returns a number with exaggerated precision:
>
>> In[3] := LegendreP[200, 43, 0.8] // Precision
>> Out[3] = MachinePrecision
>
> As I understand the documentation, expressions with only exact
> numbers and machine precision numbers always return
> MachinePrecision as the precision. If I have this correct, then
> Precision only returns useful results when expressions make use
> of Mathematica's variable precision arithmetic.
>
> Instead of Precision using Accuracy
>
> In[5]:= LegendreP[200, 43, 0.8] // Accuracy
>
> Out[5]= -102.834
>
> gives a clear indication what is returned by LegendreP[200, 43,
> 0.8] is problematic.
>
> --
> To reply via email subtract one hundred and four
>

You are only paritally right here. With MachinePrecision input
Mathemaitca does not track either Precision or Accuracy of the output
and both Precision and Accuracy are computed in purely formal manner.
Neither gives any useful information and, in particular, the value
you get for Accuracy in your above computation does not indicate
anything (in fact, a negative value of Accuracy does not indicate
that the computation is "problematic" - only that the size of the
absolute error is larger than 1, since Accuracy is defined as -Log[Abs
[e],10], where e is the error - of course only in the case of
arbitrary precision calculations).

Andrzej Kozlowski

```

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