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MathGroup Archive 2004

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Re: Simple question or how Mathematica getting on my nerves.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg45783] Re: [mg45779] Simple question or how Mathematica getting on my nerves.
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Sun, 25 Jan 2004 03:04:39 -0500 (EST)
  • References: <200401240536.AAA07517@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On 24 Jan 2004, at 05:36, George wrote:

> Although the 2 results must be the same they aren't. WHY???????
> And not only this, but they differ by 10^21!!!!!! WHY????????
>
> Please copy and paste this to Mathematica (i tried 5.0 and 4.2) to
> understand what i mean:
>
>
> \!\(k[f_] :=
>     2687176093959399272413585923303421161600\ *\((1 - f)\)\^67\ *
>       f\^61\[IndentingNewLine]
>   N[\[Integral]\_\(6214\/10000\)\%\(5242\/10000\)k[
>           f] \[DifferentialD]f]\[IndentingNewLine]
>   N[\[Integral]\_0.6214\%0.5242 k[f] \[DifferentialD]f]\)
>
>



No, they mustn't be the same, at least not in Mathematica. In 
Mathemtica, 6214/10000  and 0.6214 are not at all the same, since


Precision[0.6214]


MachinePrecision


Precision[6214/10000]

Infinity

You need a lot of precision in the limits in your case to get an 
accurate answer, compare:


k[f_] := 2687176093959399272413585923303421161600*
    (1 - f)^67*f^61

Integrate[k[f], {f, N[6214/10000, MachinePrecision],
    N[5242/10000, MachinePrecision]}]

2.056906588664101*^22


Integrate[k[f], {f, N[6214/10000, 20], N[5242/10000, 20]}]

0``-20.81782624184503


Integrate[k[f], {f, N[6214/10000, 50], N[5242/10000, 50]}]


-0.1398383104167567265`8.464671124714428

Only the last answer is accurate.



Andrzej Kozlowski
Chiba, Japan
http://www.mimuw.edu.pl/~akoz/


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