       Re: A question on interval arithmetic

• To: mathgroup at smc.vnet.net
• Subject: [mg43734] Re: A question on interval arithmetic
• From: Olaf Rogalsky <olaf.rogalsky at theorie1.physik.uni-erlangen.de>
• Date: Thu, 2 Oct 2003 02:51:45 -0400 (EDT)
• References: <blcq5l\$p5f\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Oliver Friedrich wrote:
>
> Hallo,
>
> the resistance of 2 resistors in parallel is r1*r2/(r1+r2). Now I want to
> introduce tolerances in the resistors and ask for the range of resistance
> of the combination. One may think that e.g
>
> (r1*r2)/(r1+r2)/.{r1->Interval[{10,20}],r2->Interval[{20,40}]}
>
> would lead to the correct result, but there's a trap. If I replace the
> expressions by the intervals, Mathematica evaluates the new expression assuming
> that all four intervals are independant from each other. And that's not
> correct. Taken either the minimum or the maximum from a certain interval ,
> Mathematica should stick to that, because it is nonsense to take Min[r1] and Max
> [r1] within the same expression, r1 can have only one value at a time.

In:= r1*r2/(r1+r2) /. {r1 -> Interval[{min1,max1}], r2 -> Interval[{min2,max2}]}
In:= FullSimplify[%]
In:= % /. {min1 -> 10, max1 -> 20, min2 -> 20, max2 -> 40}
Out:= Interval[{20/3, 40/3}]
--
+----------------------------------------------------------------------+
I Dr. Olaf Rogalsky                         Institut f. Theo. Physik I I
I Tel.: 09131 8528440                       Univ. Erlangen-Nuernberg   I
I Fax.: 09131 8528444                       Staudtstrasse 7 B3         I
I rogalsky at theorie1.physik.uni-erlangen.de  D-91058 Erlangen           I
+----------------------------------------------------------------------+

```

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