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[1]:= r1*r2/(r1+r2) /. {r1 -> Interval[{min1,max1}], r2 -> Interval[{min2,max2}]} In[2]:= FullSimplify[%] In[3]:= % /. {min1 -> 10, max1 -> 20, min2 -> 20, max2 -> 40} Out[4]:= 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 +----------------------------------------------------------------------+