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MathGroup Archive 1997

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(Fwd) Re: the Union of real numbers

  • To: mathgroup at smc.vnet.net
  • Subject: [mg7215] (Fwd) Re: [mg7004] the Union of real numbers
  • From: "caffa" <caffa at iabg.de>
  • Date: Fri, 16 May 1997 02:31:02 -0400 (EDT)
  • Organization: iabg.de
  • Sender: owner-wri-mathgroup at wolfram.com

Russell Towle wrote:

> I am trying to apply the Union function to a list of real numbers,
> in which many duplicates occur.  However, small differences between
> the numbers cause some of the duplicates to be retained instead of
> discarded.
>
> Suppose the list of real numbers is called k, my present work-around
> is as follows:
>
> Union [ Rationalize [ k, 10^-6 ] ].
>
> This does discard the duplicates.  Is there a better method?

Yes. Try:

   In[1]:= lst = {3.0, 2.001, 2.0, 1.01, 1.02};

   In[2]:= eps = 0.02;

   In[3]:= Union[lst, SameTest->(Abs[#1-#2]<=eps &)]

   Out[3]= {1.01, 2., 3.}

Compare:

   In[4]:= Union[Rationalize[lst, 0.02]]

               51
   Out[4]= {1, --, 2, 3}
               50

Vittorio G. Caffa

Vittorio Caffa

IABG, Abt. CC22
Einsteinstr. 20
D-85521 Ottobrunn

Tel.:  (089) 6088-2054
FAX:   (089) 6088-2121
eMail: caffa at iabg.de


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