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MathGroup Archive 1993

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problems with interval arithmetic

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: problems with interval arithmetic
  • From: fred at mi.el.utwente.nl (Fred Hugen - UT)
  • Date: Mon, 25 Oct 93 10:04:22 +0100

Hello,

I worked for while with interval arithmetic under Mma version 2.2.1 and
encountered something strange. Using constants within builIn mathematical
functions, such as Cos[Pi/2] and Sqrt[2], gives (completely) other results in
contrast to using the numerical approximations of these constants.
The following fragment shows this strange behaviour:

In[1] := exp1 = (x / Sqrt[2]) - (y / Sqrt[2]);
	 N[exp1] /. {x->Interval[{16,20}], y-> Interval[{16,20}]}
	 N[exp1 /. {x-> Interval[{16,20}] , y -> Interval[{16,20}]}]

Out[1] := Interval[{-2.82843, 2.82843}]
	  Interval[{22.6274, 28.2843}]

The first result seems to be the correct one. I can't explane the second. 
Has it to with the representation of Sqrt[2]?
	

Has anyone an explanation, or is it a bug?
(I send the same message to WRI).

						Thanks anyway,
							Fred Hugen





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