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