Re: Uniform design

*To*: mathgroup at smc.vnet.net*Subject*: [mg48185] Re: Uniform design*From*: ab_def at prontomail.com (Maxim)*Date*: Mon, 17 May 2004 03:21:53 -0400 (EDT)*References*: <c7nnc7$dm5$1@smc.vnet.net> <200405130408.AAA26737@smc.vnet.net> <c81has$4rj$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote in message news:<c81has$4rj$1 at smc.vnet.net>... > On 13 May 2004, at 13:08, Maxim wrote: > > > Also, it's strange that Solve accepts intervals (Mathematica Help for > > Interval even gives such an example), but doesn't really support them: > > > > In[7]:= > > Solve[1/(x - 1) == Interval[{-1, 1}]] > > > > Out[7]= > > {{x -> Interval[{-Infinity, Infinity}]}} > > > > Not much point in treating this equation as Solve[1/(x-1)==a,x] and > > giving incorrect result. > > > I agree that it seems strange that this sort of thing was included in > the help browser, without additional comment, for it can certainly > only be misleading. Interval arithmetic is strange and does not obey > usual rules: > > 1 + 1/Interval[{-1, 1}] > > Interval[{-Infinity, 0}, {2, Infinity}] > > and > > (1 + Interval[{-1, 1}])/Interval[{-1, 1}] > > Interval[{-Infinity, Infinity}] > > This means that the answer returned by Solve will depend on how you > choose to write your equation: > > > Solve[1/(x - 1) == Interval[{-1, 1}]] > > > {{x -> Interval[{-Infinity, Infinity}]}} > > > Solve[x - 1 == 1/Interval[{-1, 1}]] > > {{x -> Interval[{-Infinity, 0}, {2, Infinity}]}} > > > (What is actually weird is that > > > Solve[1/(x - 1) == Interval[{-1, 1}], x] > > {} > > while > > > Solve[x - 1 == 1/Interval[{-1, 1}], x] > > {{x -> Interval[{-Infinity, 0}, {2, Infinity}]}}) > > > Whether the original answer should be considered wrong or only > excessively "pessimistic" depends on the context. The usual context in > which interval arithmetic is used is for error estimation, where it is > most important that it should not return an interval smaller than the > correct one and at least in this case it does not. > > > > Andrzej Kozlowski > Chiba, Japan > http://www.mimuw.edu.pl/~akoz/ The only problem with that kind of explanation is that it's made with hindsight. In[1]:= Solve[1/(x - 1) == Interval[{-1, 0}]] Out[1]= {{x -> -1}} What happened to "pessimistic interval" here? Maxim Rytin m.r at prontomail.com

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