Re: Why Mathematica does not issue a warning when the calculations

*To*: mathgroup at smc.vnet.net*Subject*: [mg117647] Re: Why Mathematica does not issue a warning when the calculations*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Tue, 29 Mar 2011 06:53:08 -0500 (EST)

In addition (for some curious reason) Richard never bothers to point out that z = 1.0000000000000000000; Block[{$MaxPrecision = 20, $MinPrecision = 20}, Table[(z = 2*z - z), {42}]] will give the output that other systems give (with all the accompanying problems your post below mentions). In other words, his (and only his) gripe is only with Mathematica's *default* arithmetic. Andrzej Kozlowski > Richard Fateman wrote: >> On 3/21/2011 4:13 AM, John Travolta Sardus wrote: >>> With Mathematica 8.0.1 >>> >>> N[FractionalPart[(6 + Sqrt[2])^20]] >>> >>> Result: >>> >>> -160. >>> >>> Is it a problem for all numerical software being able to recognize when >>> these calculations cannot be performed with the given machine accuracy? >> >> Yes, it is a problem. There is some support for this in other >> computational systems (e.g. "inexact" traps), and Mathematica has >> some tools involving increasing the precision of results, but basically >> recognizing that your answer is wrong is, in general, a problem. >> >>> Does this happen in this case only (where a wrong result is easily >>> recognized) or in other cases too? >> >> It happens in cases where you cannot see it directly, as well. > >> To some extent this is a problem with all arithmetic that is of finite >> precision, but it is especially a problem with Mathematica because of >> its unusual arithmetic. > > The example below, and the claim above, are completely tail backwards. > > In slightly more detail, this is the customary gripe, from one poster, > about degradation of precision when using precision tracking. But that > degradation is made apparent by the low or zero precision of the result. > > By way of contrast, programs that do no tracking give arbitrarily > terrible results, only with NO warning. So they might well get wrong the > example from the original post, even when ostensibly working at high > precision. > > >> Try this >> >> z = 1.11111111111111111111 >> While [(z = 2*z - z) != 0, Print[z]] >> >> This loop should never terminate, since 2*z-z is equal to z and is >> clearly very far away from zero, and setting z=2*z-z should not >> make it any closer to zero... Yet it terminates. So a test >> internal to a Mathematica program that involves arithmetic and >> comparison can produce odd results. >> >> This phenomenon is well-known to certain denizens of this newsgroup, >> who claim it is a feature.(!) You can judge for yourself. >> >> RJF > > Richard, > > The development of Mathematica, and usage of significance arithmetic, is > not going to change. The fact that you do not like it, or even > necessarily know how to use it to advantage, will not alter that. My > advice: get past it. Move onto something more important. Justifying this > particular gripe as important is not the tack to take (since you've gone > that route before and made no impression). > > Daniel Lichtblau > Wolfram Research >

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**Re: Why Mathematica does not issue a warning when the calculations**

**Re: Why Mathematica does not issue a warning when the calculations**

**Re: Why Mathematica does not issue a warning when the calculations**