Re: terrible bug in Mathematica (//N), but why????

Dr. Fateman,
Thanks for your response, but the problem I sent you is NOT using Sin, it's
using Sinh (hyperbolic sine is not periodic, rather exponential), again I
ask why does Mathematica not make this mistake for 44 or 42 but for 43?

rgds,

"Richard Fateman" <fateman@xxxxxxxxxxxxxxx> wrote in message
news:M3lAe.162$Rv7.79@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> There is nothing whatsoever
> to say that the expression AFTER fullsimplify might
> also be quite wrong. There are many books on numerical
> analysis...
>
> If you want something "automatic" to happen, you might
> try, in Mathematica..
> N[xxxxx,50] to try to get 50 decimal digits for xxxxx
> instead of
> N[xxxxx] which will use machine precision, and will be
> be faster but of unknown accuracy.
>
> As for differences with m being 43 instead of 44...
> Sin(2*n*pi) is 0 and Sin((2*n+1)*pi) is 1. Such
> things are hardly random :)
>
> RJF
>
>
> symbio wrote:
>
>> Dear Richard,
>> can you explain how such huge error occurs if FullSimplify is not used?
>> one case gives x10^25, the other with fullsimplify gives x10^-41 (or
>> almost zero). Does this mean that fullsimplify should be applied to ALL
>> numeric calculations before //N evaluate is applied? It seems very
>> random, specially if you change the m and n from 43 to 44 or 42, you
>> don't get that error!! how do you explain that?
>>


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