The Maxima convention (which is followed by most systems I know) is that
numbers expressed with a decimal point are interpreted as floating-point
numbers. It would of course be possible to change that decision, but the
next question then would be what the output form of such objects is: if 0.8
is interpreted as 8/10 (= 4/5), should it be output as 0.8? 8/10? or 4/5?
What is the output form of 0.8 + 1/10? How about 0.8 + 1/3? And how
about 0.8 + 1/3 - 11/15?
-s
On Sun, Jan 29, 2012 at 14:51, Andrew Davis <glneolistmail at gmail.com> wrote:
> I understand all that it is not exact
> > At first I thought it was just rounding error on display
>
> but why is it not held in memory symbolically so that it can be
> factored and manipulated correctly.
>
> Thank you.
>
> On Sun, Jan 29, 2012 at 12:47 PM, Raymond Toy <toy.raymond at gmail.com>wrote:
>
>> On 1/29/12 9:34 AM, Andrew Davis wrote:
>> > Hello all,
>> >
>> > While doing some homework, maxima return some incorrect limits. I traced
>> > the problem back to the number -8.14. It is evaluated to
>> > -8.140000000001, you can test this yourself by taking the limit of
>> > (-8.14+1) as x approaches any number, or just evaluate 1-8.14. This
>> > happens on all clisp's and even on http://calc.matthen.com/ , (evaluate
>> > -8.14). At first I thought it was just rounding error on display and
>> > not internal stored like that, but take a limit that uses -8.14 and you
>> > will have undefined results where it should have a real limit
>> > ( because -8.14 can be factored in my problem but -8.14000001 could not
>> > ). This is the only number I found that does that, but I suspect more.
>>
>> This, and questions like it, are becoming a FAQ. If you want exact
>> numbers, use exact numbers instead of floating-point. So use 814/100
>> instead. 8.14 cannot be represented exactly as (binary) floating-point
>> number. In fact 8.14 differs from 814/100 by 1/1759218604441600.
>>
>> Also read "What Every Computer Scientist Should Know About
>> Floating-Point Arithmetic", by David Goldberg. Google will find
>> suitable versions.
>>
>> Ray
>>
>>
>
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