[Maxima] strange behaviour with simple decimals
belanger at truman.edu
Wed Apr 11 15:25:07 CDT 2007
"Andrey G. Grozin" <A.G.Grozin at inp.nsk.su> writes:
> On Wed, 11 Apr 2007, Jay Belanger wrote:
>> Base 10 most certainly does stand out.
>> While other bases have their uses, I would guess most people enter
>> data in base 10.
> How data are input is irrelevant for the choice of the best way to
> manipulate them.
Perhaps, but it does make base 10 stand out.
>> It may well be the case that getting small errors when doing decimal
>> arithmetic is an acceptable cost, but it was previously implied that
>> it is a silly thing to talk about. I disagree. What's more, I think
>> that if getting small errors when computing 1.4^2 is the cost of using
>> Maxima, the manual should clearly state that.
> I think that everybody should know that when one writes any number with .
> in it (a floating-point number), all subsequent calculations will be
If you do calculations in which every step can be carried out
in the current precision exactly, and yet the answer is off, then I
think something worth noting is going on.
> And as for teaching junior school children, I am sure many things are done
> wrong. A classical example is x^(1/3). School children (and even teachers)
> beleive that it is real and negative for x<0. Maxima uses a more
> consistent definition - a cut along a negative real half-axis, with an
> additional rule that when we are exactly on the cut, the value from its
> upper side is used. So, for x<0 the result is complex. I'd say that here
> (as very often) maxima is right, and the school education is wrong.
The school education certainly isn't wrong any more than Maxima is.
In this case, I suppose, you could say:
(1) x^(1/3) is a real-valued function on the reals
(2) x^(1/3) isn't a function
(3) x^(1/3) isn't a function, but let's take the principal branch
I'd hesistate to say any of these are wrong.
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