# [Maxima] strange behaviour with simple decimals

Jay Belanger 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
> approximate.

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.

Jay
```