Re: +-Inf and NaN

Since Maxima has symbols that are not float NaNs for  inf, minf, infinity,
undefined, indefinite...
it would seem superficially plausible to  unite these notations.
Not easy.
For solving inf-inf --> not zero, i've proposed and partially implemented
the idea
that inf, as well as und,  should be indexed each time it is generated. Thus
x: 1/0  returns und[1].
y: 1/0  returns und[2]

x-x returns 0.
x-y  is und[1]-und[2]  --> und[3].

how to implement?  lots of patches.
Here's another: allow rational numbers 1/0  and 0/0  and maybe -1/0


On Fri, Feb 23, 2024 at 11:05 AM Stavros Macrakis <[email protected]>
wrote:

> On Fri, Feb 23, 2024 at 12:20 PM Henry Baker <[email protected]> wrote:
>
>> ...There was a reason why Maclisp used a separate function name for float
>>
>> arithmetic functions, and it wasn't just to speed up float arithmetic.
>>
>
> Actually, that was precisely why. (plus a b) was be translated to (+$ a b)
> if a and b were of type float.
>
> The real reason is that *floats don't adhere to standard algebraic axioms*.
>>
>
> Well, since *plus* invokes floating point operations, it has the same
> issues.
>
>
>> In particular, standard "=" needs to be an *equivalence relation*, which
>>
>> means transitivity, among other things, so floating point needs its own
>>
>> brain-damaged 'equality' predicate -- perhaps IEEE-=
>>
>
> Extending data types with an NA value is pretty standard and useful, and
> not just for floats. One of these days (ha ha), we'll even get Maxima to
> realize that INF-INF does not equal 0, and that not all INFs are equal.
>
>

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