Re: [PATCH] enable basic arithmetic with infinity

[Jeroen Demeyer <jdemeyer@cage.ugent.be>]

Hi Karim,

On 2014-09-27 15:44, Karim Belabas wrote:
> Unfortunately, I made the mistake of allowing valuation(0) a long time
> ago (circa 1995).
Now that you are breaking backwards compatibility anyway, then this 
would be a good time to reconsider that decision.

Consider the following two "extreme" cases:
(A) valuation(0,p) is not allowed in any case and always raises an error.
(B) valuation(0,p) is allowed and using it in mathematical operations 
(like 2*valuation(0,p)) works.

I personally think (B) would be the best, but I much prefer (A) to what 
we have now. The current situation is a very strange middle ground: it's 
like PARI cannot really decide whether they want to allow or disallow 
people calling valuation(0,p). At least with (A) you get an error 
immediately instead of at some later time, which would make debugging 
easier. It also sends a clear message to PARI users about valuation(0,p).

> I really don't want to instrument essentially all numerical functions to
> make sense of infinities-as-actual-numbers, including beasts such as
> a+I*oo which make perfect sense for complex integrals. A related
> former TODO item was to introduce IEEE754 special values as t_REALs
> (infinities, signed 0s, NaN, etc.): I decided against it a long time ago.
I never asked for that and I also don't think that allowing 2*oo would 
force you to consider oo everywhere.