Karim Belabas on Sat, 29 Oct 2022 23:11:04 +0200

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Re: arithmetic operations with t_INFINITY

* Max Alekseyev [2022-10-29 22:38]:
> For this purpose, the function isinfinite(v) (or alike) would be more
> suitable, or checking the equality type(v) == "t_INFINITY".
> Testing "v == oo" is not mathematically rigorous [...]

If is rigorous, because we *define* valuation(0, p) := +oo or
poldegree(0) := -oo, i.e. those two sentinel objects +oo and -oo are
returned by specific functions to indicate well-specified conditions.
(As explained before, those are not "arithmetic objects" that could for
instance be returned or incorporated into a floating point computation
as we could expect from a standard such as IEEE 754.)



P.S. oo can also be used as loop or integral endpoint as in
  intnum(x = 1, oo, 1/x^2)
  for (k = 1, oo, ...)

Karim Belabas, IMB (UMR 5251), Université de Bordeaux
Vice-président en charge du Numérique
T: (+33) 05 40 00 29 77; http://www.math.u-bordeaux.fr/~kbelabas/