+oo / -oo (infinity)

[Karim Belabas <Karim.Belabas@math.u-bordeaux.fr>]

Hi pari-dev,

after toying with the idea for a few years, I finally bit the bullet
and introduced a new type t_INFINITY, containing only 2 objects \pm\infty
(printed respectively as +oo / -oo).

It's meant as a "placeholder" for functions that accept
\pm\infty as a parameter or produce it as a result:

  ? poldegree(0)
  %1 = -oo
  ? valuation(0, 2)
  %2 = +oo
  ? K = nfinit(x^2+1); P = idealprimedec(K,2)[1];
  ? nfeltval(K,0,P)
  %4 = +oo
  ? idealval(K,[;],P)
  %5 = +oo
  ? intnum(t=0, +oo, 1/(t^2+1))
  %6 = 1.5707963267948966192313216916397514421

The only implemented methods are: negation, comparison with real scalars (and
infinities), equality tests and all variants of print():

  ? -(-oo)
  %7 = +oo
  ? -oo < Pi
  %8 = 1
  ? -oo < +oo
  %9 = 1
  ? oo == 1
  %10 = 0
  ? oo == oo
  %11 = 1
  ? printtex(-oo)
  -\infty

1) In particular, you can't "compute" with such objects:

  ? oo + 1
  ***   at top-level: oo+1
  ***                   ^--
  *** _+_: forbidden addition t_INT + t_INFINITY.
  ? I * oo
  ***   at top-level: I*oo
  ***                  ^---
  *** _*_: forbidden multiplication t_COMPLEX * t_INFINITY.

2) This isn't meant to handle floating point overflow either

  ? exp(1e100)
    ***   at top-level: exp(1e100)
    ***                 ^----------
    *** exp: overflow in expo().


It's a bit sad to "waste" a type for only two objects so far, but it was the
only sensible possibility. (I definitely didn't want to abuse one of the
existing types, e.g. taking advantage of "impossible values" for t_REAL
codewords.) 

Cheers,

    K.B.
--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite Bordeaux 1          Fax: (+33) (0)5 40 00 69 50
351, cours de la Liberation    http://www.math.u-bordeaux1.fr/~kbelabas/
F-33405 Talence (France)       http://pari.math.u-bordeaux1.fr/  [PARI/GP]
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