Re: ispolygonal

[Karim Belabas <Karim.Belabas@math.u-bordeaux1.fr>]

* Bill Allombert [2012-05-08 23:34]:
> I am experimenting with ispolygonal:
> 
> ? ispolygonal(36,2)
>   ***   at top-level: ispolygonal(36,2)
>   ***                 ^-----------------
>   *** ispolygonal: incorrect type in ispolygonal (t_INT).
> 
> This is confusing since 2 is a t_INT.

The rationale was to avoid the e_MISC error type [ which is essentially
impossible to trap cleanly ], and consider that the expected input
"type" was 'a t_INT in Z_{> 2}'.

This is a bit far-fetched and potentially confusing, I temporarily changed
it to e_MISC.

Presumably we need a general error type for "violated inequality" ?

  pari_err(e_INEQ, "ispolygonal", "s > 2", s);

==>

 incorrect value in %s (need %s). Was: %s


Similar checks occur quite often,

  (14:13) gp > vector(-1)
  ***   at top-level: vector(-1)
  ***                 ^----------
  *** vector: incorrect type in vector [negative dimension] (t_INT).

  pari_err(e_INEQ, "vector", "n >= 0", n);


  (14:16) gp > primes(-1)
  ***   at top-level: primes(-1)
  ***                 ^----------
  *** primes: incorrect type in primes [negative dimension] (t_INT).

  pari_err(e_INEQ, "primes", "n >= 0", n);

  (14:18) gp > sigma(0)
  ***   at top-level: sigma(0)
  ***                 ^--------
  *** sigma: zero argument in an arithmetic function.

  pari_err(e_INEQ, "sigma", "x != 0", x);

etc.


> 
> ? [ispolygonal(36,3,&N),N]
> %7 = [1,9223372036854775816]
> 
> N is wrong obviously
> 
> ? [ispolygonal(33496046025275818831719453356591156886^2,3,&N),N]
> %19 = [1,47370562574818466718159911997304784776]
> 
> N is wrong, it should be 47370562574818466708936539960450008968

Both of these had the same origin, and were specific to s = 3 [ which
I had special-cased anyway, but not enough, thereby later treating s - 4
as an ulong ]. Fixed in master.

What do people think about the function name ? Obviously,
ispolygonalinteger() would be clearer but quite a bit more verbose than
our usual functions.

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/~belabas/
F-33405 Talence (France)       http://pari.math.u-bordeaux1.fr/  [PARI/GP]
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