Re: algdep() regression

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

On Tue, 18 Feb 2003, Igor Schein wrote:
> \\ pari-2.2.4:
>
> ? algdep(2^46,1)
> x - 70368744177664
>
> \\ pari-2.2.5
>
> ? algdep(2^46,1)
> 1
>
> Manual does warn about a possibility of an infinite loop, but not a
> completely bogus result.

It's not completely bogus: it tells you there does not exist a linear
combination of height less than 1 [trivial but true...].

> I can still trick it into giving a correct answer by doing
>
> algdep(precision(2^46.,29),1)
>
> but that shouldn't be necessary (I think?).

No it shouldn't. It was a typo in fact: I had changed the routine to depend
on the accuracy of the inputs. But if the input was exact, the computation
was done at precision -1 ... [ later on fixed to DEFAULTPREC, but that was
clearly not enough for large inputs ].

If infinite accuracy is detected, I now launch extendedgcd() instead to find
a small linear combination [ based on Havas/Majewski/Matthews's HNFLLL ideas,
about twice faster than kerint / integral LLL. Wrote it 5 years ago, had
never found a use for it before :-) ].

    Karim.
-- 
Karim Belabas                    Tel: (+33) (0)1 69 15 57 48
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Université Paris-Sud             Email: Karim.Belabas@math.u-psud.fr
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