Re: znlog() behavior

[Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>]

On Wed, Jul 20, 2011 at 09:17:15PM +0200, Karim Belabas wrote:
> * Max Alekseyev [2011-07-20 20:57]:
> > Yet another problematic input:
> > 
> > ? znlog(3,Mod(3,8),znorder(Mod(3,8)))
> >   ***   at top-level: znlog(3,Mod(3,8),zno
> >   ***                 ^--------------------
> >   *** znlog: not a primitive root in znlog.
> >   ***   Break loop: type 'break' to go back to GP
> > 
> > I would expect it to simply return 1.
> 
> This one is a bug. Ackowledged :-)

Yes. I do not understand what kind of business znlog is doing, since Fp_log 
works:

? install(Fp_log,GGGG)
? Fp_log(3,3,2,8)
%3 = 1

It seems something in znlog assume the group is cyclic.
However the general question of whether some discrete log exist in a non cyclic Z/nZ
is probably harder than computing a discrete log assuming it exists.

For example, does
znlog(Mod(2298855537794180990195437251312444783755704421573, 59370428236762430669117195238685640183456843999797),Mod(35632422881419485197515454439741009824191527361551, 59370428236762430669117195238685640183456843999797),883849447146151864513469)
exists ?

Cheers,
Bill.