Hi Martin,
danke für die schnelle Rückmeldung. So wie es scheint basiert der Test auf
DDF, was vermutlich langsamer ist im Vergleich zu Rabins Test wenn grad(f)
= p = prim. Im allgemeinen Fall aber die schnellere Variante.
Danke nochmal,
viele Grüße
Am Mittwoch, 7. Mai 2014 15:35:45 UTC+2 schrieb Martin Albrecht:
>
> Here's how to find out:
>
> sage: P.<x> = GF(2)[]
> sage: f = P.random_element()
> sage: f.is_irreducible??
> <snip>
> if 0 == GF2X_IterIrredTest(self.x):
> return False
> else:
> return True
>
> Okay, what's GF2X_IterIrredTest?
>
> sage: search_src("GF2X_IterIrredTest")
> libs/ntl/ntl_GF2X_decl.pxd:62: long GF2X_IterIrredTest "IterIrredTest"
> (GF2X_c f)
>
> This leads us to NTL's IterIrredTest, searching for it leads to:
>
> http://www.shoup.net/ntl/doc/GF2XFactoring.txt
>
> long IterIrredTest(const GF2X& f);
>
> // performs an iterative deterministic irreducibility test, based on
> // DDF. Fast on average (when f has a small factor).
>
> Gruß,
> Martin
>
> On Wednesday 07 May 2014 05:51:11 Silke Johler wrote:
> > Hi everyone,
> >
> > I would like to know which test Sage uses to test irreducibility of a
> > polynomial over GF(2). Is it Rabin`s Test? How to compute the first
> > condition? I am not asking for the command, just the
> > technique<http://www.dict.cc/englisch-deutsch/technique.html> .
> >
> > Thanks.
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