PARI/GP Bug report logs - #1151
rnfequation(,,1) is broken

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X-Loop: allomber@math.u-bordeaux.fr
From: allomber@math.u-bordeaux.fr (PARI/GP Bug Tracking System)
To: Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>
Subject: Bug#1151 acknowledged by developer
         (Re: Bug#1151: rnfequation(,,1) is broken)
Message-ID: <handler.1151.D1151.129719794614970.notifdone@pari.math.u-bordeaux.fr>
In-Reply-To: <20101218155503.GC9570@yellowpig>
References: <20110208204736.GA18741@math.u-bordeaux1.fr> <20101218155503.GC9570@yellowpig>
X-PARI/GP-PR-Message: they-closed 1151
X-PARI/GP-PR-Package: pari
X-PARI/GP-PR-Keywords: 
Reply-To: 1151@pari.math.u-bordeaux.fr

This is an automatic notification regarding your Bug report
#1151: rnfequation(,,1) is broken,
which was filed against the pari package.

It has been closed by one of the developers, namely
Karim Belabas <Karim.Belabas@math.u-bordeaux1.fr>.

Their explanation is attached below.  If this explanation is
unsatisfactory and you have not received a better one in a separate
message then please contact the developer, by replying to this email.

Bill Allombert
(administrator, PARI/GP bugs database)

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Date: Tue, 8 Feb 2011 21:47:36 +0100
From: Karim Belabas <Karim.Belabas@math.u-bordeaux1.fr>
To: Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>,
	1151-close@pari.math.u-bordeaux.fr
Subject: Re: Bug#1151: rnfequation(,,1) is broken
Message-ID: <20110208204736.GA18741@math.u-bordeaux1.fr>
References: <20101218155503.GC9570@yellowpig>
 <20110131235925.GE3266@yellowpig>
 <20110201162149.GF3266@yellowpig>
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User-Agent: Mutt/1.5.20 (2009-06-14)

* Bill Allombert [2011-02-01 17:57]:
> On Tue, Feb 01, 2011 at 12:59:25AM +0100, Bill Allombert wrote:
> > On Sat, Dec 18, 2010 at 04:55:03PM +0100, Bill Allombert wrote:
> > > Package: pari
> > > Version: 2.4.3, 2.3.5
> > > 
> > > Hello Karim,
> > > This issue was reported on the pari-users list
> > > <http://pari.math.u-bordeaux.fr/archives/pari-users-1012/msg00004.html>.
> > > I report it for reference.
> > > 
> > > ? f = (y^17-1)/(y-1);
> > > ? g = Mod(1,f)*x+Mod(y^6,f);
> > > ? rnfequation(f,g,1);
> > >   ***   at top-level: rnfequation(f,g,1)
> > >   ***                 ^------------------
> > >   *** rnfequation: the PARI stack overflows !
> > 
> > Well, according to my calculation the correct LERS is:
> > (-x^4 + x^3 - x^2)*y + (-x^7 + x^6 - x^5)
> > 
> > Furthermore, the values returned by Flx_resultant_all for x=2 are 144 times too large.
> > For x=3 the values are random but the quotient H0/H1 seems correct
> 
> The attached patch is probably incorrect, but it allows both 'make test-all' and 
> this test
> for(i=1,16,print(i);rnfequation(polcyclo(17,y),-x+y^i,1))
> 
> to work. Strange...

Fixed in svn, using quite different formulas (cf Algorithm 3.3.7 in GTM138).

Thanks !

    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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