Re: bug in nfsubfields()

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

[Igor:]
> another one of post-2.0.11 bugs:
> 
> ? nfisincl(x^2-2,x^4-2*x^2+9)
> [-1/6*x^3 + 5/6*x, 1/6*x^3 - 5/6*x]
> ? nfsubfields(nfinit(x^4-2*x^2+9),2)
> []

[or polredabs(x^4-2*x^2+9) --> x^4 + 1 which obviously has 3 quadratic
subfields].

I simplified a (Hensel-type) bound, but forgot that the "power basis" we use
may have an index (here 24), which should also be taken into account. Here's
a patch.

   Karim.

*** src/modules/subfield.c.orig Tue Dec 15 16:30:32 1998
--- src/modules/subfield.c      Thu Jan  7 17:30:46 1999
***************
*** 507,516 ****
  static GEN
  embedding_of_potential_subfields(GEN nf,GEN g,GEN DATA,GEN rootsA,GEN delta)
  {
!   GEN w0_inQ,w0,w1,h0,gp,p2,f,unmodp,p,ind;
    long av = avma, av1;
  
    f=(GEN)nf[1]; ind=(GEN)nf[4]; p=(GEN)DATA[2];
    gp=deriv(g,varn(g)); unmodp=gmodulsg(1,p);
    av1 = avma;
    w0 = interpolation_polynomial(gmul(rootsA,unmodp), delta);
--- 507,517 ----
  static GEN
  embedding_of_potential_subfields(GEN nf,GEN g,GEN DATA,GEN rootsA,GEN delta)
  {
!   GEN w0_inQ,w0,w1,h0,gp,p2,f,unmodp,p,ind, maxp;
    long av = avma, av1;
  
    f=(GEN)nf[1]; ind=(GEN)nf[4]; p=(GEN)DATA[2];
+   maxp=mulii((GEN)DATA[13],ind);
    gp=deriv(g,varn(g)); unmodp=gmodulsg(1,p);
    av1 = avma;
    w0 = interpolation_polynomial(gmul(rootsA,unmodp), delta);
***************
*** 544,550 ****
        fprintferr("Old Q-polynomial: "); outerr(w0_inQ);
        fprintferr("New Q-polynomial: "); outerr(p2);
      }
!     if (cmpii(p, (GEN)DATA[13]) > 0)
      {
        if (DEBUGLEVEL) fprintferr("coeff too big for embedding\n");
        avma=av; return gzero;
--- 545,551 ----
        fprintferr("Old Q-polynomial: "); outerr(w0_inQ);
        fprintferr("New Q-polynomial: "); outerr(p2);
      }
!     if (cmpii(p, maxp) > 0)
      {
        if (DEBUGLEVEL) fprintferr("coeff too big for embedding\n");
        avma=av; return gzero;

--
Karim Belabas                    email: Karim.Belabas@math.u-psud.fr
Dep. de Mathematiques, Bat. 425
Universite Paris-Sud             Tel: (00 33) 1 69 15 57 48
F-91405 Orsay (France)           Fax: (00 33) 1 69 15 60 19
--
PARI/GP Home Page: http://pari.home.ml.org