Re: idealstar()

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

The bug is in zprimestar:

this function only handles correctly :
_the case p<<2^32
_the case f=pr[4]=1

So idealstar(K,2^61-1) works (f=1)
but not 
idealstar(K,2^31-1) nor idealstar(K,2^31+129) (f=4)

--------base3.c--1151---
zprimestar(GEN nf,GEN pr,GEN ep,GEN x,GEN arch)
{
  long av=avma,av1,N,f,nbp,j,n,m,tetpil,i,e,a,b;
  GEN prh,p,pefm1,list,v,p1,p2,p3,p4,prk,uv,g0,newgen,pra,prb;
  GEN *gptr[2];

  if(DEBUGLEVEL>=4)
    { fprintferr("on traite pr = %Z ^ %Z\n",(long)pr,(long)ep); flusherr(); }
  prh=prime_to_ideal(nf,pr); N=lg(prh)-1;
  f=itos((GEN)pr[4]); p=(GEN)pr[1];

  pefm1 = addis(gpowgs(p,f), -1);
  if(DEBUGLEVEL>=4) {fprintferr("prh etc... calcule\n");flusherr();}
  v = zerocol(N);
  if (f==1) v[1]=gener(p)[2];
-----^^^^^^----------------------------f==1:OK
  else
  {
    GEN prhall = cgetg(3,t_VEC);
    long psim = itos(p);
----------------^^^^------------------------------itos: p<2^31-1
    list = (GEN)factor(pefm1)[1]; nbp=lg(list)-1;
    prhall[1]=(long)prh; prhall[2]=zero;
    for (n=psim; ; n++)
__________^^^^^^^^^^^^______________________p<2^31-1 may be too large

    {
      m=n;
      for (i=1; i<=N; i++)
g	if (!gcmp1(gcoeff(prh,i,i))) { v[i]=lstoi(m%psim); m/=psim; }
      for (j=1; j<=nbp; j++)
      {
        p1 = divii(pefm1,(GEN)list[j]);
	p1 = lift_intern(element_powmodpr(nf,v,p1,prhall));
        if (isnfscalar(p1) && gcmp1((GEN)p1[1])) break;
      }
      if (j>nbp) break;
    }

Bill