GEN
gcdii(GEN a, GEN b)
{
long v, w;
pari_sp av;
GEN t;
switch (absi_cmp(a,b))
{
case 0: return absi(a);
case -1: swap(a,b);
}
if (!signe(b)) return absi(a);
/* here |a|>|b|>0. Try single precision first */
if (lgefint(a)==3)
return igcduu((ulong)a[2], (ulong)b[2]);
if (lgefint(b)==3)
{
ulong u = resiu(a,(ulong)b[2]);
if (!u) return absi(b);
return igcduu((ulong)b[2], u);
}
/* larger than gcd: "avma=av" gerepile (erasing t) is valid */
av = avma; (void)new_chunk(lgefint(b)+1); /* HACK */
t = remii(a,b);
if (!signe(t)) { avma=av; return absi(b); }
a = b; b = t;
v = vali(a); a = shifti(a,-v); setabssign(a);
w = vali(b); b = shifti(b,-w); setabssign(b);
if (w < v) v = w;
switch(absi_cmp(a,b))
{
case 0: avma=av; a=shifti(a,v); return a;
case -1: swap(a,b);
}
if (is_pm1(b)) { avma=av; return int2n(v); }
{
/* general case */
/*This serve two purposes: 1) mpn_gcd destroy its input and need an extra
* limb 2) this allows us to use icopy instead of gerepile later. NOTE: we
* must put u before d else the final icopy could fail.
*/
GEN res= cgeti(lgefint(a)+1);
GEN ca = icopy_ef(a,lgefint(a)+1);
GEN cb = icopy_ef(b,lgefint(b)+1);
long l = mpn_gcd(LIMBS(res), LIMBS(ca), NLIMBS(ca), LIMBS(cb), NLIMBS(cb));
res[1] = evalsigne(1)|evallgefint(l+2);
avma=av;
return shifti(res,v);
}
}
/* return 0 if |g[i]| > M[i] for some i; 1 otherwise */
static long
ok_coeffs(GEN g,GEN M)
{
long i, lg = lg(g)-1; /* g is monic, and cst term is ok */
for (i=3; i<lg; i++)
if (absi_cmp(gel(g,i), gel(M,i)) > 0) return 0;
return 1;
}
/* Return a subfield, gen_0 [ change p ] or NULL [ not a subfield ] */
static GEN
subfield(GEN A, blockdata *B)
{
long N, i, j, d, lf, m = lg(A)-1;
GEN M, pe, pol, fhk, g, e, d_1_term, delta, listdelta, whichdelta;
GEN T = B->S->T, p = B->S->p, firstroot = B->S->firstroot;
pol= (GEN)B->DATA[1]; N = degpol(pol); d = N/m; /* m | N */
pe = (GEN)B->DATA[2];
fhk= (GEN)B->DATA[3];
M = (GEN)B->DATA[8];
delta = cgetg(m+1,t_VEC);
whichdelta = cgetg(N+1, t_VECSMALL);
d_1_term = gen_0;
for (i=1; i<=m; i++)
{
GEN Ai = gel(A,i), p1 = (GEN)fhk[Ai[1]];
for (j=2; j<=d; j++)
p1 = Fq_mul(p1, (GEN)fhk[Ai[j]], T, pe);
gel(delta,i) = p1;
if (DEBUGLEVEL>2) fprintferr("delta[%ld] = %Z\n",i,p1);
/* g = prod (X - delta[i])
* if g o h = 0 (pol), we'll have h(Ai[j]) = delta[i] for all j */
/* fk[k] belongs to block number whichdelta[k] */
for (j=1; j<=d; j++) whichdelta[Ai[j]] = i;
if (typ(p1) == t_POL) p1 = constant_term(p1);
d_1_term = addii(d_1_term, p1);
}
d_1_term = centermod(d_1_term, pe); /* Tr(g) */
if (absi_cmp(d_1_term, gel(M,3)) > 0) {
if (DEBUGLEVEL>1) fprintferr("d-1 test failed\n");
return NULL;
}
g = FqV_roots_to_pol(delta, T, pe, 0);
g = centermod(polsimplify(g), pe); /* assume g in Z[X] */
if (DEBUGLEVEL>2) fprintferr("pol. found = %Z\n",g);
if (!ok_coeffs(g,M)) {
if (DEBUGLEVEL>1) fprintferr("coeff too big for pol g(x)\n");
return NULL;
}
if (!FpX_is_squarefree(g, p)) {
if (DEBUGLEVEL>1) fprintferr("changing f(x): p divides disc(g)\n");
compute_data(B);
return subfield(A, B);
}
lf = lg(firstroot); listdelta = cgetg(lf, t_VEC);
for (i=1; i<lf; i++) listdelta[i] = delta[whichdelta[firstroot[i]]];
if (DEBUGLEVEL) fprintferr("candidate = %Z\n", g);
e = embedding(g, B->DATA, B->S, B->PD->den, listdelta);
if (!e) return NULL;
if (DEBUGLEVEL) fprintferr("embedding = %Z\n", e);
return _subfield(g, e);
}
