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);
}
}
/* pol^2 mod (polcyclo(5),N) */
static GEN
sqrmod5(GEN pol, Red *R)
{
GEN c2,b,c,d,A,B,C,D;
long lv = lg(pol);
if (lv==2) return pol;
if (lv==3) return sqrconst(pol, R);
c = gel(pol,3); c2 = shifti(c,1);
d = gel(pol,2);
if (lv==4)
{
A = sqri(d);
B = mulii(c2, d);
C = sqri(c);
A = centermodii(A, R->N, R->N2);
B = centermodii(B, R->N, R->N2);
C = centermodii(C, R->N, R->N2); return mkpoln(3,A,B,C);
}
b = gel(pol,4);
if (lv==5)
{
A = mulii(b, subii(c2,b));
B = addii(sqri(c), mulii(b, subii(shifti(d,1),b)));
C = subii(mulii(c2,d), sqri(b));
D = mulii(subii(d,b), addii(d,b));
}
else
{ /* lv == 6 */
GEN a = gel(pol,5), a2 = shifti(a,1);
/* 2a(d - c) + b(2c - b) */
A = addii(mulii(a2, subii(d,c)), mulii(b, subii(c2,b)));
/* c(c - 2a) + b(2d - b) */
B = addii(mulii(c, subii(c,a2)), mulii(b, subii(shifti(d,1),b)));
/* (a-b)(a+b) + 2c(d - a) */
C = addii(mulii(subii(a,b),addii(a,b)), mulii(c2,subii(d,a)));
/* 2a(b - c) + (d-b)(d+b) */
D = addii(mulii(a2, subii(b,c)), mulii(subii(d,b), addii(d,b)));
}
A = centermodii(A, R->N, R->N2);
B = centermodii(B, R->N, R->N2);
C = centermodii(C, R->N, R->N2);
D = centermodii(D, R->N, R->N2); return mkpoln(4,A,B,C,D);
}
/* Assume P in nfX form [ unifpol(,t_COL) ], lc(P) != 0 mod p.
* Reduce P to Zp[X]/(T) mod p^a */
static GEN
ZqX(GEN P, GEN pk, GEN T, GEN proj)
{
long i, l = lg(P);
GEN z, pks2 = shifti(pk,-1);
z = cgetg(l,t_POL); z[1] = P[1];
for (i=2; i<l; i++) gel(z,i) = nf_to_Zq(gel(P,i),T,pk,pks2,proj);
return normalizepol(z);
}
/* pol^2 mod (x^2+1,N) */
static GEN
sqrmod4(GEN pol, Red *R)
{
GEN a,b,A,B;
long lv = lg(pol);
if (lv==2) return pol;
if (lv==3) return sqrconst(pol, R);
a = gel(pol,3);
b = gel(pol,2);
A = centermodii(mulii(a, shifti(b,1)), R->N, R->N2);
B = centermodii(mulii(subii(b,a),addii(b,a)), R->N, R->N2);
return makepoldeg1(A,B);
}
/* Return e(t) = \prod_{p-1 | t} p^{1+v_p(t)}}
* faet contains the odd prime divisors of e(t) */
static GEN
compute_e(ulong t, GEN *faet)
{
GEN L, P, D = divisorsu(t);
long l = lg(D);
ulong k;
P = vecsmalltrunc_init(l);
L = vecsmalltrunc_init(l);
for (k=l-1; k>1; k--) /* k != 1: avoid d = 1 */
{
ulong d = D[k];
if (uisprime(++d))
{ /* we want q = 1 (mod p) prime, not too large */
if (d > 50000000) return gen_0;
vecsmalltrunc_append(P, d);
vecsmalltrunc_append(L, upowuu(d, 1 + u_lval(t,d)));
}
}
if (faet) *faet = P;
return shifti(zv_prod_Z(L), 2 + u_lval(t,2));
}
int
ratlift(GEN x, GEN m, GEN *a, GEN *b, GEN amax, GEN bmax)
{
GEN d,d1,v,v1,q,r;
pari_sp av = avma, av1, lim;
long lb,lr,lbb,lbr,s,s0;
ulong vmax;
ulong xu,xu1,xv,xv1; /* Lehmer stage recurrence matrix */
int lhmres; /* Lehmer stage return value */
if ((typ(x) | typ(m) | typ(amax) | typ(bmax)) != t_INT) pari_err(arither1);
if (signe(bmax) <= 0)
pari_err(talker, "ratlift: bmax must be > 0, found\n\tbmax=%Z\n", bmax);
if (signe(amax) < 0)
pari_err(talker, "ratilft: amax must be >= 0, found\n\tamax=%Z\n", amax);
/* check 2*amax*bmax < m */
if (cmpii(shifti(mulii(amax, bmax), 1), m) >= 0)
pari_err(talker, "ratlift: must have 2*amax*bmax < m, found\n\tamax=%Z\n\tbmax=%Z\n\tm=%Z\n", amax,bmax,m);
/* we _could_ silently replace x with modii(x,m) instead of the following,
* but let's leave this up to the caller
*/
avma = av; s = signe(x);
if (s < 0 || cmpii(x,m) >= 0)
pari_err(talker, "ratlift: must have 0 <= x < m, found\n\tx=%Z\n\tm=%Z\n", x,m);
/* special cases x=0 and/or amax=0 */
if (s == 0)
{
if (a != NULL) *a = gen_0;
if (b != NULL) *b = gen_1;
return 1;
}
else if (signe(amax)==0)
return 0;
/* assert: m > x > 0, amax > 0 */
/* check here whether a=x, b=1 is a solution */
if (cmpii(x,amax) <= 0)
{
if (a != NULL) *a = icopy(x);
if (b != NULL) *b = gen_1;
return 1;
}
/* There is no special case for single-word numbers since this is
* mainly meant to be used with large moduli.
*/
(void)new_chunk(lgefint(bmax) + lgefint(amax)); /* room for a,b */
d = m; d1 = x;
v = gen_0; v1 = gen_1;
/* assert d1 > amax, v1 <= bmax here */
lb = lgefint(bmax);
lbb = bfffo(*int_MSW(bmax));
s = 1;
av1 = avma; lim = stack_lim(av, 1);
/* general case: Euclidean division chain starting with m div x, and
* with bounds on the sequence of convergents' denoms v_j.
* Just to be different from what invmod and bezout are doing, we work
* here with the all-nonnegative matrices [u,u1;v,v1]=prod_j([0,1;1,q_j]).
* Loop invariants:
* (a) (sign)*[-v,v1]*x = [d,d1] (mod m) (componentwise)
* (sign initially +1, changes with each Euclidean step)
* so [a,b] will be obtained in the form [-+d,v] or [+-d1,v1];
* this congruence is a consequence of
* (b) [x,m]~ = [u,u1;v,v1]*[d1,d]~,
* where u,u1 is the usual numerator sequence starting with 1,0
* instead of 0,1 (just multiply the eqn on the left by the inverse
* matrix, which is det*[v1,-u1;-v,u], where "det" is the same as the
* "(sign)" in (a)). From m = v*d1 + v1*d and
* (c) d > d1 >= 0, 0 <= v < v1,
* we have d >= m/(2*v1), so while v1 remains smaller than m/(2*amax),
* the pair [-(sign)*d,v] satisfies (1) but violates (2) (d > amax).
* Conversely, v1 > bmax indicates that no further solutions will be
* forthcoming; [-(sign)*d,v] will be the last, and first, candidate.
* Thus there's at most one point in the chain division where a solution
* can live: v < bmax, v1 >= m/(2*amax) > bmax, and this is acceptable
* iff in fact d <= amax (e.g. m=221, x=34 or 35, amax=bmax=10 fail on
* this count while x=32,33,36,37 succeed). However, a division may leave
* a zero residue before we ever reach this point (consider m=210, x=35,
* amax=bmax=10), and our caller may find that gcd(d,v) > 1 (numerous
* examples -- keep m=210 and consider any of x=29,31,32,33,34,36,37,38,
* 39,40,41).
* Furthermore, at the start of the loop body we have in fact
* (c') 0 <= v < v1 <= bmax, d > d1 > amax >= 0,
* (and are never done already).
*
* Main loop is similar to those of invmod() and bezout(), except for
* having to determine appropriate vmax bounds, and checking termination
* conditions. The signe(d1) condition is only for paranoia
*/
while (lgefint(d) > 3 && signe(d1))
{
/* determine vmax for lgcdii so as to ensure v won't overshoot.
* If v+v1 > bmax, the next step would take v1 beyond the limit, so
* since [+-d1,v1] is not a solution, we give up. Otherwise if v+v1
* is way shorter than bmax, use vmax=MAXULUNG. Otherwise, set vmax
* to a crude lower approximation of bmax/(v+v1), or to 1, which will
* allow the inner loop to do one step
*/
r = addii(v,v1);
lr = lb - lgefint(r);
lbr = bfffo(*int_MSW(r));
if (cmpii(r,bmax) > 0) /* done, not found */
{
avma = av;
return 0;
}
else if (lr > 1) /* still more than a word's worth to go */
{
vmax = MAXULONG;
}
else /* take difference of bit lengths */
{
lr = (lr << TWOPOTBITS_IN_LONG) - lbb + lbr;
if ((ulong)lr > BITS_IN_LONG)
vmax = MAXULONG;
else if (lr == 0)
vmax = 1UL;
else
vmax = 1UL << (lr-1);
/* the latter is pessimistic but faster than a division */
}
/* do a Lehmer-Jebelean round */
lhmres = lgcdii((ulong *)d, (ulong *)d1, &xu, &xu1, &xv, &xv1, vmax);
if (lhmres != 0) /* check progress */
{ /* apply matrix */
if ((lhmres == 1) || (lhmres == -1))
{
s = -s;
if (xv1 == 1)
{
/* re-use v+v1 computed above */
v=v1; v1=r;
r = subii(d,d1); d=d1; d1=r;
}
else
{
r = subii(d, mului(xv1,d1)); d=d1; d1=r;
r = addii(v, mului(xv1,v1)); v=v1; v1=r;
}
}
else
{
r = subii(muliu(d,xu), muliu(d1,xv));
d1 = subii(muliu(d,xu1), muliu(d1,xv1)); d = r;
r = addii(muliu(v,xu), muliu(v1,xv));
v1 = addii(muliu(v,xu1), muliu(v1,xv1)); v = r;
if (lhmres&1)
{
setsigne(d,-signe(d));
s = -s;
}
else if (signe(d1))
{
setsigne(d1,-signe(d1));
}
}
/* check whether we're done. Assert v <= bmax here. Examine v1:
* if v1 > bmax, check d and return 0 or 1 depending on the outcome;
* if v1 <= bmax, check d1 and return 1 if d1 <= amax, otherwise
* proceed.
*/
if (cmpii(v1,bmax) > 0) /* certainly done */
{
avma = av;
if (cmpii(d,amax) <= 0) /* done, found */
{
if (a != NULL)
{
*a = icopy(d);
setsigne(*a,-s); /* sign opposite to s */
}
if (b != NULL) *b = icopy(v);
return 1;
}
else /* done, not found */
return 0;
}
else if (cmpii(d1,amax) <= 0) /* also done, found */
{
avma = av;
if (a != NULL)
{
if (signe(d1))
{
*a = icopy(d1);
setsigne(*a,s); /* same sign as s */
}
else
*a = gen_0;
}
if (b != NULL) *b = icopy(v1);
return 1;
}
} /* lhmres != 0 */
if (lhmres <= 0 && signe(d1))
{
q = dvmdii(d,d1,&r);
#ifdef DEBUG_LEHMER
fprintferr("Full division:\n");
printf(" q = "); output(q); sleep (1);
#endif
d=d1; d1=r;
r = addii(v,mulii(q,v1));
v=v1; v1=r;
s = -s;
/* check whether we are done now. Since we weren't before the div, it
* suffices to examine v1 and d1 -- the new d (former d1) cannot cut it
*/
if (cmpii(v1,bmax) > 0) /* done, not found */
{
avma = av;
return 0;
}
else if (cmpii(d1,amax) <= 0) /* done, found */
{
avma = av;
if (a != NULL)
{
if (signe(d1))
{
*a = icopy(d1);
setsigne(*a,s); /* same sign as s */
}
else
*a = gen_0;
}
if (b != NULL) *b = icopy(v1);
return 1;
}
}
if (low_stack(lim, stack_lim(av,1)))
{
GEN *gptr[4]; gptr[0]=&d; gptr[1]=&d1; gptr[2]=&v; gptr[3]=&v1;
if(DEBUGMEM>1) pari_warn(warnmem,"ratlift");
gerepilemany(av1,gptr,4);
}
} /* end while */
/* Postprocessing - final sprint. Since we usually underestimate vmax,
* this function needs a loop here instead of a simple conditional.
* Note we can only get here when amax fits into one word (which will
* typically not be the case!). The condition is bogus -- d1 is never
* zero at the start of the loop. There will be at most a few iterations,
* so we don't bother collecting garbage
*/
while (signe(d1))
{
/* Assertions: lgefint(d)==lgefint(d1)==3.
* Moreover, we aren't done already, or we would have returned by now.
* Recompute vmax...
*/
#ifdef DEBUG_RATLIFT
fprintferr("rl-fs: d,d1=%Z,%Z\n", d, d1);
fprintferr("rl-fs: v,v1=%Z,%Z\n", v, v1);
#endif
r = addii(v,v1);
lr = lb - lgefint(r);
lbr = bfffo(*int_MSW(r));
if (cmpii(r,bmax) > 0) /* done, not found */
{
avma = av;
return 0;
}
else if (lr > 1) /* still more than a word's worth to go */
{
vmax = MAXULONG; /* (cannot in fact happen) */
}
else /* take difference of bit lengths */
{
lr = (lr << TWOPOTBITS_IN_LONG) - lbb + lbr;
if ((ulong)lr > BITS_IN_LONG)
vmax = MAXULONG;
else if (lr == 0)
vmax = 1UL;
else
vmax = 1UL << (lr-1); /* as above */
}
#ifdef DEBUG_RATLIFT
fprintferr("rl-fs: vmax=%lu\n", vmax);
#endif
/* single-word "Lehmer", discarding the gcd or whatever it returns */
(void)rgcduu((ulong)*int_MSW(d), (ulong)*int_MSW(d1), vmax, &xu, &xu1, &xv, &xv1, &s0);
#ifdef DEBUG_RATLIFT
fprintferr("rl-fs: [%lu,%lu; %lu,%lu] %s\n",
xu, xu1, xv, xv1,
s0 < 0 ? "-" : "+");
#endif
if (xv1 == 1) /* avoid multiplications */
{
/* re-use v+v1 computed above */
v=v1; v1=r;
r = subii(d,d1); d=d1; d1=r;
s = -s;
}
else if (xu == 0) /* and xv==1, xu1==1, xv1 > 1 */
{
r = subii(d, mului(xv1,d1)); d=d1; d1=r;
r = addii(v, mului(xv1,v1)); v=v1; v1=r;
s = -s;
}
else
{
r = subii(muliu(d,xu), muliu(d1,xv));
d1 = subii(muliu(d,xu1), muliu(d1,xv1)); d = r;
r = addii(muliu(v,xu), muliu(v1,xv));
v1 = addii(muliu(v,xu1), muliu(v1,xv1)); v = r;
if (s0 < 0)
{
setsigne(d,-signe(d));
s = -s;
}
else if (signe(d1)) /* sic: might vanish now */
{
setsigne(d1,-signe(d1));
}
}
/* check whether we're done, as above. Assert v <= bmax. Examine v1:
* if v1 > bmax, check d and return 0 or 1 depending on the outcome;
* if v1 <= bmax, check d1 and return 1 if d1 <= amax, otherwise proceed.
*/
if (cmpii(v1,bmax) > 0) /* certainly done */
{
avma = av;
if (cmpii(d,amax) <= 0) /* done, found */
{
if (a != NULL)
{
*a = icopy(d);
setsigne(*a,-s); /* sign opposite to s */
}
if (b != NULL) *b = icopy(v);
return 1;
}
else /* done, not found */
return 0;
}
else if (cmpii(d1,amax) <= 0) /* also done, found */
{
avma = av;
if (a != NULL)
{
if (signe(d1))
{
*a = icopy(d1);
setsigne(*a,s); /* same sign as s */
}
else
*a = gen_0;
}
if (b != NULL) *b = icopy(v1);
return 1;
}
} /* while */
/* get here when we have run into d1 == 0 before returning... in fact,
* this cannot happen.
*/
pari_err(talker, "ratlift failed to catch d1 == 0\n");
/* NOTREACHED */
return 0;
}
/* Naive recombination of modular factors: combine up to maxK modular
* factors, degree <= klim and divisible by hint
*
* target = polynomial we want to factor
* famod = array of modular factors. Product should be congruent to
* target/lc(target) modulo p^a
* For true factors: S1,S2 <= p^b, with b <= a and p^(b-a) < 2^31 */
static GEN
nfcmbf(nfcmbf_t *T, GEN p, long a, long maxK, long klim)
{
GEN pol = T->pol, nf = T->nf, famod = T->fact, dn = T->dn;
GEN bound = T->bound;
GEN nfpol = gel(nf,1);
long K = 1, cnt = 1, i,j,k, curdeg, lfamod = lg(famod)-1, dnf = degpol(nfpol);
GEN res = cgetg(3, t_VEC);
pari_sp av0 = avma;
GEN pk = gpowgs(p,a), pks2 = shifti(pk,-1);
GEN ind = cgetg(lfamod+1, t_VECSMALL);
GEN degpol = cgetg(lfamod+1, t_VECSMALL);
GEN degsofar = cgetg(lfamod+1, t_VECSMALL);
GEN listmod = cgetg(lfamod+1, t_COL);
GEN fa = cgetg(lfamod+1, t_COL);
GEN lc = absi(leading_term(pol)), lt = is_pm1(lc)? NULL: lc;
GEN C2ltpol, C = T->L->topowden, Tpk = T->L->Tpk;
GEN Clt = mul_content(C, lt);
GEN C2lt = mul_content(C,Clt);
const double Bhigh = get_Bhigh(lfamod, dnf);
trace_data _T1, _T2, *T1, *T2;
pari_timer ti;
TIMERstart(&ti);
if (maxK < 0) maxK = lfamod-1;
C2ltpol = C2lt? gmul(C2lt,pol): pol;
{
GEN q = ceil_safe(sqrtr(T->BS_2));
GEN t1,t2, ltdn, lt2dn;
GEN trace1 = cgetg(lfamod+1, t_MAT);
GEN trace2 = cgetg(lfamod+1, t_MAT);
ltdn = mul_content(lt, dn);
lt2dn= mul_content(ltdn, lt);
for (i=1; i <= lfamod; i++)
{
pari_sp av = avma;
GEN P = gel(famod,i);
long d = degpol(P);
degpol[i] = d; P += 2;
t1 = gel(P,d-1);/* = - S_1 */
t2 = gsqr(t1);
if (d > 1) t2 = gsub(t2, gmul2n(gel(P,d-2), 1));
/* t2 = S_2 Newton sum */
t2 = typ(t2)!=t_INT? FpX_rem(t2, Tpk, pk): modii(t2, pk);
if (lt)
{
if (typ(t2)!=t_INT) {
t1 = FpX_red(gmul(ltdn, t1), pk);
t2 = FpX_red(gmul(lt2dn,t2), pk);
} else {
t1 = remii(mulii(ltdn, t1), pk);
t2 = remii(mulii(lt2dn,t2), pk);
}
}
gel(trace1,i) = gclone( nf_bestlift(t1, NULL, T->L) );
gel(trace2,i) = gclone( nf_bestlift(t2, NULL, T->L) ); avma = av;
}
T1 = init_trace(&_T1, trace1, T->L, q);
T2 = init_trace(&_T2, trace2, T->L, q);
for (i=1; i <= lfamod; i++) {
gunclone(gel(trace1,i));
gunclone(gel(trace2,i));
}
}
degsofar[0] = 0; /* sentinel */
/* ind runs through strictly increasing sequences of length K,
* 1 <= ind[i] <= lfamod */
nextK:
if (K > maxK || 2*K > lfamod) goto END;
if (DEBUGLEVEL > 3)
fprintferr("\n### K = %d, %Z combinations\n", K,binomial(utoipos(lfamod), K));
setlg(ind, K+1); ind[1] = 1;
i = 1; curdeg = degpol[ind[1]];
for(;;)
{ /* try all combinations of K factors */
for (j = i; j < K; j++)
{
degsofar[j] = curdeg;
ind[j+1] = ind[j]+1; curdeg += degpol[ind[j+1]];
}
if (curdeg <= klim && curdeg % T->hint == 0) /* trial divide */
{
GEN t, y, q, list;
pari_sp av;
av = avma;
/* d - 1 test */
if (T1)
{
t = get_trace(ind, T1);
if (rtodbl(QuickNormL2(t,DEFAULTPREC)) > Bhigh)
{
if (DEBUGLEVEL>6) fprintferr(".");
avma = av; goto NEXT;
}
}
/* d - 2 test */
if (T2)
{
t = get_trace(ind, T2);
if (rtodbl(QuickNormL2(t,DEFAULTPREC)) > Bhigh)
{
if (DEBUGLEVEL>3) fprintferr("|");
avma = av; goto NEXT;
}
}
avma = av;
y = lt; /* full computation */
for (i=1; i<=K; i++)
{
GEN q = gel(famod, ind[i]);
if (y) q = gmul(y, q);
y = FqX_centermod(q, Tpk, pk, pks2);
}
y = nf_pol_lift(y, bound, T);
if (!y)
{
if (DEBUGLEVEL>3) fprintferr("@");
avma = av; goto NEXT;
}
/* try out the new combination: y is the candidate factor */
q = RgXQX_divrem(C2ltpol, y, nfpol, ONLY_DIVIDES);
if (!q)
{
if (DEBUGLEVEL>3) fprintferr("*");
avma = av; goto NEXT;
}
/* found a factor */
list = cgetg(K+1, t_VEC);
gel(listmod,cnt) = list;
for (i=1; i<=K; i++) list[i] = famod[ind[i]];
y = Q_primpart(y);
gel(fa,cnt++) = QXQX_normalize(y, nfpol);
/* fix up pol */
pol = q;
for (i=j=k=1; i <= lfamod; i++)
{ /* remove used factors */
if (j <= K && i == ind[j]) j++;
else
{
famod[k] = famod[i];
update_trace(T1, k, i);
update_trace(T2, k, i);
degpol[k] = degpol[i]; k++;
}
}
lfamod -= K;
if (lfamod < 2*K) goto END;
i = 1; curdeg = degpol[ind[1]];
if (C2lt) pol = Q_primpart(pol);
if (lt) lt = absi(leading_term(pol));
Clt = mul_content(C, lt);
C2lt = mul_content(C,Clt);
C2ltpol = C2lt? gmul(C2lt,pol): pol;
if (DEBUGLEVEL > 2)
{
fprintferr("\n"); msgTIMER(&ti, "to find factor %Z",y);
fprintferr("remaining modular factor(s): %ld\n", lfamod);
}
continue;
}
NEXT:
for (i = K+1;;)
{
if (--i == 0) { K++; goto nextK; }
if (++ind[i] <= lfamod - K + i)
{
curdeg = degsofar[i-1] + degpol[ind[i]];
if (curdeg <= klim) break;
}
}
}
END:
if (degpol(pol) > 0)
{ /* leftover factor */
if (signe(leading_term(pol)) < 0) pol = gneg_i(pol);
if (C2lt && lfamod < 2*K) pol = QXQX_normalize(Q_primpart(pol), nfpol);
setlg(famod, lfamod+1);
gel(listmod,cnt) = shallowcopy(famod);
gel(fa,cnt++) = pol;
}
if (DEBUGLEVEL>6) fprintferr("\n");
if (cnt == 2) {
avma = av0;
gel(res,1) = mkvec(T->pol);
gel(res,2) = mkvec(T->fact);
}
else
{
setlg(listmod, cnt); setlg(fa, cnt);
gel(res,1) = fa;
gel(res,2) = listmod;
res = gerepilecopy(av0, res);
}
return res;
}
/* d = requested degree for subfield. Return DATA, valid for given pol, S and d
* If DATA != NULL, translate pol [ --> pol(X+1) ] and update DATA
* 1: polynomial pol
* 2: p^e (for Hensel lifts) such that p^e > max(M),
* 3: Hensel lift to precision p^e of DATA[4]
* 4: roots of pol in F_(p^S->lcm),
* 5: number of polynomial changes (translations)
* 6: Bezout coefficients associated to the S->ff[i]
* 7: Hadamard bound for coefficients of h(x) such that g o h = 0 mod pol.
* 8: bound M for polynomials defining subfields x PD->den
* 9: *[i] = interpolation polynomial for S->ff[i] [= 1 on the first root
S->firstroot[i], 0 on the others] */
static void
compute_data(blockdata *B)
{
GEN ffL, roo, pe, p1, p2, fk, fhk, MM, maxroot, pol;
primedata *S = B->S;
GEN p = S->p, T = S->T, ff = S->ff, DATA = B->DATA;
long i, j, l, e, N, lff = lg(ff);
if (DEBUGLEVEL>1) fprintferr("Entering compute_data()\n\n");
pol = B->PD->pol; N = degpol(pol);
roo = B->PD->roo;
if (DATA) /* update (translate) an existing DATA */
{
GEN Xm1 = gsub(pol_x[varn(pol)], gen_1);
GEN TR = addis(gel(DATA,5), 1);
GEN mTR = negi(TR), interp, bezoutC;
gel(DATA,5) = TR;
pol = translate_pol(gel(DATA,1), gen_m1);
l = lg(roo); p1 = cgetg(l, t_VEC);
for (i=1; i<l; i++) gel(p1,i) = gadd(TR, gel(roo,i));
roo = p1;
fk = gel(DATA,4); l = lg(fk);
for (i=1; i<l; i++) gel(fk,i) = gsub(Xm1, gel(fk,i));
bezoutC = gel(DATA,6); l = lg(bezoutC);
interp = gel(DATA,9);
for (i=1; i<l; i++)
{
if (degpol(interp[i]) > 0) /* do not turn pol_1[0] into gen_1 */
{
p1 = translate_pol(gel(interp,i), gen_m1);
gel(interp,i) = FpXX_red(p1, p);
}
if (degpol(bezoutC[i]) > 0)
{
p1 = translate_pol(gel(bezoutC,i), gen_m1);
gel(bezoutC,i) = FpXX_red(p1, p);
}
}
ff = cgetg(lff, t_VEC); /* copy, don't overwrite! */
for (i=1; i<lff; i++)
gel(ff,i) = FpX_red(translate_pol((GEN)S->ff[i], mTR), p);
}
else
{
DATA = cgetg(10,t_VEC);
fk = S->fk;
gel(DATA,5) = gen_0;
gel(DATA,6) = shallowcopy(S->bezoutC);
gel(DATA,9) = shallowcopy(S->interp);
}
gel(DATA,1) = pol;
MM = gmul2n(bound_for_coeff(B->d, roo, &maxroot), 1);
gel(DATA,8) = MM;
e = logint(shifti(vecmax(MM),20), p, &pe); /* overlift 2^20 [for d-1 test] */
gel(DATA,2) = pe;
gel(DATA,4) = roots_from_deg1(fk);
/* compute fhk = hensel_lift_fact(pol,fk,T,p,pe,e) in 2 steps
* 1) lift in Zp to precision p^e */
ffL = hensel_lift_fact(pol, ff, NULL, p, pe, e);
fhk = NULL;
for (l=i=1; i<lff; i++)
{ /* 2) lift factorization of ff[i] in Qp[X] / T */
GEN F, L = gel(ffL,i);
long di = degpol(L);
F = cgetg(di+1, t_VEC);
for (j=1; j<=di; j++) F[j] = fk[l++];
L = hensel_lift_fact(L, F, T, p, pe, e);
fhk = fhk? shallowconcat(fhk, L): L;
}
gel(DATA,3) = roots_from_deg1(fhk);
p1 = mulsr(N, gsqrt(gpowgs(utoipos(N-1),N-1),DEFAULTPREC));
p2 = gpowgs(maxroot, B->size + N*(N-1)/2);
p1 = gdiv(gmul(p1,p2), gsqrt(B->PD->dis,DEFAULTPREC));
gel(DATA,7) = mulii(shifti(ceil_safe(p1), 1), B->PD->den);
if (DEBUGLEVEL>1) {
fprintferr("f = %Z\n",DATA[1]);
fprintferr("p = %Z, lift to p^%ld\n", p, e);
fprintferr("2 * Hadamard bound * ind = %Z\n",DATA[7]);
fprintferr("2 * M = %Z\n",DATA[8]);
}
if (B->DATA) {
DATA = gclone(DATA);
if (isclone(B->DATA)) gunclone(B->DATA);
}
B->DATA = DATA;
}
