static GEN
nf_to_Zq(GEN x, GEN T, GEN pk, GEN pks2, GEN proj)
{
GEN y;
if (typ(x) != t_COL) return centermodii(x, pk, pks2);
y = gmul(proj, x);
if (!T) return centermodii(y, pk, pks2);
y = RgV_to_RgX(y, varn(T));
return centermod_i(FpX_rem(y, T, pk), pk, pks2);
}
/* 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);
}
static GEN
sqrconst(GEN pol, Red *R)
{
GEN z = cgetg(3,t_POL);
gel(z,2) = centermodii(sqri(gel(pol,2)), R->N, R->N2);
z[1] = pol[1]; return z;
}
static GEN
_powpolmodsimple(Cache *C, Red *R, GEN jac)
{
pari_sp av = avma;
GEN w = mulmat_pol(C->matvite, jac);
long j, ph = lg(w);
R->red = &_redsimple;
for (j=1; j<ph; j++)
gel(w,j) = _powpolmod(C, centermodii(gel(w,j), R->N, R->N2), R, &sqrmod);
w = centermod_i( gmul(C->matinvvite, w), R->N, R->N2 );
w = gerepileupto(av, w);
return RgV_to_RgX(w, 0);
}
/* reduce coeffs mod (T,pk), then center mod pk */
static GEN
FqX_centermod(GEN z, GEN T, GEN pk, GEN pks2)
{
long i, l;
GEN y;
if (!T) return centermod_i(z, pk, pks2);
y = FpXQX_red(z, T, pk); l = lg(y);
for (i = 2; i < l; i++)
{
GEN c = gel(y,i);
if (typ(c) == t_INT)
c = centermodii(c, pk, pks2);
else
c = FpX_center(c, pk);
gel(y,i) = c;
}
return y;
}
/* 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);
}
static GEN
_redsimple(GEN x, Red *R) { return centermodii(x, R->N, R->N2); }
