GEN
orpari(GEN a, GEN b/*closure*/)
{
GEN g;
if (!gequal0(a))
return gen_1;
g=closure_evalgen(b);
if (!g) return g;
return gequal0(g)?gen_0:gen_1;
}
GEN
ifpari_multi(GEN g, GEN a/*closure*/)
{
long i, nb = lg(a)-1;
if (!gequal0(g)) /* false */
return closure_evalgen(gel(a,1));
for(i=2;i<nb;i+=2)
{
GEN g = closure_evalgen(gel(a,i));
if (!g) return g;
if (!gequal0(g))
return closure_evalgen(gel(a,i+1));
}
return i<=nb? closure_evalgen(gel(a,i)): gnil;
}
GEN
ifpari(GEN g, GEN a/*closure*/, GEN b/*closure*/)
{
if (gequal0(g)) /* false */
return b?closure_evalgen(b):gnil;
else /* true */
return a?closure_evalgen(a):gnil;
}
void
ifpari_void(GEN g, GEN a/*closure*/, GEN b/*closure*/)
{
if (gequal0(g)) /* false */
{
if(b) closure_evalvoid(b);
}
else /* true */
{
if(a) closure_evalvoid(a);
}
}
/* return d = gcd(a,b), sets u, v such that au + bv = gcd(a,b) */
GEN
extgcd(GEN A, GEN B, GEN *U, GEN *V)
{
pari_sp av = avma;
GEN ux = gen_1, vx = gen_0, a = A, b = B;
if (typ(a) != t_INT) pari_err_TYPE("extgcd",a);
if (typ(b) != t_INT) pari_err_TYPE("extgcd",b);
if (signe(a) < 0) { a = negi(a); ux = negi(ux); }
while (!gequal0(b))
{
GEN r, q = dvmdii(a, b, &r), v = vx;
vx = subii(ux, mulii(q, vx));
ux = v; a = b; b = r;
}
*U = ux;
*V = diviiexact( subii(a, mulii(A,ux)), B );
gerepileall(av, 3, &a, U, V); return a;
}
static GEN
bnflog_i(GEN bnf, GEN ell)
{
long prec0, prec;
GEN nf, US, vdegS, S, T, M, CLp, CLt, Ftilde, vtG, ellk;
GEN D, Ap, cycAp, bnfS;
long i, j, lS, lvAp;
checkbnf(bnf);
nf = checknf(bnf);
S = idealprimedec(nf, ell);
bnfS = bnfsunit0(bnf, S, nf_GENMAT, LOWDEFAULTPREC); /* S-units */
US = leafcopy(gel(bnfS,1));
prec0 = maxss(30, vtilde_prec(nf, US, ell));
US = shallowconcat(bnf_get_fu(bnf), US);
settyp(US, t_COL);
T = padicfact(nf, S, prec0);
lS = lg(S); Ftilde = cgetg(lS, t_VECSMALL);
for (j = 1; j < lS; j++) Ftilde[j] = ftilde(nf, gel(S,j), gel(T,j));
CLp = CL_prime(bnf, ell, S);
cycAp = gel(CLp,1);
Ap = gel(CLp,2);
for(;;)
{
CLt = CL_tilde(nf, US, ell, T, Ftilde, &vtG, prec0);
if (CLt) break;
prec0 <<= 1;
T = padicfact(nf, S, prec0);
}
prec = ellexpo(cycAp, ell) + ellexpo(CLt,ell) + 1;
if (prec == 1) return mkvec3(cgetg(1,t_VEC), cgetg(1,t_VEC), cgetg(1,t_VEC));
vdegS = get_vdegS(Ftilde, ell, prec0);
ellk = powiu(ell, prec);
lvAp = lg(Ap);
if (lvAp > 1)
{
GEN Kcyc = bnf_get_cyc(bnf);
GEN C = zeromatcopy(lvAp-1, lS-1);
GEN Rell = gel(CLp,3), Uell = gel(CLp,4), ordS = gel(CLp,5);
for (i = 1; i < lvAp; i++)
{
GEN a, b, bi, A = gel(Ap,i), d = gel(cycAp,i);
bi = isprincipal(bnf, A);
a = vecmodii(ZC_Z_mul(bi,d), Kcyc);
/* a in subgroup generated by S = Rell; hence b integral */
b = hnf_invimage(Rell, a);
b = vecmodii(ZM_ZC_mul(Uell, ZC_neg(b)), ordS);
A = mkvec2(A, cgetg(1,t_MAT));
A = idealpowred(nf, A, d);
/* find a principal representative of A_i^cycA_i up to elements of S */
a = isprincipalfact(bnf,gel(A,1),S,b,nf_GENMAT|nf_FORCE);
if (!gequal0(gel(a,1))) pari_err_BUG("bnflog");
a = famat_mul_shallow(gel(A,2), gel(a,2)); /* principal part */
if (lg(a) == 1) continue;
for (j = 1; j < lS; j++)
gcoeff(C,i,j) = vtilde(nf, a, gel(T,j), gel(vdegS,j), ell, prec0);
}
C = gmod(gneg(C),ellk);
C = shallowtrans(C);
M = mkmat2(mkcol2(diagonal_shallow(cycAp), C), mkcol2(gen_0, vtG));
M = shallowmatconcat(M); /* relation matrix */
}
else
M = vtG;
M = ZM_hnfmodid(M, ellk);
D = matsnf0(M, 4);
if (lg(D) == 1 || !dvdii(gel(D,1), ellk))
pari_err_BUG("bnflog [missing Z_l component]");
D = vecslice(D,2,lg(D)-1);
return mkvec3(D, CLt, ellsylow(cycAp, ell));
}
