GEN
shallowmatconcat(GEN v)
{
long i, j, h, l = lg(v), L = 0, H = 0;
GEN M, maxh, maxl;
if (l == 1) return cgetg(1,t_MAT);
switch(typ(v))
{
case t_VEC:
for (i = 1; i < l; i++)
{
GEN c = gel(v,i);
GEN s = _matsize(c);
H = maxss(H, s[1]);
L += s[2];
}
M = zeromatcopy(H, L);
L = 0;
for (i = 1; i < l; i++)
{
GEN c = gel(v,i);
GEN s = _matsize(c);
matfill(M, c, 0, L, 1);
L += s[2];
}
return M;
case t_COL:
for (i = 1; i < l; i++)
{
GEN c = gel(v,i);
GEN s = _matsize(c);
H += s[1];
L = maxss(L, s[2]);
}
M = zeromatcopy(H, L);
H = 0;
for (i = 1; i < l; i++)
{
GEN c = gel(v,i);
GEN s = _matsize(c);
matfill(M, c, H, 0, 1);
H += s[1];
}
return M;
case t_MAT:
h = lgcols(v);
maxh = zero_zv(h-1);
maxl = zero_zv(l-1);
for (j = 1; j < l; j++)
for (i = 1; i < h; i++)
{
GEN c = gcoeff(v,i,j);
GEN s = _matsize(c);
if (s[1] > maxh[i]) maxh[i] = s[1];
if (s[2] > maxl[j]) maxl[j] = s[2];
}
for (i = 1, H = 0; i < h; i++) H += maxh[i];
for (j = 1, L = 0; j < l; j++) L += maxl[j];
M = zeromatcopy(H, L);
for (j = 1, L = 0; j < l; j++)
{
for (i = 1, H = 0; i < h; i++)
{
GEN c = gcoeff(v,i,j);
matfill(M, c, H, L, minss(maxh[i], maxl[j]));
H += maxh[i];
}
L += maxl[j];
}
return M;
default:
pari_err_TYPE("shallowmatconcat", v);
return NULL;
}
}
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));
}
