/* K a bnf, compute Cl'(K) = ell-Sylow of Cl(K) / (places above ell). * Return [D, u, R0, U0, ordS] * - D: cyclic factors for Cl'(K) * - u: generators of cyclic factors (all coprime to ell) * - R0: subgroup isprincipal(<S>) (divides K.cyc) * - U0: generators of R0 are of the form S . U0 * - ordS[i] = order of S[i] in CL(K) */ static GEN CL_prime(GEN K, GEN ell, GEN Sell) { GEN g, ordS, R0, U0, U, D, u, cyc = bnf_get_cyc(K); long i, l, lD, lS = lg(Sell); g = leafcopy(bnf_get_gen(K)); l = lg(g); for (i = 1; i < l; i++) { GEN A = gel(g,i), a = gcoeff(A,1,1); long v = Z_pvalrem(a, ell, &a); if (v) gel(g,i) = hnfmodid(A, a); /* make coprime to ell */ } R0 = cgetg(lS, t_MAT); ordS = cgetg(lS, t_VEC); for (i = 1; i < lS; i++) { gel(R0,i) = isprincipal(K, gel(Sell,i)); gel(ordS,i) = charorder(cyc, gel(R0,i)); /* order of Sell[i] */ } R0 = shallowconcat(R0, diagonal_shallow(cyc)); /* R0 = subgroup generated by S in Cl(K) [ divides diagonal(K.cyc) ]*/ R0 = ZM_hnfall(R0, &U0, 2); /* [S | cyc] * U0 = R0 in HNF */ D = ZM_snfall(R0, &U,NULL); D = RgM_diagonal_shallow(D); lD = lg(D); u = ZM_inv(U, gen_1); settyp(u, t_VEC); for (i = 1; i < lD; i++) gel(u,i) = idealfactorback(K,g,gel(u,i),1); setlg(U0, l); U0 = rowslice(U0,1,lS-1); /* restrict to 'S' part */ return mkvec5(D, u, R0, U0, ordS); }
static GEN nf_combine_factors(nfcmbf_t *T, GEN polred, GEN p, long a, long klim) { GEN res, L, listmod, famod = T->fact, nf = T->nf; long l, maxK = 3, nft = lg(famod)-1; pari_timer ti; if (DEBUGLEVEL>2) TIMERstart(&ti); T->fact = hensel_lift_fact(polred, famod, T->L->Tpk, p, T->L->pk, a); if (nft < 11) maxK = -1; /* few modular factors: try all posibilities */ if (DEBUGLEVEL>2) msgTIMER(&ti, "Hensel lift"); L = nfcmbf(T, p, a, maxK, klim); if (DEBUGLEVEL>2) msgTIMER(&ti, "Naive recombination"); res = gel(L,1); listmod = gel(L,2); l = lg(listmod)-1; famod = gel(listmod,l); if (maxK >= 0 && lg(famod)-1 > 2*maxK) { if (l > 1) { T->pol = gel(res,l); T->polbase = unifpol(nf, gel(res,l), t_COL); } L = nf_LLL_cmbf(T, p, a, maxK); /* remove last elt, possibly unfactored. Add all new ones. */ setlg(res, l); res = shallowconcat(res, L); } return res; }
static void append(GEN D, GEN a) { long i,l = lg(D), m = lg(a); GEN x = D + (l-1); for (i=1; i<m; i++) x[i] = a[i]; setlg(D, l+m-1); }
/* We want to be able to reconstruct x, |x|^2 < C, from x mod pr^k */ static double bestlift_bound(GEN C, long d, double alpha, GEN Npr) { const double y = 1 / (alpha - 0.25); /* = 2 if alpha = 3/4 */ double t; if (typ(C) != t_REAL) C = gmul(C, real_1(DEFAULTPREC)); setlg(C, DEFAULTPREC); t = rtodbl(mplog(gmul2n(divrs(C,d), 4))) * 0.5 + (d-1) * log(1.5 * sqrt(y)); return ceil((t * d) / log(gtodouble(Npr))); }
static GEN ellsylow(GEN cyc, GEN ell) { long i, l; GEN d = cgetg_copy(cyc, &l); for (i = 1; i < l; i++) { GEN c = gel(cyc,i), a; if (!Z_pvalrem(c, ell, &a)) break; gel(d,i) = diviiexact(c, a); } setlg(d, i); return d; }
GEN subfields(GEN nf, GEN d0) { pari_sp av = avma; long N, v0, d = itos(d0); GEN LSB, pol, G; poldata PD; primedata S; blockdata B; pol = get_nfpol(nf, &nf); /* in order to treat trivial cases */ v0 = varn(pol); N = degpol(pol); if (d == N) return gerepilecopy(av, _subfield(pol, pol_x[v0])); if (d == 1) return gerepilecopy(av, _subfield(pol_x[v0], pol)); if (d < 1 || d > N || N % d) return cgetg(1,t_VEC); /* much easier if nf is Galois (WSS) */ G = galoisconj4(nf? nf: pol, NULL, 1); if (typ(G) != t_INT) { /* Bingo */ GEN L = galoissubgroups(G), F; long k,i, l = lg(L), o = N/d; F = cgetg(l, t_VEC); k = 1; for (i=1; i<l; i++) { GEN H = gel(L,i); if (group_order(H) == o) gel(F,k++) = lift_intern(galoisfixedfield(G, gel(H,1), 0, v0)); } setlg(F, k); return gerepilecopy(av, F); } subfields_poldata(nf? nf: pol, &PD); B.PD = &PD; B.S = &S; B.N = N; B.d = d; B.size = N/d; choose_prime(&S, PD.pol, PD.dis); LSB = subfields_of_given_degree(&B); (void)delete_var(); /* from choose_prime */ avma = av; if (!LSB) return cgetg(1, t_VEC); G = gcopy(LSB); gunclone(LSB); return fix_var(G, v0); }
static GEN nf_DDF_roots(GEN pol, GEN polred, GEN nfpol, GEN lt, GEN init_fa, long nbf, long fl, nflift_t *L) { long Cltx_r[] = { evaltyp(t_POL)|_evallg(4), 0,0,0 }; long i, m; GEN C2ltpol, C = L->topowden; GEN Clt = mul_content(C, lt); GEN C2lt = mul_content(C,Clt); GEN z; if (L->Tpk) { int cof = (degpol(pol) > nbf); /* non trivial cofactor ? */ z = FqX_split_roots(init_fa, L->Tp, L->p, cof? polred: NULL); z = hensel_lift_fact(polred, z, L->Tpk, L->p, L->pk, L->k); if (cof) setlg(z, lg(z)-1); /* remove cofactor */ z = roots_from_deg1(z); } else z = rootpadicfast(polred, L->p, L->k); Cltx_r[1] = evalsigne(1) | evalvarn(varn(pol)); gel(Cltx_r,3) = Clt? Clt: gen_1; C2ltpol = C2lt? gmul(C2lt, pol): pol; for (m=1,i=1; i<lg(z); i++) { GEN q, r = gel(z,i); r = nf_bestlift_to_pol(lt? gmul(lt,r): r, NULL, L); gel(Cltx_r,2) = gneg(r); /* check P(r) == 0 */ q = RgXQX_divrem(C2ltpol, Cltx_r, nfpol, ONLY_DIVIDES); /* integral */ if (q) { C2ltpol = C2lt? gmul(Clt,q): q; if (Clt) r = gdiv(r, Clt); gel(z,m++) = r; } else if (fl == 2) return cgetg(1, t_VEC); } z[0] = evaltyp(t_VEC) | evallg(m); return z; }
void print_all_user_fun(int member) { pari_sp av = avma; long iL = 0, lL = 1024; GEN L = cgetg(lL+1, t_VECSMALL); entree *ep; int i; for (i = 0; i < functions_tblsz; i++) for (ep = functions_hash[i]; ep; ep = ep->next) { const char *f; int is_member; if (EpVALENCE(ep) != EpVAR || typ((GEN)ep->value)!=t_CLOSURE) continue; f = ep->name; is_member = (f[0] == '_' && f[1] == '.'); if (member != is_member) continue; if (iL >= lL) { GEN oL = L; long j; lL *= 2; L = cgetg(lL+1, t_VECSMALL); for (j = 1; j <= iL; j++) gel(L,j) = gel(oL,j); } L[++iL] = (long)ep; } if (iL) { setlg(L, iL+1); L = gen_sort(L, NULL, &cmp_epname); for (i = 1; i <= iL; i++) { ep = (entree*)L[i]; pari_printf("%s =\n %Ps\n\n", ep->name, ep->value); } } avma = av; }
/* 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; }
/* return the factorization of the square-free polynomial x. The coeffs of x are in Z_nf and its leading term is a rational integer. deg(x) > 1, deg(nfpol) > 1 If fl = 1, return only the roots of x in nf If fl = 2, as fl=1 if pol splits, [] otherwise */ static GEN nfsqff(GEN nf, GEN pol, long fl) { long n, nbf, dpol = degpol(pol); GEN pr, C0, polbase, init_fa = NULL; GEN N2, rep, polmod, polred, lt, nfpol = gel(nf,1); nfcmbf_t T; nflift_t L; pari_timer ti, ti_tot; if (DEBUGLEVEL>2) { TIMERstart(&ti); TIMERstart(&ti_tot); } n = degpol(nfpol); polbase = unifpol(nf, pol, t_COL); if (typ(polbase) != t_POL) pari_err(typeer, "nfsqff"); polmod = lift_intern( unifpol(nf, pol, t_POLMOD) ); if (dpol == 1) return mkvec(QXQX_normalize(polmod, nfpol)); /* heuristic */ if (dpol*3 < n) { GEN z, t; long i; if (DEBUGLEVEL>2) fprintferr("Using Trager's method\n"); z = (GEN)polfnf(polmod, nfpol)[1]; if (fl) { long l = lg(z); for (i = 1; i < l; i++) { t = gel(z,i); if (degpol(t) > 1) break; gel(z,i) = gneg(gdiv(gel(t,2), gel(t,3))); } setlg(z, i); if (fl == 2 && i != l) return cgetg(1,t_VEC); } return z; } nbf = nf_pick_prime(5, nf, polbase, fl, <, &init_fa, &pr, &L.Tp); if (fl == 2 && nbf < dpol) return cgetg(1,t_VEC); if (nbf <= 1) { if (!fl) return mkvec(QXQX_normalize(polmod, nfpol)); /* irreducible */ if (!nbf) return cgetg(1,t_VEC); /* no root */ } if (DEBUGLEVEL>2) { msgTIMER(&ti, "choice of a prime ideal"); fprintferr("Prime ideal chosen: %Z\n", pr); } pol = simplify_i(lift(polmod)); L.tozk = gel(nf,8); L.topow= Q_remove_denom(gel(nf,7), &L.topowden); T.ZC = L2_bound(nf, L.tozk, &(T.dn)); T.Br = nf_root_bounds(pol, nf); if (lt) T.Br = gmul(T.Br, lt); if (fl) C0 = normlp(T.Br, 2, n); else C0 = nf_factor_bound(nf, polbase); /* bound for T_2(Q_i), Q | P */ T.bound = mulrr(T.ZC, C0); /* bound for |Q_i|^2 in Z^n on chosen Z-basis */ N2 = mulsr(dpol*dpol, normlp(T.Br, 4, n)); /* bound for T_2(lt * S_2) */ T.BS_2 = mulrr(T.ZC, N2); /* bound for |S_2|^2 on chosen Z-basis */ if (DEBUGLEVEL>2) { msgTIMER(&ti, "bound computation"); fprintferr(" 1) T_2 bound for %s: %Z\n", fl?"root":"factor", C0); fprintferr(" 2) Conversion from T_2 --> | |^2 bound : %Z\n", T.ZC); fprintferr(" 3) Final bound: %Z\n", T.bound); } L.p = gel(pr,1); if (L.Tp && degpol(L.Tp) == 1) L.Tp = NULL; bestlift_init(0, nf, pr, T.bound, &L); if (DEBUGLEVEL>2) TIMERstart(&ti); polred = ZqX_normalize(polbase, lt, &L); /* monic */ if (fl) { GEN z = nf_DDF_roots(pol, polred, nfpol, lt, init_fa, nbf, fl, &L); if (lg(z) == 1) return cgetg(1, t_VEC); return z; } { pari_sp av = avma; if (L.Tp) rep = FqX_split_all(init_fa, L.Tp, L.p); else { long d; rep = cgetg(dpol + 1, t_VEC); gel(rep,1) = FpX_red(polred,L.p); d = FpX_split_Berlekamp((GEN*)(rep + 1), L.p); setlg(rep, d + 1); } T.fact = gerepilecopy(av, sort_vecpol(rep, &cmp_pol)); } if (DEBUGLEVEL>2) msgTIMER(&ti, "splitting mod %Z", pr); T.pr = pr; T.L = &L; T.polbase = polbase; T.pol = pol; T.nf = nf; T.hint = 1; /* useless */ rep = nf_combine_factors(&T, polred, L.p, L.k, dpol-1); if (DEBUGLEVEL>2) fprintferr("Total Time: %ld\n===========\n", TIMER(&ti_tot)); return rep; }
static GEN print_block_system(blockdata *B, GEN Y, GEN SB) { long i, j, l, ll, lp, u, v, ns, r = lg(Y), N = B->N; long *k, *n, **e, *t; GEN D, De, Z, cyperm, perm, VOID = cgetg(1, t_VECSMALL); if (DEBUGLEVEL>5) fprintferr("Y = %Z\n",Y); n = new_chunk(N+1); D = cget1(N+1, t_VEC); t = new_chunk(r+1); k = new_chunk(r+1); Z = cgetg(r+1, t_VEC); for (ns=0,i=1; i<r; i++) { GEN Yi = gel(Y,i); long ki = 0, si = lg(Yi)-1; for (j=1; j<=si; j++) { n[j] = lg(Yi[j])-1; ki += n[j]; } ki /= B->size; De = cgetg(ki+1,t_VEC); for (j=1; j<=ki; j++) gel(De,j) = VOID; for (j=1; j<=si; j++) { GEN cy = gel(Yi,j); for (l=1,lp=0; l<=n[j]; l++) { lp++; if (lp > ki) lp = 1; gel(De,lp) = vecsmall_append(gel(De,lp), cy[l]); } } append(D, De); if (si>1 && ki>1) { GEN p1 = cgetg(si,t_VEC); for (j=2; j<=si; j++) p1[j-1] = Yi[j]; ns++; t[ns] = si-1; k[ns] = ki-1; gel(Z,ns) = p1; } } if (DEBUGLEVEL>2) fprintferr("\nns = %ld\n",ns); if (!ns) return test_block(B, SB, D); setlg(Z, ns+1); e = (long**)new_chunk(ns+1); for (i=1; i<=ns; i++) { e[i] = new_chunk(t[i]+1); for (j=1; j<=t[i]; j++) e[i][j] = 0; } cyperm= cgetg(N+1,t_VECSMALL); perm = cgetg(N+1,t_VECSMALL); i = ns; do { pari_sp av = avma; for (u=1; u<=N; u++) perm[u] = u; for (u=1; u<=ns; u++) for (v=1; v<=t[u]; v++) perm_mul_i(perm, cycle_power_to_perm(cyperm, gmael(Z,u,v), e[u][v])); SB = test_block(B, SB, im_block_by_perm(D,perm)); avma = av; /* i = 1..ns, j = 1..t[i], e[i][j] loop through 0..k[i]. * TODO: flatten to 1-dimensional loop */ if (++e[ns][t[ns]] > k[ns]) { j = t[ns]-1; while (j>=1 && e[ns][j] == k[ns]) j--; if (j >= 1) { e[ns][j]++; for (l=j+1; l<=t[ns]; l++) e[ns][l] = 0; } else { i = ns-1; while (i>=1) { j = t[i]; while (j>=1 && e[i][j] == k[i]) j--; if (j<1) i--; else { e[i][j]++; for (l=j+1; l<=t[i]; l++) e[i][l] = 0; for (ll=i+1; ll<=ns; ll++) for (l=1; l<=t[ll]; l++) e[ll][l] = 0; break; } } } } } while (i > 0); return SB; }
/* Computation of potential block systems of given size d associated to a * rational prime p: give a row vector of row vectors containing the * potential block systems of imprimitivity; a potential block system is a * vector of row vectors (enumeration of the roots). */ static GEN calc_block(blockdata *B, GEN Z, GEN Y, GEN SB) { long r = lg(Z), lK, i, j, t, tp, T, u, nn, lnon, lY; GEN K, n, non, pn, pnon, e, Yp, Zp, Zpp; pari_sp av0 = avma; if (DEBUGLEVEL>3) { fprintferr("lg(Z) = %ld, lg(Y) = %ld\n", r,lg(Y)); if (DEBUGLEVEL > 5) { fprintferr("Z = %Z\n",Z); fprintferr("Y = %Z\n",Y); } } lnon = min(BIL, r); e = new_chunk(BIL); n = new_chunk(r); non = new_chunk(lnon); pnon = new_chunk(lnon); pn = new_chunk(lnon); Zp = cgetg(lnon,t_VEC); Zpp = cgetg(lnon,t_VEC); nn = 0; for (i=1; i<r; i++) { n[i] = lg(Z[i])-1; nn += n[i]; } lY = lg(Y); Yp = cgetg(lY+1,t_VEC); for (j=1; j<lY; j++) Yp[j] = Y[j]; { pari_sp av = avma; long k = nn / B->size; for (j = 1; j < r; j++) if (n[j] % k) break; if (j == r) { gel(Yp,lY) = Z; SB = print_block_system(B, Yp, SB); avma = av; } } gel(Yp,lY) = Zp; K = divisors(utoipos(n[1])); lK = lg(K); for (i=1; i<lK; i++) { long ngcd = n[1], k = itos(gel(K,i)), dk = B->size*k, lpn = 0; for (j=2; j<r; j++) if (n[j]%k == 0) { if (++lpn >= BIL) pari_err(talker,"overflow in calc_block"); pn[lpn] = n[j]; pnon[lpn] = j; ngcd = cgcd(ngcd, n[j]); } if (dk % ngcd) continue; T = 1<<lpn; if (lpn == r-2) { T--; /* done already above --> print_block_system */ if (!T) continue; } if (dk == n[1]) { /* empty subset, t = 0. Split out for clarity */ Zp[1] = Z[1]; setlg(Zp, 2); for (u=1,j=2; j<r; j++) Zpp[u++] = Z[j]; setlg(Zpp, u); SB = calc_block(B, Zpp, Yp, SB); } for (t = 1; t < T; t++) { /* loop through all non-empty subsets of [1..lpn] */ for (nn=n[1],tp=t, u=1; u<=lpn; u++,tp>>=1) { if (tp&1) { nn += pn[u]; e[u] = 1; } else e[u] = 0; } if (dk != nn) continue; for (j=1; j<r; j++) non[j]=0; Zp[1] = Z[1]; for (u=2,j=1; j<=lpn; j++) if (e[j]) { Zp[u] = Z[pnon[j]]; non[pnon[j]] = 1; u++; } setlg(Zp, u); for (u=1,j=2; j<r; j++) if (!non[j]) Zpp[u++] = Z[j]; setlg(Zpp, u); SB = calc_block(B, Zpp, Yp, SB); } } avma = av0; return SB; }