Code coverage tests

This page documents the degree to which the PARI/GP source code is tested by our public test suite, distributed with the source distribution in directory src/test/. This is measured by the gcov utility; we then process gcov output using the lcov frond-end.

We test a few variants depending on Configure flags on the pari.math.u-bordeaux.fr machine (x86_64 architecture), and agregate them in the final report:

The target is to exceed 90% coverage for all mathematical modules (given that branches depending on DEBUGLEVEL or DEBUGMEM are not covered). This script is run to produce the results below.

LCOV - code coverage report
Current view: top level - basemath - buch3.c (source / functions) Hit Total Coverage
Test: PARI/GP v2.16.2 lcov report (development 29115-f22e516b23) Lines: 1509 1615 93.4 %
Date: 2024-02-22 08:05:55 Functions: 120 125 96.0 %
Legend: Lines: hit not hit

          Line data    Source code
       1             : /* Copyright (C) 2000  The PARI group.
       2             : 
       3             : This file is part of the PARI/GP package.
       4             : 
       5             : PARI/GP is free software; you can redistribute it and/or modify it under the
       6             : terms of the GNU General Public License as published by the Free Software
       7             : Foundation; either version 2 of the License, or (at your option) any later
       8             : version. It is distributed in the hope that it will be useful, but WITHOUT
       9             : ANY WARRANTY WHATSOEVER.
      10             : 
      11             : Check the License for details. You should have received a copy of it, along
      12             : with the package; see the file 'COPYING'. If not, write to the Free Software
      13             : Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. */
      14             : 
      15             : /*******************************************************************/
      16             : /*                                                                 */
      17             : /*                       RAY CLASS FIELDS                          */
      18             : /*                                                                 */
      19             : /*******************************************************************/
      20             : #include "pari.h"
      21             : #include "paripriv.h"
      22             : 
      23             : #define DEBUGLEVEL DEBUGLEVEL_bnr
      24             : 
      25             : static GEN
      26     1460644 : bnr_get_El(GEN bnr) { return gel(bnr,3); }
      27             : static GEN
      28     1840282 : bnr_get_U(GEN bnr) { return gel(bnr,4); }
      29             : static GEN
      30       12824 : bnr_get_Ui(GEN bnr) { return gmael(bnr,4,3); }
      31             : 
      32             : /* faster than Buchray */
      33             : GEN
      34          35 : bnfnarrow(GEN bnf)
      35             : {
      36             :   GEN nf, cyc, gen, Cyc, Gen, A, GD, v, w, H, invpi, L, R, u, U0, Uoo, archp, sarch;
      37             :   long r1, j, l, t, RU;
      38             :   pari_sp av;
      39             : 
      40          35 :   bnf = checkbnf(bnf);
      41          35 :   nf = bnf_get_nf(bnf);
      42          35 :   r1 = nf_get_r1(nf); if (!r1) return gcopy( bnf_get_clgp(bnf) );
      43             : 
      44             :   /* simplified version of nfsign_units; r1 > 0 so bnf.tu = -1 */
      45          35 :   av = avma; archp = identity_perm(r1);
      46          35 :   A = bnf_get_logfu(bnf); RU = lg(A)+1;
      47          35 :   invpi = invr( mppi(nf_get_prec(nf)) );
      48          35 :   v = cgetg(RU,t_MAT); gel(v, 1) = const_vecsmall(r1, 1); /* nfsign(-1) */
      49          98 :   for (j=2; j<RU; j++) gel(v,j) = nfsign_from_logarch(gel(A,j-1), invpi, archp);
      50             :   /* up to here */
      51             : 
      52          35 :   v = Flm_image(v, 2); t = lg(v)-1;
      53          35 :   if (t == r1) { set_avma(av); return gcopy( bnf_get_clgp(bnf) ); }
      54             : 
      55          28 :   v = Flm_suppl(v,2); /* v = (sgn(U)|H) in GL_r1(F_2) */
      56          28 :   H = zm_to_ZM( vecslice(v, t+1, r1) ); /* supplement H of sgn(U) */
      57          28 :   w = rowslice(Flm_inv(v,2), t+1, r1); /* H*w*z = proj of z on H // sgn(U) */
      58             : 
      59          28 :   sarch = nfarchstar(nf, NULL, archp);
      60          28 :   cyc = bnf_get_cyc(bnf);
      61          28 :   gen = bnf_get_gen(bnf); l = lg(gen);
      62          28 :   L = cgetg(l,t_MAT); GD = gmael(bnf,9,3);
      63          63 :   for (j=1; j<l; j++)
      64             :   {
      65          35 :     GEN z = nfsign_from_logarch(gel(GD,j), invpi, archp);
      66          35 :     gel(L,j) = zc_to_ZC( Flm_Flc_mul(w, z, 2) );
      67             :   }
      68             :   /* [cyc, 0; L, 2] = relation matrix for Cl_f */
      69          28 :   R = shallowconcat(
      70             :     vconcat(diagonal_shallow(cyc), L),
      71             :     vconcat(zeromat(l-1, r1-t), scalarmat_shallow(gen_2,r1-t)));
      72          28 :   Cyc = ZM_snf_group(R, NULL, &u);
      73          28 :   U0 = rowslice(u, 1, l-1);
      74          28 :   Uoo = ZM_mul(H, rowslice(u, l, nbrows(u)));
      75          28 :   l = lg(Cyc); Gen = cgetg(l,t_VEC);
      76          91 :   for (j = 1; j < l; j++)
      77             :   {
      78          63 :     GEN g = gel(U0,j), s = gel(Uoo,j);
      79          63 :     g = (lg(g) == 1)? gen_1: Q_primpart( idealfactorback(nf,gen,g,0) );
      80          63 :     if (!ZV_equal0(s))
      81             :     {
      82          28 :       GEN a = set_sign_mod_divisor(nf, ZV_to_Flv(s,2), gen_1, sarch);
      83          28 :       g = is_pm1(g)? a: idealmul(nf, a, g);
      84             :     }
      85          63 :     gel(Gen,j) = g;
      86             :   }
      87          28 :   return gerepilecopy(av, mkvec3(shifti(bnf_get_no(bnf),r1-t), Cyc, Gen));
      88             : }
      89             : 
      90             : /********************************************************************/
      91             : /**                                                                **/
      92             : /**                  REDUCTION MOD IDELE                           **/
      93             : /**                                                                **/
      94             : /********************************************************************/
      95             : 
      96             : static GEN
      97       26628 : compute_fact(GEN nf, GEN U, GEN gen)
      98             : {
      99       26628 :   long i, j, l = lg(U), h = lgcols(U); /* l > 1 */
     100       26628 :   GEN basecl = cgetg(l,t_VEC), G;
     101             : 
     102       26628 :   G = mkvec2(NULL, trivial_fact());
     103       57519 :   for (j = 1; j < l; j++)
     104             :   {
     105       30891 :     GEN z = NULL;
     106      104069 :     for (i = 1; i < h; i++)
     107             :     {
     108       73178 :       GEN g, e = gcoeff(U,i,j); if (!signe(e)) continue;
     109             : 
     110       33348 :       g = gel(gen,i);
     111       33348 :       if (typ(g) != t_MAT)
     112             :       {
     113       22365 :         if (z)
     114        2296 :           gel(z,2) = famat_mulpow_shallow(gel(z,2), g, e);
     115             :         else
     116       20069 :           z = mkvec2(NULL, to_famat_shallow(g, e));
     117       22365 :         continue;
     118             :       }
     119       10983 :       gel(G,1) = g;
     120       10983 :       g = idealpowred(nf,G,e);
     121       10983 :       z = z? idealmulred(nf,z,g): g;
     122             :     }
     123       30891 :     gel(z,2) = famat_reduce(gel(z,2));
     124       30891 :     gel(basecl,j) = z;
     125             :   }
     126       26628 :   return basecl;
     127             : }
     128             : 
     129             : static int
     130       15484 : too_big(GEN nf, GEN bet)
     131             : {
     132       15484 :   GEN x = nfnorm(nf,bet);
     133       15484 :   switch (typ(x))
     134             :   {
     135        9051 :     case t_INT: return abscmpii(x, gen_1);
     136        6433 :     case t_FRAC: return abscmpii(gel(x,1), gel(x,2));
     137             :   }
     138           0 :   pari_err_BUG("wrong type in too_big");
     139             :   return 0; /* LCOV_EXCL_LINE */
     140             : }
     141             : 
     142             : /* true nf; GTM 193: Algo 4.3.4. Reduce x mod divisor */
     143             : static GEN
     144       15036 : idealmoddivisor_aux(GEN nf, GEN x, GEN f, GEN sarch)
     145             : {
     146       15036 :   pari_sp av = avma;
     147             :   GEN a, A;
     148             : 
     149       15036 :   if ( is_pm1(gcoeff(f,1,1)) ) /* f = 1 */
     150             :   {
     151         476 :     A = idealred(nf, mkvec2(x, gen_1));
     152         476 :     A = nfinv(nf, gel(A,2));
     153             :   }
     154             :   else
     155             :   {/* given coprime integral ideals x and f (f HNF), compute "small"
     156             :     * G in x, such that G = 1 mod (f). GTM 193: Algo 4.3.3 */
     157       14560 :     GEN G = idealaddtoone_raw(nf, x, f);
     158       14560 :     GEN D = idealaddtoone_i(nf, idealdiv(nf,G,x), f);
     159       14560 :     A = nfdiv(nf,D,G);
     160             :   }
     161       15036 :   if (too_big(nf,A) > 0) return gc_const(av, x);
     162       13517 :   a = set_sign_mod_divisor(nf, NULL, A, sarch);
     163       13517 :   if (a != A && too_big(nf,A) > 0) return gc_const(av, x);
     164       13517 :   return idealmul(nf, a, x);
     165             : }
     166             : 
     167             : GEN
     168        4214 : idealmoddivisor(GEN bnr, GEN x)
     169             : {
     170        4214 :   GEN nf = bnr_get_nf(bnr), bid = bnr_get_bid(bnr);
     171        4214 :   return idealmoddivisor_aux(nf, x, bid_get_ideal(bid), bid_get_sarch(bid));
     172             : }
     173             : 
     174             : /* v_pr(L0 * cx) */
     175             : static long
     176       18067 : fast_val(GEN L0, GEN cx, GEN pr)
     177             : {
     178       18067 :   pari_sp av = avma;
     179       18067 :   long v = typ(L0) == t_INT? 0: ZC_nfval(L0,pr);
     180       18067 :   if (cx)
     181             :   {
     182        9632 :     long w = Q_pval(cx, pr_get_p(pr));
     183        9632 :     if (w) v += w * pr_get_e(pr);
     184             :   }
     185       18067 :   return gc_long(av,v);
     186             : }
     187             : 
     188             : /* x coprime to fZ, return y = x mod fZ, y integral */
     189             : static GEN
     190        4382 : make_integral_Z(GEN x, GEN fZ)
     191             : {
     192        4382 :   GEN d, y = Q_remove_denom(x, &d);
     193        4382 :   if (d) y = FpC_Fp_mul(y, Fp_inv(d, fZ), fZ);
     194        4382 :   return y;
     195             : }
     196             : 
     197             : /* p pi^(-1) mod f */
     198             : static GEN
     199        9856 : get_pinvpi(GEN nf, GEN fZ, GEN p, GEN pi, GEN *v)
     200             : {
     201        9856 :   if (!*v) {
     202        4382 :     GEN invpi = nfinv(nf, pi);
     203        4382 :     *v = make_integral_Z(RgC_Rg_mul(invpi, p), mulii(p, fZ));
     204             :   }
     205        9856 :   return *v;
     206             : }
     207             : /* uniformizer pi for pr, coprime to F/p */
     208             : static GEN
     209        9996 : get_pi(GEN F, GEN pr, GEN *v)
     210             : {
     211        9996 :   if (!*v) *v = pr_uniformizer(pr, F);
     212        9996 :   return *v;
     213             : }
     214             : 
     215             : /* true nf */
     216             : static GEN
     217       33397 : bnr_grp(GEN nf, GEN U, GEN gen, GEN cyc, GEN bid)
     218             : {
     219       33397 :   GEN h = ZV_prod(cyc);
     220             :   GEN f, fZ, basecl, fa, pr, t, EX, sarch, F, P, vecpi, vecpinvpi;
     221             :   long i,j,l,lp;
     222             : 
     223       33397 :   if (lg(U) == 1) return mkvec3(h, cyc, cgetg(1, t_VEC));
     224       26628 :   basecl = compute_fact(nf, U, gen); /* generators in factored form */
     225       26628 :   EX = gel(bid_get_cyc(bid),1); /* exponent of (O/f)^* */
     226       26628 :   f  = bid_get_ideal(bid); fZ = gcoeff(f,1,1);
     227       26628 :   fa = bid_get_fact(bid);
     228       26628 :   sarch = bid_get_sarch(bid);
     229       26628 :   P = gel(fa,1); F = prV_lcm_capZ(P);
     230             : 
     231       26628 :   lp = lg(P);
     232       26628 :   vecpinvpi = cgetg(lp, t_VEC);
     233       26628 :   vecpi  = cgetg(lp, t_VEC);
     234       66220 :   for (i=1; i<lp; i++)
     235             :   {
     236       39592 :     pr = gel(P,i);
     237       39592 :     gel(vecpi,i)    = NULL; /* to be computed if needed */
     238       39592 :     gel(vecpinvpi,i) = NULL; /* to be computed if needed */
     239             :   }
     240             : 
     241       26628 :   l = lg(basecl);
     242       57519 :   for (i=1; i<l; i++)
     243             :   {
     244             :     GEN p, pi, pinvpi, dmulI, mulI, G, I, A, e, L, newL;
     245             :     long la, v, k;
     246             :     pari_sp av;
     247             :     /* G = [I, A=famat(L,e)] is a generator, I integral */
     248       30891 :     G = gel(basecl,i);
     249       30891 :     I = gel(G,1);
     250       30891 :     A = gel(G,2); L = gel(A,1); e = gel(A,2);
     251             :     /* if no reduction took place in compute_fact, everybody is still coprime
     252             :      * to f + no denominators */
     253       30891 :     if (!I) { gel(basecl,i) = famat_to_nf_moddivisor(nf, L, e, bid); continue; }
     254       10822 :     if (lg(A) == 1) { gel(basecl,i) = I; continue; }
     255             : 
     256             :     /* compute mulI so that mulI * I coprime to f
     257             :      * FIXME: use idealcoprime ??? (Less efficient. Fix idealcoprime!) */
     258       10822 :     dmulI = mulI = NULL;
     259       26005 :     for (j=1; j<lp; j++)
     260             :     {
     261       15183 :       pr = gel(P,j);
     262       15183 :       v  = idealval(nf, I, pr);
     263       15183 :       if (!v) continue;
     264        3801 :       p  = pr_get_p(pr);
     265        3801 :       pi = get_pi(F, pr, &gel(vecpi,j));
     266        3801 :       pinvpi = get_pinvpi(nf, fZ, p, pi, &gel(vecpinvpi,j));
     267        3801 :       t = nfpow_u(nf, pinvpi, (ulong)v);
     268        3801 :       mulI = mulI? nfmuli(nf, mulI, t): t;
     269        3801 :       t = powiu(p, v);
     270        3801 :       dmulI = dmulI? mulii(dmulI, t): t;
     271             :     }
     272             : 
     273             :     /* make all components of L coprime to f.
     274             :      * Assuming (L^e * I, f) = 1, then newL^e * mulI = L^e */
     275       10822 :     la = lg(e); newL = cgetg(la, t_VEC);
     276       21798 :     for (k=1; k<la; k++)
     277             :     {
     278       10976 :       GEN cx, LL = nf_to_scalar_or_basis(nf, gel(L,k));
     279       10976 :       GEN L0 = Q_primitive_part(LL, &cx); /* LL = L0*cx (faster nfval) */
     280       29043 :       for (j=1; j<lp; j++)
     281             :       {
     282       18067 :         pr = gel(P,j);
     283       18067 :         v  = fast_val(L0,cx, pr); /* = val_pr(LL) */
     284       18067 :         if (!v) continue;
     285        6195 :         p  = pr_get_p(pr);
     286        6195 :         pi = get_pi(F, pr, &gel(vecpi,j));
     287        6195 :         if (v > 0)
     288             :         {
     289        6055 :           pinvpi = get_pinvpi(nf, fZ, p, pi, &gel(vecpinvpi,j));
     290        6055 :           t = nfpow_u(nf,pinvpi, (ulong)v);
     291        6055 :           LL = nfmul(nf, LL, t);
     292        6055 :           LL = gdiv(LL, powiu(p, v));
     293             :         }
     294             :         else
     295             :         {
     296         140 :           t = nfpow_u(nf,pi,(ulong)(-v));
     297         140 :           LL = nfmul(nf, LL, t);
     298             :         }
     299             :       }
     300       10976 :       LL = make_integral(nf,LL,f,P);
     301       10976 :       gel(newL,k) = typ(LL) == t_INT? LL: FpC_red(LL, fZ);
     302             :     }
     303             : 
     304       10822 :     av = avma;
     305             :     /* G in nf, = L^e mod f */
     306       10822 :     G = famat_to_nf_modideal_coprime(nf, newL, e, f, EX);
     307       10822 :     if (mulI)
     308             :     {
     309        3787 :       G = nfmuli(nf, G, mulI);
     310        3787 :       G = typ(G) == t_COL? ZC_hnfrem(G, ZM_Z_mul(f, dmulI))
     311        3787 :                          : modii(G, mulii(fZ,dmulI));
     312        3787 :       G = RgC_Rg_div(G, dmulI);
     313             :     }
     314       10822 :     G = set_sign_mod_divisor(nf,A,G,sarch);
     315       10822 :     I = idealmul(nf,I,G);
     316             :     /* more or less useless, but cheap at this point */
     317       10822 :     I = idealmoddivisor_aux(nf,I,f,sarch);
     318       10822 :     gel(basecl,i) = gerepilecopy(av, I);
     319             :   }
     320       26628 :   return mkvec3(h, cyc, basecl);
     321             : }
     322             : 
     323             : /********************************************************************/
     324             : /**                                                                **/
     325             : /**                   INIT RAY CLASS GROUP                         **/
     326             : /**                                                                **/
     327             : /********************************************************************/
     328             : GEN
     329      312884 : bnr_subgroup_check(GEN bnr, GEN H, GEN *pdeg)
     330             : {
     331      312884 :   GEN no = bnr_get_no(bnr);
     332      312882 :   if (H && isintzero(H)) H = NULL;
     333      312880 :   if (H)
     334             :   {
     335      154342 :     GEN h, cyc = bnr_get_cyc(bnr);
     336      154342 :     switch(typ(H))
     337             :     {
     338        2576 :       case t_INT:
     339        2576 :         H = scalarmat_shallow(H, lg(cyc)-1);
     340             :         /* fall through */
     341       75410 :       case t_MAT:
     342       75410 :         RgM_check_ZM(H, "bnr_subgroup_check");
     343       75410 :         H = ZM_hnfmodid(H, cyc);
     344       75411 :         break;
     345       78932 :       case t_VEC:
     346       78932 :         if (char_check(cyc, H)) { H = charker(cyc, H); break; }
     347           0 :       default: pari_err_TYPE("bnr_subgroup_check", H);
     348             :     }
     349      154343 :     h = ZM_det_triangular(H);
     350      154342 :     if (equalii(h, no)) H = NULL; else no = h;
     351             :   }
     352      312881 :   if (pdeg) *pdeg = no;
     353      312881 :   return H;
     354             : }
     355             : 
     356             : void
     357        4200 : bnr_subgroup_sanitize(GEN *pbnr, GEN *pH)
     358             : {
     359        4200 :   GEN D, cnd, mod, cyc, bnr = *pbnr, H = *pH;
     360             : 
     361        4200 :   if (nftyp(bnr)==typ_BNF) bnr = Buchray(bnr, gen_1, nf_INIT);
     362        4081 :   else checkbnr(bnr);
     363        4186 :   cyc = bnr_get_cyc(bnr);
     364        4186 :   if (!H) mod = cyc_get_expo(cyc);
     365        3794 :   else switch(typ(H))
     366             :   {
     367        2793 :     case t_INT: mod = H; break;
     368           7 :     case t_VEC:
     369           7 :       if (!char_check(cyc, H))
     370           0 :         pari_err_TYPE("bnr_subgroup_sanitize [character]", H);
     371           7 :       H = charker(cyc, H); /* character -> subgroup */
     372         994 :     case t_MAT:
     373         994 :       H = hnfmodid(H, cyc); /* make sure H is a left divisor of Mat(cyc) */
     374         980 :       D = ZM_snf(H); /* structure of Cl_f / H */
     375         980 :       mod = lg(D) == 1? gen_1: gel(D,1);
     376         980 :       break;
     377           7 :     default: pari_err_TYPE("bnr_subroup_sanitize [subgroup]", H);
     378           0 :       mod = NULL;
     379             :   }
     380        4165 :   cnd = bnrconductormod(bnr, H, mod);
     381        4165 :   *pbnr = gel(cnd,2); *pH = gel(cnd,3);
     382        4165 : }
     383             : void
     384        1386 : bnr_char_sanitize(GEN *pbnr, GEN *pchi)
     385             : {
     386        1386 :   GEN cnd, cyc, bnr = *pbnr, chi = *pchi;
     387             : 
     388        1386 :   if (nftyp(bnr)==typ_BNF) bnr = Buchray(bnr, gen_1, nf_INIT);
     389        1386 :   else checkbnr(bnr);
     390        1386 :   cyc = bnr_get_cyc(bnr);
     391        1386 :   if (typ(chi) != t_VEC || !char_check(cyc, chi))
     392           0 :     pari_err_TYPE("bnr_char_sanitize [character]", chi);
     393        1386 :   cnd = bnrconductormod(bnr, chi, charorder(cyc, chi));
     394        1386 :   *pbnr = gel(cnd,2); *pchi = gel(cnd,3);
     395        1386 : }
     396             : 
     397             : 
     398             : /* c a rational content (NULL or t_INT or t_FRAC), return u*c as a ZM/d */
     399             : static GEN
     400      226886 : ZM_content_mul(GEN u, GEN c, GEN *pd)
     401             : {
     402      226886 :   *pd = gen_1;
     403      226886 :   if (c)
     404             :   {
     405      151756 :     if (typ(c) == t_FRAC) { *pd = gel(c,2); c = gel(c,1); }
     406      151756 :     if (!is_pm1(c)) u = ZM_Z_mul(u, c);
     407             :   }
     408      226888 :   return u;
     409             : }
     410             : 
     411             : /* bnr natural generators: bnf gens made coprime to modulus + bid gens.
     412             :  * Beware: if bnr includes MOD, we may have #El < #bnf.ge*/
     413             : static GEN
     414       49686 : get_Gen(GEN bnf, GEN bid, GEN El)
     415             : {
     416       49686 :   GEN nf = bnf_get_nf(bnf), gen = bnf_get_gen(bnf), Gen;
     417       49686 :   long i, l = lg(El);
     418       49686 :   if (lg(gen) > l) gen = vec_shorten(gen, l-1);
     419       49686 :   Gen = shallowconcat(gen, bid_get_gen(bid));
     420       68712 :   for (i = 1; i < l; i++)
     421             :   {
     422       19026 :     GEN e = gel(El,i);
     423       19026 :     if (!isint1(e)) gel(Gen,i) = idealmul(nf, gel(El,i), gel(Gen,i));
     424             :   }
     425       49686 :   return Gen;
     426             : }
     427             : 
     428             : static GEN
     429      256797 : Buchraymod_i(GEN bnf, GEN module, long flag, GEN MOD)
     430             : {
     431             :   GEN nf, cyc0, cyc, gen, Cyc, clg, h, logU, U, Ui, vu;
     432             :   GEN bid, cycbid, H, El;
     433             :   long RU, Ri, j, ngen;
     434      256797 :   const long add_gen = flag & nf_GEN;
     435      256797 :   const long do_init = flag & nf_INIT;
     436             : 
     437      256797 :   if (MOD && typ(MOD) != t_INT)
     438           0 :     pari_err_TYPE("bnrinit [incorrect cycmod]", MOD);
     439      256797 :   bnf = checkbnf(bnf);
     440      256785 :   nf = bnf_get_nf(bnf);
     441      256779 :   RU = lg(nf_get_roots(nf))-1; /* #K.futu */
     442      256777 :   El = NULL; /* gcc -Wall */
     443      256777 :   cyc = cyc0 = bnf_get_cyc(bnf);
     444      256773 :   gen = bnf_get_gen(bnf); ngen = lg(cyc)-1;
     445             : 
     446      256775 :   bid = checkbid_i(module);
     447      256772 :   if (!bid) bid = Idealstarmod(nf,module,nf_GEN|nf_INIT, MOD);
     448      256823 :   cycbid = bid_get_cyc(bid);
     449      256821 :   if (MOD) cyc = ZV_snfclean(ZV_snf_gcd(cyc, MOD));
     450      256817 :   Ri = lg(cycbid)-1;
     451      256817 :   if (Ri || add_gen || do_init)
     452             :   {
     453      256815 :     GEN fx = bid_get_fact(bid);
     454      256814 :     long n = Ri? ngen: lg(cyc)-1;
     455      256814 :     El = cgetg(n+1, t_VEC);
     456      293936 :     for (j = 1; j <= n; j++)
     457             :     {
     458       37119 :       GEN c = idealcoprimefact(nf, gel(gen,j), fx);
     459       37121 :       gel(El,j) = nf_to_scalar_or_basis(nf,c);
     460             :     }
     461             :   }
     462      256819 :   if (!Ri)
     463             :   {
     464       29925 :     GEN no, Gen = add_gen? get_Gen(bnf, bid, El): NULL;
     465       29925 :     if (MOD) { ngen = lg(cyc)-1; no = ZV_prod(cyc); } else no = bnf_get_no(bnf);
     466       29925 :     clg = add_gen? mkvec3(no, cyc, Gen): mkvec2(no, cyc);
     467       29925 :     if (!do_init) return clg;
     468       29925 :     U = matid(ngen);
     469       29925 :     U = mkvec3(U, cgetg(1,t_MAT), U);
     470       29925 :     vu = mkvec3(cgetg(1,t_MAT), matid(RU), gen_1);
     471       29924 :     return mkvecn(6, bnf, bid, El, U, clg, vu);
     472             :   }
     473             : 
     474      226894 :   logU = ideallog_units0(bnf, bid, MOD);
     475      226873 :   if (do_init)
     476             :   { /* (log(Units)|D) * u = (0 | H) */
     477      226873 :     GEN c1,c2, u,u1,u2, Hi, D = shallowconcat(logU, diagonal_shallow(cycbid));
     478      226887 :     H = ZM_hnfall_i(D, &u, 1);
     479      226880 :     u1 = matslice(u, 1,RU, 1,RU);
     480      226891 :     u2 = matslice(u, 1,RU, RU+1,lg(u)-1);
     481             :     /* log(Units) (u1|u2) = (0|H) (mod D), H HNF */
     482             : 
     483      226896 :     u1 = ZM_lll(u1, 0.99, LLL_INPLACE);
     484      226879 :     Hi = Q_primitive_part(RgM_inv_upper(H), &c1);
     485      226870 :     u2 = ZM_mul(ZM_reducemodmatrix(u2,u1), Hi);
     486      226870 :     u2 = Q_primitive_part(u2, &c2);
     487      226876 :     u2 = ZM_content_mul(u2, mul_content(c1,c2), &c2);
     488      226888 :     vu = mkvec3(u2,u1,c2); /* u2/c2 = H^(-1) (mod Im u1) */
     489             :   }
     490             :   else
     491             :   {
     492           0 :     H = ZM_hnfmodid(logU, cycbid);
     493           0 :     vu = NULL; /* -Wall */
     494             :   }
     495      226887 :   if (!ngen)
     496      201071 :     h = H;
     497             :   else
     498             :   {
     499       25816 :     GEN L = cgetg(ngen+1, t_MAT), cycgen = bnf_build_cycgen(bnf);
     500       52415 :     for (j=1; j<=ngen; j++)
     501             :     {
     502       26600 :       GEN c = gel(cycgen,j), e = gel(El,j);
     503       26600 :       if (!equali1(e)) c = famat_mulpow_shallow(c, e, gel(cyc0,j));
     504       26600 :       gel(L,j) = ideallogmod(nf, c, bid, MOD); /* = log(Gen[j]^cyc[j]) */
     505             :     }
     506             :     /* [cyc0, 0; -L, H] = relation matrix for generators Gen of Cl_f */
     507       25815 :     h = shallowconcat(vconcat(diagonal_shallow(cyc0), ZM_neg(L)),
     508             :                       vconcat(zeromat(ngen, Ri), H));
     509       25816 :     h = MOD? ZM_hnfmodid(h, MOD): ZM_hnf(h);
     510             :   }
     511      226886 :   Cyc = ZM_snf_group(h, &U, &Ui);
     512             :   /* Gen = clg.gen*U, clg.gen = Gen*Ui */
     513       33397 :   clg = add_gen? bnr_grp(nf, Ui, get_Gen(bnf, bid, El), Cyc, bid)
     514      226881 :                : mkvec2(ZV_prod(Cyc), Cyc);
     515      226883 :   if (!do_init) return clg;
     516      226883 :   U = mkvec3(vecslice(U, 1,ngen), vecslice(U,ngen+1,lg(U)-1), Ui);
     517      226886 :   return mkvecn(6, bnf, bid, El, U, clg, vu);
     518             : }
     519             : GEN
     520       41342 : Buchray(GEN bnf, GEN f, long flag)
     521       41342 : { return Buchraymod(bnf, f, flag, NULL); }
     522             : GEN
     523      253379 : Buchraymod(GEN bnf, GEN f, long flag, GEN MOD)
     524             : {
     525      253379 :   pari_sp av = avma;
     526      253379 :   return gerepilecopy(av, Buchraymod_i(bnf, f, flag, MOD));
     527             : }
     528             : GEN
     529      211230 : bnrinitmod(GEN bnf, GEN f, long flag, GEN MOD)
     530             : {
     531      211230 :   switch(flag)
     532             :   {
     533      211185 :     case 0: flag = nf_INIT; break;
     534          49 :     case 1: flag = nf_INIT | nf_GEN; break;
     535           0 :     default: pari_err_FLAG("bnrinit");
     536             :   }
     537      211234 :   return Buchraymod(bnf, f, flag, MOD);
     538             : }
     539             : GEN
     540           0 : bnrinit0(GEN bnf, GEN ideal, long flag)
     541           0 : { return bnrinitmod(bnf, ideal, flag, NULL); }
     542             : 
     543             : GEN
     544         112 : bnrclassno(GEN bnf,GEN ideal)
     545             : {
     546             :   GEN h, D, bid, cycbid;
     547         112 :   pari_sp av = avma;
     548             : 
     549         112 :   bnf = checkbnf(bnf);
     550         112 :   h = bnf_get_no(bnf);
     551         112 :   bid = checkbid_i(ideal);
     552         112 :   if (!bid) bid = Idealstar(bnf_get_nf(bnf), ideal, nf_INIT);
     553         105 :   cycbid = bid_get_cyc(bid);
     554         105 :   if (lg(cycbid) == 1) { set_avma(av); return icopy(h); }
     555          84 :   D = ideallog_units(bnf, bid); /* (Z_K/f)^* / units ~ Z^n / D */
     556          84 :   D = ZM_hnfmodid(D,cycbid);
     557          84 :   return gerepileuptoint(av, mulii(h, ZM_det_triangular(D)));
     558             : }
     559             : GEN
     560         105 : bnrclassno0(GEN A, GEN B, GEN C)
     561             : {
     562         105 :   pari_sp av = avma;
     563         105 :   GEN h, H = NULL;
     564             :   /* adapted from ABC_to_bnr, avoid costly bnrinit if possible */
     565         105 :   if (typ(A) == t_VEC)
     566         105 :     switch(lg(A))
     567             :     {
     568          14 :       case 7: /* bnr */
     569          14 :         checkbnr(A); H = B;
     570          14 :         break;
     571          91 :       case 11: /* bnf */
     572          91 :         if (!B) pari_err_TYPE("bnrclassno [bnf+missing conductor]",A);
     573          91 :         if (!C) return bnrclassno(A, B);
     574           7 :         A = Buchray(A, B, nf_INIT); H = C;
     575           7 :         break;
     576           0 :       default: checkbnf(A);/*error*/
     577             :     }
     578           0 :   else checkbnf(A);/*error*/
     579             : 
     580          21 :   H = bnr_subgroup_check(A, H, &h);
     581          21 :   if (!H) { set_avma(av); return icopy(h); }
     582          14 :   return gerepileuptoint(av, h);
     583             : }
     584             : 
     585             : /* ZMV_ZCV_mul for two matrices U = [Ux,Uy], it may have more components
     586             :  * (ignored) and vectors x,y */
     587             : static GEN
     588     1338040 : ZM2_ZC2_mul(GEN U, GEN x, GEN y)
     589             : {
     590     1338040 :   GEN Ux = gel(U,1), Uy = gel(U,2);
     591     1338040 :   if (lg(Ux) == 1) return ZM_ZC_mul(Uy,y);
     592      163174 :   if (lg(Uy) == 1) return ZM_ZC_mul(Ux,x);
     593      163174 :   return ZC_add(ZM_ZC_mul(Ux,x), ZM_ZC_mul(Uy,y));
     594             : }
     595             : 
     596             : GEN
     597     1455793 : bnrisprincipalmod(GEN bnr, GEN x, GEN MOD, long flag)
     598             : {
     599     1455793 :   pari_sp av = avma;
     600             :   GEN E, G, clgp, bnf, nf, bid, ex, cycray, alpha, El;
     601             :   int trivialbid;
     602             : 
     603     1455793 :   checkbnr(bnr);
     604     1455793 :   El = bnr_get_El(bnr);
     605     1455793 :   cycray = bnr_get_cyc(bnr);
     606     1455793 :   if (MOD && flag) pari_err_FLAG("bnrisprincipalmod [MOD!=NULL and flag!=0]");
     607     1455793 :   if (lg(cycray) == 1 && !(flag & nf_GEN)) return cgetg(1,t_COL);
     608     1455632 :   if (MOD) cycray = ZV_snf_gcd(cycray, MOD);
     609             : 
     610     1455631 :   bnf = bnr_get_bnf(bnr); nf = bnf_get_nf(bnf);
     611     1455631 :   bid = bnr_get_bid(bnr);
     612     1455631 :   trivialbid = lg(bid_get_cyc(bid)) == 1;
     613     1455631 :   if (trivialbid)
     614             :   {
     615      117592 :     ex = isprincipal(bnf, x);
     616      117592 :     setlg(ex, lg(cycray)); /* can happen with MOD */
     617             :   }
     618             :   else
     619             :   {
     620     1338039 :     GEN v = bnfisprincipal0(bnf, x, nf_FORCE|nf_GENMAT);
     621     1338040 :     GEN e = gel(v,1), b = gel(v,2);
     622     1338040 :     long i, j = lg(e);
     623     1505942 :     for (i = 1; i < j; i++) /* modify b as if bnf.gen were El*bnf.gen */
     624      167902 :       if (typ(gel(El,i)) != t_INT && signe(gel(e,i))) /* <==> != 1 */
     625       31959 :         b = famat_mulpow_shallow(b, gel(El,i), negi(gel(e,i)));
     626     1338040 :     if (!MOD && !(flag & nf_GEN)) MOD = gel(cycray,1);
     627     1338040 :     ex = ZM2_ZC2_mul(bnr_get_U(bnr), e, ideallogmod(nf, b, bid, MOD));
     628             :   }
     629     1455632 :   ex = ZV_ZV_mod(ex, cycray);
     630     1455631 :   if (!(flag & (nf_GEN|nf_GENMAT))) return gerepileupto(av, ex);
     631             : 
     632             :   /* compute generator */
     633        7049 :   E = ZC_neg(ex);
     634        7049 :   clgp = bnr_get_clgp(bnr);
     635        7049 :   if (lg(clgp) == 4)
     636          21 :     G = abgrp_get_gen(clgp);
     637             :   else
     638             :   {
     639        7028 :     G = get_Gen(bnf, bid, El);
     640        7028 :     E = ZM_ZC_mul(bnr_get_Ui(bnr), E);
     641             :   }
     642        7049 :   alpha = isprincipalfact(bnf, x, G, E, nf_GENMAT|nf_GEN_IF_PRINCIPAL|nf_FORCE);
     643        7049 :   if (alpha == gen_0) pari_err_BUG("isprincipalray");
     644        7049 :   if (!trivialbid)
     645             :   {
     646        7049 :     GEN v = gel(bnr,6), u2 = gel(v,1), u1 = gel(v,2), du2 = gel(v,3);
     647        7049 :     GEN y = ZM_ZC_mul(u2, ideallog(nf, alpha, bid));
     648        7049 :     if (!is_pm1(du2)) y = ZC_Z_divexact(y,du2);
     649        7049 :     y = ZC_reducemodmatrix(y, u1);
     650        7049 :     if (!ZV_equal0(y))
     651             :     {
     652        4998 :       GEN U = shallowcopy(bnf_build_units(bnf));
     653        4998 :       settyp(U, t_COL);
     654        4998 :       alpha = famat_div_shallow(alpha, mkmat2(U,y));
     655             :     }
     656             :   }
     657        7049 :   alpha = famat_reduce(alpha);
     658        7049 :   if (!(flag & nf_GENMAT)) alpha = nffactorback(nf, alpha, NULL);
     659        7049 :   return gerepilecopy(av, mkvec2(ex,alpha));
     660             : }
     661             : 
     662             : GEN
     663      410908 : bnrisprincipal(GEN bnr, GEN x, long flag)
     664      410908 : { return bnrisprincipalmod(bnr, x, NULL, flag); }
     665             : 
     666             : GEN
     667      403824 : isprincipalray(GEN bnr, GEN x) { return bnrisprincipal(bnr,x,0); }
     668             : GEN
     669           0 : isprincipalraygen(GEN bnr, GEN x) { return bnrisprincipal(bnr,x,nf_GEN); }
     670             : 
     671             : /* N! / N^N * (4/pi)^r2 * sqrt(|D|) */
     672             : GEN
     673           0 : minkowski_bound(GEN D, long N, long r2, long prec)
     674             : {
     675           0 :   pari_sp av = avma;
     676           0 :   GEN c = divri(mpfactr(N,prec), powuu(N,N));
     677           0 :   if (r2) c = mulrr(c, powru(divur(4,mppi(prec)), r2));
     678           0 :   c = mulrr(c, gsqrt(absi_shallow(D),prec));
     679           0 :   return gerepileuptoleaf(av, c);
     680             : }
     681             : 
     682             : /* N = [K:Q] > 1, D = disc(K) */
     683             : static GEN
     684          63 : zimmertbound(GEN D, long N, long R2)
     685             : {
     686          63 :   pari_sp av = avma;
     687             :   GEN w;
     688             : 
     689          63 :   if (N > 20) w = minkowski_bound(D, N, R2, DEFAULTPREC);
     690             :   else
     691             :   {
     692          63 :     const double c[19][11] = {
     693             : {/*2*/  0.6931,     0.45158},
     694             : {/*3*/  1.71733859, 1.37420604},
     695             : {/*4*/  2.91799837, 2.50091538, 2.11943331},
     696             : {/*5*/  4.22701425, 3.75471588, 3.31196660},
     697             : {/*6*/  5.61209925, 5.09730381, 4.60693851, 4.14303665},
     698             : {/*7*/  7.05406203, 6.50550021, 5.97735406, 5.47145968},
     699             : {/*8*/  8.54052636, 7.96438858, 7.40555445, 6.86558259, 6.34608077},
     700             : {/*9*/ 10.0630022,  9.46382812, 8.87952524, 8.31139202, 7.76081149},
     701             : {/*10*/11.6153797, 10.9966020, 10.3907654,  9.79895170, 9.22232770, 8.66213267},
     702             : {/*11*/13.1930961, 12.5573772, 11.9330458, 11.3210061, 10.7222412, 10.1378082},
     703             : {/*12*/14.7926394, 14.1420915, 13.5016616, 12.8721114, 12.2542699, 11.6490374,
     704             :        11.0573775},
     705             : {/*13*/16.4112395, 15.7475710, 15.0929680, 14.4480777, 13.8136054, 13.1903162,
     706             :        12.5790381},
     707             : {/*14*/18.0466672, 17.3712806, 16.7040780, 16.0456127, 15.3964878, 14.7573587,
     708             :        14.1289364, 13.5119848},
     709             : {/*15*/19.6970961, 19.0111606, 18.3326615, 17.6620757, 16.9999233, 16.3467686,
     710             :        15.7032228, 15.0699480},
     711             : {/*16*/21.3610081, 20.6655103, 19.9768082, 19.2953176, 18.6214885, 17.9558093,
     712             :        17.2988108, 16.6510652, 16.0131906},
     713             : 
     714             : {/*17*/23.0371259, 22.3329066, 21.6349299, 20.9435607, 20.2591899, 19.5822454,
     715             :        18.9131878, 18.2525157, 17.6007672},
     716             : 
     717             : {/*18*/24.7243611, 24.0121449, 23.3056902, 22.6053167, 21.9113705, 21.2242247,
     718             :        20.5442836, 19.8719830, 19.2077941, 18.5522234},
     719             : 
     720             : {/*19*/26.4217792, 25.7021950, 24.9879497, 24.2793271, 23.5766321, 22.8801952,
     721             :        22.1903709, 21.5075437, 20.8321263, 20.1645647},
     722             : {/*20*/28.1285704, 27.4021674, 26.6807314, 25.9645140, 25.2537867, 24.5488420,
     723             :        23.8499943, 23.1575823, 22.4719720, 21.7935548, 21.1227537}
     724             :     };
     725          63 :     w = mulrr(dbltor(exp(-c[N-2][R2])), gsqrt(absi_shallow(D),DEFAULTPREC));
     726             :   }
     727          63 :   return gerepileuptoint(av, ceil_safe(w));
     728             : }
     729             : 
     730             : /* return \gamma_n^n if known, an upper bound otherwise */
     731             : GEN
     732          63 : Hermite_bound(long n, long prec)
     733             : {
     734             :   GEN h,h1;
     735             :   pari_sp av;
     736             : 
     737          63 :   switch(n)
     738             :   {
     739          35 :     case 1: return gen_1;
     740          14 :     case 2: retmkfrac(utoipos(4), utoipos(3));
     741           7 :     case 3: return gen_2;
     742           7 :     case 4: return utoipos(4);
     743           0 :     case 5: return utoipos(8);
     744           0 :     case 6: retmkfrac(utoipos(64), utoipos(3));
     745           0 :     case 7: return utoipos(64);
     746           0 :     case 8: return utoipos(256);
     747           0 :     case 24: return int2n(48);
     748             :   }
     749           0 :   av = avma;
     750           0 :   h  = powru(divur(2,mppi(prec)), n);
     751           0 :   h1 = sqrr(ggamma(uutoQ(n+4,2),prec));
     752           0 :   return gerepileuptoleaf(av, mulrr(h,h1));
     753             : }
     754             : 
     755             : /* 1 if L (= nf != Q) primitive for sure, 0 if MAYBE imprimitive (may have a
     756             :  * subfield K) */
     757             : static long
     758          35 : isprimitive(GEN nf)
     759             : {
     760          35 :   long p, i, l, ep, N = nf_get_degree(nf);
     761             :   GEN D, fa;
     762             : 
     763          35 :   p = ucoeff(factoru(N), 1,1); /* smallest prime | N */
     764          35 :   if (p == N) return 1; /* prime degree */
     765             : 
     766             :   /* N = [L:Q] = product of primes >= p, same is true for [L:K]
     767             :    * d_L = t d_K^[L:K] --> check that some q^p divides d_L */
     768           0 :   D = nf_get_disc(nf);
     769           0 :   fa = gel(absZ_factor_limit(D,0),2); /* list of v_q(d_L). Don't check large primes */
     770           0 :   if (mod2(D)) i = 1;
     771             :   else
     772             :   { /* q = 2 */
     773           0 :     ep = itos(gel(fa,1));
     774           0 :     if ((ep>>1) >= p) return 0; /* 2 | d_K ==> 4 | d_K */
     775           0 :     i = 2;
     776             :   }
     777           0 :   l = lg(fa);
     778           0 :   for ( ; i < l; i++)
     779             :   {
     780           0 :     ep = itos(gel(fa,i));
     781           0 :     if (ep >= p) return 0;
     782             :   }
     783           0 :   return 1;
     784             : }
     785             : 
     786             : static GEN
     787           0 : dft_bound(void)
     788             : {
     789           0 :   if (DEBUGLEVEL>1) err_printf("Default bound for regulator: 0.2\n");
     790           0 :   return dbltor(0.2);
     791             : }
     792             : 
     793             : static GEN
     794          35 : regulatorbound(GEN bnf)
     795             : {
     796             :   long N, R1, R2, R;
     797             :   GEN nf, dK, p1, c1;
     798             : 
     799          35 :   nf = bnf_get_nf(bnf); N = nf_get_degree(nf);
     800          35 :   if (!isprimitive(nf)) return dft_bound();
     801             : 
     802          35 :   dK = absi_shallow(nf_get_disc(nf));
     803          35 :   nf_get_sign(nf, &R1, &R2); R = R1+R2-1;
     804          35 :   c1 = (!R2 && N<12)? int2n(N & (~1UL)): powuu(N,N);
     805          35 :   if (cmpii(dK,c1) <= 0) return dft_bound();
     806             : 
     807          35 :   p1 = sqrr(glog(gdiv(dK,c1),DEFAULTPREC));
     808          35 :   p1 = divru(gmul2n(powru(divru(mulru(p1,3),N*(N*N-1)-6*R2),R),R2), N);
     809          35 :   p1 = sqrtr(gdiv(p1, Hermite_bound(R, DEFAULTPREC)));
     810          35 :   if (DEBUGLEVEL>1) err_printf("Mahler bound for regulator: %Ps\n",p1);
     811          35 :   return gmax_shallow(p1, dbltor(0.2));
     812             : }
     813             : 
     814             : static int
     815       70553 : is_unit(GEN M, long r1, GEN x)
     816             : {
     817       70553 :   pari_sp av = avma;
     818       70553 :   GEN Nx = ground( embed_norm(RgM_zc_mul(M,x), r1) );
     819       70553 :   return gc_bool(av, is_pm1(Nx));
     820             : }
     821             : 
     822             : /* True nf. FIXME: should use smallvectors */
     823             : static double
     824          42 : minimforunits(GEN nf, long BORNE, ulong w)
     825             : {
     826          42 :   const long prec = MEDDEFAULTPREC;
     827          42 :   long n, r1, i, j, k, *x, cnt = 0;
     828          42 :   pari_sp av = avma;
     829             :   GEN r, M;
     830             :   double p, norme, normin;
     831             :   double **q,*v,*y,*z;
     832          42 :   double eps=0.000001, BOUND = BORNE * 1.00001;
     833             : 
     834          42 :   if (DEBUGLEVEL>=2)
     835             :   {
     836           0 :     err_printf("Searching minimum of T2-form on units:\n");
     837           0 :     if (DEBUGLEVEL>2) err_printf("   BOUND = %ld\n",BORNE);
     838             :   }
     839          42 :   n = nf_get_degree(nf); r1 = nf_get_r1(nf);
     840          42 :   minim_alloc(n+1, &q, &x, &y, &z, &v);
     841          42 :   M = gprec_w(nf_get_M(nf), prec);
     842          42 :   r = gaussred_from_QR(nf_get_G(nf), prec);
     843         231 :   for (j=1; j<=n; j++)
     844             :   {
     845         189 :     v[j] = gtodouble(gcoeff(r,j,j));
     846         651 :     for (i=1; i<j; i++) q[i][j] = gtodouble(gcoeff(r,i,j));
     847             :   }
     848          42 :   normin = (double)BORNE*(1-eps);
     849          42 :   k=n; y[n]=z[n]=0;
     850          42 :   x[n] = (long)(sqrt(BOUND/v[n]));
     851             : 
     852       70553 :   for(;;x[1]--)
     853             :   {
     854             :     do
     855             :     {
     856       71901 :       if (k>1)
     857             :       {
     858        1348 :         long l = k-1;
     859        1348 :         z[l] = 0;
     860        5033 :         for (j=k; j<=n; j++) z[l] += q[l][j]*x[j];
     861        1348 :         p = (double)x[k] + z[k];
     862        1348 :         y[l] = y[k] + p*p*v[k];
     863        1348 :         x[l] = (long)floor(sqrt((BOUND-y[l])/v[l])-z[l]);
     864        1348 :         k = l;
     865             :       }
     866             :       for(;;)
     867             :       {
     868       73102 :         p = (double)x[k] + z[k];
     869       73102 :         if (y[k] + p*p*v[k] <= BOUND) break;
     870        1201 :         k++; x[k]--;
     871             :       }
     872             :     }
     873       71901 :     while (k>1);
     874       70595 :     if (!x[1] && y[1]<=eps) break;
     875             : 
     876       70567 :     if (DEBUGLEVEL>8) err_printf(".");
     877       70567 :     if (++cnt == 5000) return -1.; /* too expensive */
     878             : 
     879       70553 :     p = (double)x[1] + z[1]; norme = y[1] + p*p*v[1];
     880       70553 :     if (is_unit(M, r1, x) && norme < normin)
     881             :     {
     882             :       /* exclude roots of unity */
     883          56 :       if (norme < 2*n)
     884             :       {
     885          42 :         GEN t = nfpow_u(nf, zc_to_ZC(x), w);
     886          42 :         if (typ(t) != t_COL || ZV_isscalar(t)) continue;
     887             :       }
     888          21 :       normin = norme*(1-eps);
     889          21 :       if (DEBUGLEVEL>=2) err_printf("*");
     890             :     }
     891             :   }
     892          28 :   if (DEBUGLEVEL>=2) err_printf("\n");
     893          28 :   set_avma(av);
     894          28 :   return normin;
     895             : }
     896             : 
     897             : #undef NBMAX
     898             : static int
     899        1804 : is_zero(GEN x, long bitprec) { return (gexpo(x) < -bitprec); }
     900             : 
     901             : static int
     902        1228 : is_complex(GEN x, long bitprec) { return !is_zero(imag_i(x), bitprec); }
     903             : 
     904             : /* assume M_star t_REAL
     905             :  * FIXME: what does this do ? To be rewritten */
     906             : static GEN
     907          28 : compute_M0(GEN M_star,long N)
     908             : {
     909             :   long m1,m2,n1,n2,n3,lr,lr1,lr2,i,j,l,vx,vy,vz,vM;
     910             :   GEN pol,p1,p2,p3,p4,p5,p6,p7,p8,p9,u,v,w,r,r1,r2,M0,M0_pro,S,P,M;
     911             :   GEN f1,f2,f3,g1,g2,g3,pg1,pg2,pg3,pf1,pf2,pf3,X,Y,Z;
     912          28 :   long bitprec = 24;
     913             : 
     914          28 :   if (N == 2) return gmul2n(sqrr(gacosh(gmul2n(M_star,-1),0)), -1);
     915          21 :   vx = fetch_var(); X = pol_x(vx);
     916          21 :   vy = fetch_var(); Y = pol_x(vy);
     917          21 :   vz = fetch_var(); Z = pol_x(vz);
     918          21 :   vM = fetch_var(); M = pol_x(vM);
     919             : 
     920          21 :   M0 = NULL; m1 = N/3;
     921          56 :   for (n1=1; n1<=m1; n1++) /* 1 <= n1 <= n2 <= n3 < N */
     922             :   {
     923          35 :     m2 = (N-n1)>>1;
     924         112 :     for (n2=n1; n2<=m2; n2++)
     925             :     {
     926          77 :       pari_sp av = avma; n3=N-n1-n2;
     927          77 :       if (n1==n2 && n1==n3) /* n1 = n2 = n3 = m1 = N/3 */
     928             :       {
     929           7 :         p1 = divru(M_star, m1);
     930           7 :         p4 = sqrtr_abs( mulrr(addsr(1,p1),subrs(p1,3)) );
     931           7 :         p5 = subrs(p1,1);
     932           7 :         u = gen_1;
     933           7 :         v = gmul2n(addrr(p5,p4),-1);
     934           7 :         w = gmul2n(subrr(p5,p4),-1);
     935           7 :         M0_pro=gmul2n(mulur(m1,addrr(sqrr(logr_abs(v)),sqrr(logr_abs(w)))), -2);
     936           7 :         if (DEBUGLEVEL>2)
     937           0 :           err_printf("[ %ld, %ld, %ld ]: %.28Pg\n",n1,n2,n3,M0_pro);
     938           7 :         if (!M0 || gcmp(M0_pro,M0) < 0) M0 = M0_pro;
     939             :       }
     940          70 :       else if (n1==n2 || n2==n3)
     941          42 :       { /* n3 > N/3 >= n1 */
     942          42 :         long k = N - 2*n2;
     943          42 :         p2 = deg1pol_shallow(stoi(-n2), M_star, vx); /* M* - n2 X */
     944          42 :         p3 = gmul(powuu(k,k),
     945             :                   gpowgs(gsubgs(RgX_Rg_mul(p2, M_star), k*k), n2));
     946          42 :         pol = gsub(p3, RgX_mul(monomial(powuu(n2,n2), n2, vx),
     947             :                                gpowgs(p2, N-n2)));
     948          42 :         r = roots(pol, DEFAULTPREC); lr = lg(r);
     949         378 :         for (i=1; i<lr; i++)
     950             :         {
     951             :           GEN n2S;
     952         336 :           S = real_i(gel(r,i));
     953         336 :           if (is_complex(gel(r,i), bitprec) || signe(S) <= 0) continue;
     954             : 
     955         182 :           n2S = mulur(n2,S);
     956         182 :           p4 = subrr(M_star, n2S);
     957         182 :           P = divrr(mulrr(n2S,p4), subrs(mulrr(M_star,p4),k*k));
     958         182 :           p5 = subrr(sqrr(S), gmul2n(P,2));
     959         182 :           if (gsigne(p5) < 0) continue;
     960             : 
     961         140 :           p6 = sqrtr(p5);
     962         140 :           v = gmul2n(subrr(S,p6),-1);
     963         140 :           if (gsigne(v) <= 0) continue;
     964             : 
     965         126 :           u = gmul2n(addrr(S,p6),-1);
     966         126 :           w = gpow(P, sstoQ(-n2,k), 0);
     967         126 :           p6 = mulur(n2, addrr(sqrr(logr_abs(u)), sqrr(logr_abs(v))));
     968         126 :           M0_pro = gmul2n(addrr(p6, mulur(k, sqrr(logr_abs(w)))),-2);
     969         126 :           if (DEBUGLEVEL>2)
     970           0 :             err_printf("[ %ld, %ld, %ld ]: %.28Pg\n",n1,n2,n3,M0_pro);
     971         126 :           if (!M0 || gcmp(M0_pro,M0) < 0) M0 = M0_pro;
     972             :         }
     973             :       }
     974             :       else
     975             :       {
     976          28 :         f1 = gsub(gadd(gmulsg(n1,X),gadd(gmulsg(n2,Y),gmulsg(n3,Z))), M);
     977          28 :         f2 =         gmulsg(n1,gmul(Y,Z));
     978          28 :         f2 = gadd(f2,gmulsg(n2,gmul(X,Z)));
     979          28 :         f2 = gadd(f2,gmulsg(n3,gmul(X,Y)));
     980          28 :         f2 = gsub(f2,gmul(M,gmul(X,gmul(Y,Z))));
     981          28 :         f3 = gsub(gmul(gpowgs(X,n1),gmul(gpowgs(Y,n2),gpowgs(Z,n3))), gen_1);
     982             :         /* f1 = n1 X + n2 Y + n3 Z - M */
     983             :         /* f2 = n1 YZ + n2 XZ + n3 XY */
     984             :         /* f3 = X^n1 Y^n2 Z^n3 - 1*/
     985          28 :         g1=resultant(f1,f2); g1=primpart(g1);
     986          28 :         g2=resultant(f1,f3); g2=primpart(g2);
     987          28 :         g3=resultant(g1,g2); g3=primpart(g3);
     988          28 :         pf1=gsubst(f1,vM,M_star); pg1=gsubst(g1,vM,M_star);
     989          28 :         pf2=gsubst(f2,vM,M_star); pg2=gsubst(g2,vM,M_star);
     990          28 :         pf3=gsubst(f3,vM,M_star); pg3=gsubst(g3,vM,M_star);
     991             :         /* g3 = Res_Y,Z(f1,f2,f3) */
     992          28 :         r = roots(pg3,DEFAULTPREC); lr = lg(r);
     993         476 :         for (i=1; i<lr; i++)
     994             :         {
     995         448 :           w = real_i(gel(r,i));
     996         448 :           if (is_complex(gel(r,i), bitprec) || signe(w) <= 0) continue;
     997         140 :           p1=gsubst(pg1,vz,w);
     998         140 :           p2=gsubst(pg2,vz,w);
     999         140 :           p3=gsubst(pf1,vz,w);
    1000         140 :           p4=gsubst(pf2,vz,w);
    1001         140 :           p5=gsubst(pf3,vz,w);
    1002         140 :           r1 = roots(p1, DEFAULTPREC); lr1 = lg(r1);
    1003         420 :           for (j=1; j<lr1; j++)
    1004             :           {
    1005         280 :             v = real_i(gel(r1,j));
    1006         280 :             if (is_complex(gel(r1,j), bitprec) || signe(v) <= 0
    1007         280 :              || !is_zero(gsubst(p2,vy,v), bitprec)) continue;
    1008             : 
    1009         164 :             p7=gsubst(p3,vy,v);
    1010         164 :             p8=gsubst(p4,vy,v);
    1011         164 :             p9=gsubst(p5,vy,v);
    1012         164 :             r2 = roots(p7, DEFAULTPREC); lr2 = lg(r2);
    1013         328 :             for (l=1; l<lr2; l++)
    1014             :             {
    1015         164 :               u = real_i(gel(r2,l));
    1016         164 :               if (is_complex(gel(r2,l), bitprec) || signe(u) <= 0
    1017         164 :                || !is_zero(gsubst(p8,vx,u), bitprec)
    1018         164 :                || !is_zero(gsubst(p9,vx,u), bitprec)) continue;
    1019             : 
    1020         164 :               M0_pro =              mulur(n1, sqrr(logr_abs(u)));
    1021         164 :               M0_pro = gadd(M0_pro, mulur(n2, sqrr(logr_abs(v))));
    1022         164 :               M0_pro = gadd(M0_pro, mulur(n3, sqrr(logr_abs(w))));
    1023         164 :               M0_pro = gmul2n(M0_pro,-2);
    1024         164 :               if (DEBUGLEVEL>2)
    1025           0 :                 err_printf("[ %ld, %ld, %ld ]: %.28Pg\n",n1,n2,n3,M0_pro);
    1026         164 :               if (!M0 || gcmp(M0_pro,M0) < 0) M0 = M0_pro;
    1027             :             }
    1028             :           }
    1029             :         }
    1030             :       }
    1031          77 :       if (!M0) set_avma(av); else M0 = gerepilecopy(av, M0);
    1032             :     }
    1033             :   }
    1034         105 :   for (i=1;i<=4;i++) (void)delete_var();
    1035          21 :   return M0? M0: gen_0;
    1036             : }
    1037             : 
    1038             : static GEN
    1039          63 : lowerboundforregulator(GEN bnf, GEN units)
    1040             : {
    1041          63 :   long i, N, R2, RU = lg(units)-1;
    1042             :   GEN nf, M0, M, G, minunit;
    1043             :   double bound;
    1044             : 
    1045          63 :   if (!RU) return gen_1;
    1046          63 :   nf = bnf_get_nf(bnf);
    1047          63 :   N = nf_get_degree(nf);
    1048          63 :   R2 = nf_get_r2(nf);
    1049             : 
    1050          63 :   G = nf_get_G(nf);
    1051          63 :   minunit = gnorml2(RgM_RgC_mul(G, gel(units,1))); /* T2(units[1]) */
    1052         112 :   for (i=2; i<=RU; i++)
    1053             :   {
    1054          49 :     GEN t = gnorml2(RgM_RgC_mul(G, gel(units,i)));
    1055          49 :     if (gcmp(t,minunit) < 0) minunit = t;
    1056             :   }
    1057          63 :   if (gexpo(minunit) > 30) return NULL;
    1058             : 
    1059          42 :   bound = minimforunits(nf, itos(gceil(minunit)), bnf_get_tuN(bnf));
    1060          42 :   if (bound < 0) return NULL;
    1061          28 :   if (DEBUGLEVEL>1) err_printf("M* = %Ps\n", dbltor(bound));
    1062          28 :   M0 = compute_M0(dbltor(bound), N);
    1063          28 :   if (DEBUGLEVEL>1) err_printf("M0 = %.28Pg\n",M0);
    1064          28 :   M = gmul2n(divru(gdiv(powrs(M0,RU),Hermite_bound(RU, DEFAULTPREC)),N),R2);
    1065          28 :   if (cmprr(M, dbltor(0.04)) < 0) return NULL;
    1066          28 :   M = sqrtr(M);
    1067          28 :   if (DEBUGLEVEL>1)
    1068           0 :     err_printf("(lower bound for regulator) M = %.28Pg\n",M);
    1069          28 :   return M;
    1070             : }
    1071             : 
    1072             : /* upper bound for the index of bnf.fu in the full unit group */
    1073             : static GEN
    1074          63 : bound_unit_index(GEN bnf, GEN units)
    1075             : {
    1076          63 :   pari_sp av = avma;
    1077          63 :   GEN x = lowerboundforregulator(bnf, units);
    1078          63 :   if (!x) { set_avma(av); x = regulatorbound(bnf); }
    1079          63 :   return gerepileuptoint(av, ground(gdiv(bnf_get_reg(bnf), x)));
    1080             : }
    1081             : 
    1082             : /* Compute a square matrix of rank #beta attached to a family
    1083             :  * (P_i), 1<=i<=#beta, of primes s.t. N(P_i) = 1 mod p, and
    1084             :  * (P_i,beta[j]) = 1 for all i,j. nf = true nf */
    1085             : static void
    1086        1715 : primecertify(GEN nf, GEN beta, ulong p, GEN bad)
    1087             : {
    1088        1715 :   long lb = lg(beta), rmax = lb - 1;
    1089             :   GEN M, vQ, L;
    1090             :   ulong q;
    1091             :   forprime_t T;
    1092             : 
    1093        1715 :   if (p == 2)
    1094          49 :     L = cgetg(1,t_VECSMALL);
    1095             :   else
    1096        1666 :     L = mkvecsmall(p);
    1097        1715 :   (void)u_forprime_arith_init(&T, 1, ULONG_MAX, 1, p);
    1098        1715 :   M = cgetg(lb,t_MAT); setlg(M,1);
    1099        3647 :   while ((q = u_forprime_next(&T)))
    1100             :   {
    1101             :     GEN qq, gg, og;
    1102             :     long lQ, i, j;
    1103             :     ulong g, m;
    1104        3647 :     if (!umodiu(bad,q)) continue;
    1105             : 
    1106        3283 :     qq = utoipos(q);
    1107        3283 :     vQ = idealprimedec_limit_f(nf,qq,1);
    1108        3283 :     lQ = lg(vQ); if (lQ == 1) continue;
    1109             : 
    1110             :     /* cf rootsof1_Fl */
    1111        2128 :     g = pgener_Fl_local(q, L);
    1112        2128 :     m = (q-1) / p;
    1113        2128 :     gg = utoipos( Fl_powu(g, m, q) ); /* order p in (Z/q)^* */
    1114        2128 :     og = mkmat2(mkcol(utoi(p)), mkcol(gen_1)); /* order of g */
    1115             : 
    1116        2128 :     if (DEBUGLEVEL>3) err_printf("       generator of (Zk/Q)^*: %lu\n", g);
    1117        2821 :     for (i = 1; i < lQ; i++)
    1118             :     {
    1119        2408 :       GEN C = cgetg(lb, t_VECSMALL);
    1120        2408 :       GEN Q = gel(vQ,i); /* degree 1 */
    1121        2408 :       GEN modpr = zkmodprinit(nf, Q);
    1122             :       long r;
    1123             : 
    1124        7028 :       for (j = 1; j < lb; j++)
    1125             :       {
    1126        4620 :         GEN t = nf_to_Fp_coprime(nf, gel(beta,j), modpr);
    1127        4620 :         t = utoipos( Fl_powu(t[2], m, q) );
    1128        4620 :         C[j] = itou( Fp_log(t, gg, og, qq) ) % p;
    1129             :       }
    1130        2408 :       r = lg(M);
    1131        2408 :       gel(M,r) = C; setlg(M, r+1);
    1132        2408 :       if (Flm_rank(M, p) != r) { setlg(M,r); continue; }
    1133             : 
    1134        2191 :       if (DEBUGLEVEL>2)
    1135             :       {
    1136           0 :         if (DEBUGLEVEL>3)
    1137             :         {
    1138           0 :           err_printf("       prime ideal Q: %Ps\n",Q);
    1139           0 :           err_printf("       matrix log(b_j mod Q_i): %Ps\n", M);
    1140             :         }
    1141           0 :         err_printf("       new rank: %ld\n",r);
    1142             :       }
    1143        2191 :       if (r == rmax) return;
    1144             :     }
    1145             :   }
    1146           0 :   pari_err_BUG("primecertify");
    1147             : }
    1148             : 
    1149             : struct check_pr {
    1150             :   long w; /* #mu(K) */
    1151             :   GEN mu; /* generator of mu(K) */
    1152             :   GEN fu;
    1153             :   GEN cyc;
    1154             :   GEN cycgen;
    1155             :   GEN bad; /* p | bad <--> p | some element occurring in cycgen */
    1156             : };
    1157             : 
    1158             : static void
    1159        1715 : check_prime(ulong p, GEN nf, struct check_pr *S)
    1160             : {
    1161        1715 :   pari_sp av = avma;
    1162        1715 :   long i,b, lc = lg(S->cyc), lf = lg(S->fu);
    1163        1715 :   GEN beta = cgetg(lf+lc, t_VEC);
    1164             : 
    1165        1715 :   if (DEBUGLEVEL>1) err_printf("  *** testing p = %lu\n",p);
    1166        1785 :   for (b=1; b<lc; b++)
    1167             :   {
    1168        1484 :     if (umodiu(gel(S->cyc,b), p)) break; /* p \nmid cyc[b] */
    1169          70 :     if (b==1 && DEBUGLEVEL>2) err_printf("     p divides h(K)\n");
    1170          70 :     gel(beta,b) = gel(S->cycgen,b);
    1171             :   }
    1172        1715 :   if (S->w % p == 0)
    1173             :   {
    1174          49 :     if (DEBUGLEVEL>2) err_printf("     p divides w(K)\n");
    1175          49 :     gel(beta,b++) = S->mu;
    1176             :   }
    1177        3787 :   for (i=1; i<lf; i++) gel(beta,b++) = gel(S->fu,i);
    1178        1715 :   setlg(beta, b); /* beta = [cycgen[i] if p|cyc[i], tu if p|w, fu] */
    1179        1715 :   if (DEBUGLEVEL>3) err_printf("     Beta list = %Ps\n",beta);
    1180        1715 :   primecertify(nf, beta, p, S->bad); set_avma(av);
    1181        1715 : }
    1182             : 
    1183             : static void
    1184          63 : init_bad(struct check_pr *S, GEN nf, GEN gen)
    1185             : {
    1186          63 :   long i, l = lg(gen);
    1187          63 :   GEN bad = gen_1;
    1188             : 
    1189         126 :   for (i=1; i < l; i++)
    1190          63 :     bad = lcmii(bad, gcoeff(gel(gen,i),1,1));
    1191         126 :   for (i = 1; i < l; i++)
    1192             :   {
    1193          63 :     GEN c = gel(S->cycgen,i);
    1194             :     long j;
    1195          63 :     if (typ(c) == t_MAT)
    1196             :     {
    1197          63 :       GEN g = gel(c,1);
    1198         455 :       for (j = 1; j < lg(g); j++)
    1199             :       {
    1200         392 :         GEN h = idealhnf_shallow(nf, gel(g,j));
    1201         392 :         bad = lcmii(bad, gcoeff(h,1,1));
    1202             :       }
    1203             :     }
    1204             :   }
    1205          63 :   S->bad = bad;
    1206          63 : }
    1207             : 
    1208             : long
    1209          63 : bnfcertify0(GEN bnf, long flag)
    1210             : {
    1211          63 :   pari_sp av = avma;
    1212             :   long N;
    1213             :   GEN nf, cyc, B, U;
    1214             :   ulong bound, p;
    1215             :   struct check_pr S;
    1216             :   forprime_t T;
    1217             : 
    1218          63 :   bnf = checkbnf(bnf);
    1219          63 :   nf = bnf_get_nf(bnf);
    1220          63 :   N = nf_get_degree(nf); if (N==1) return 1;
    1221          63 :   B = zimmertbound(nf_get_disc(nf), N, nf_get_r2(nf));
    1222          63 :   if (is_bigint(B))
    1223           0 :     pari_warn(warner,"Zimmert's bound is large (%Ps), certification will take a long time", B);
    1224          63 :   if (!is_pm1(nf_get_index(nf)))
    1225             :   {
    1226          42 :     GEN D = nf_get_diff(nf), L;
    1227          42 :     if (DEBUGLEVEL>1) err_printf("**** Testing Different = %Ps\n",D);
    1228          42 :     L = bnfisprincipal0(bnf, D, nf_FORCE);
    1229          42 :     if (DEBUGLEVEL>1) err_printf("     is %Ps\n", L);
    1230             :   }
    1231          63 :   if (DEBUGLEVEL)
    1232             :   {
    1233           0 :     err_printf("PHASE 1 [CLASS GROUP]: are all primes good ?\n");
    1234           0 :     err_printf("  Testing primes <= %Ps\n", B);
    1235             :   }
    1236          63 :   bnftestprimes(bnf, B);
    1237          63 :   if (flag) return 1;
    1238             : 
    1239          63 :   U = bnf_build_units(bnf);
    1240          63 :   cyc = bnf_get_cyc(bnf);
    1241          63 :   S.w = bnf_get_tuN(bnf);
    1242          63 :   S.mu = gel(U,1);
    1243          63 :   S.fu = vecslice(U,2,lg(U)-1);
    1244          63 :   S.cyc = cyc;
    1245          63 :   S.cycgen = bnf_build_cycgen(bnf);
    1246          63 :   init_bad(&S, nf, bnf_get_gen(bnf));
    1247             : 
    1248          63 :   B = bound_unit_index(bnf, S.fu);
    1249          63 :   if (DEBUGLEVEL)
    1250             :   {
    1251           0 :     err_printf("PHASE 2 [UNITS/RELATIONS]: are all primes good ?\n");
    1252           0 :     err_printf("  Testing primes <= %Ps\n", B);
    1253             :   }
    1254          63 :   bound = itou_or_0(B);
    1255          63 :   if (!bound) pari_err_OVERFLOW("bnfcertify [too many primes to check]");
    1256          63 :   if (u_forprime_init(&T, 2, bound))
    1257        1757 :     while ( (p = u_forprime_next(&T)) ) check_prime(p, nf, &S);
    1258          63 :   if (lg(cyc) > 1)
    1259             :   {
    1260          28 :     GEN f = Z_factor(cyc_get_expo(cyc)), P = gel(f,1);
    1261             :     long i;
    1262          28 :     if (DEBUGLEVEL>1) err_printf("  Primes dividing h(K)\n\n");
    1263          35 :     for (i = lg(P)-1; i; i--)
    1264             :     {
    1265          28 :       p = itou(gel(P,i)); if (p <= bound) break;
    1266           7 :       check_prime(p, nf, &S);
    1267             :     }
    1268             :   }
    1269          63 :   return gc_long(av,1);
    1270             : }
    1271             : long
    1272          35 : bnfcertify(GEN bnf) { return bnfcertify0(bnf, 0); }
    1273             : 
    1274             : /*******************************************************************/
    1275             : /*                                                                 */
    1276             : /*        RAY CLASS FIELDS: CONDUCTORS AND DISCRIMINANTS           */
    1277             : /*                                                                 */
    1278             : /*******************************************************************/
    1279             : /* \chi(gen[i]) = zeta_D^chic[i])
    1280             :  * denormalize: express chi(gen[i]) in terms of zeta_{cyc[i]} */
    1281             : GEN
    1282      202587 : char_denormalize(GEN cyc, GEN D, GEN chic)
    1283             : {
    1284      202587 :   long i, l = lg(chic);
    1285      202587 :   GEN chi = cgetg(l, t_VEC);
    1286             :   /* \chi(gen[i]) = e(chic[i] / D) = e(chi[i] / cyc[i])
    1287             :    * hence chi[i] = chic[i]cyc[i]/ D  mod cyc[i] */
    1288      800303 :   for (i = 1; i < l; ++i)
    1289             :   {
    1290      597716 :     GEN di = gel(cyc, i), t = diviiexact(mulii(di, gel(chic,i)), D);
    1291      597716 :     gel(chi, i) = modii(t, di);
    1292             :   }
    1293      202587 :   return chi;
    1294             : }
    1295             : static GEN
    1296         595 : bnrchar_i(GEN bnr, GEN g, GEN v)
    1297             : {
    1298         595 :   long i, h, l = lg(g), t = typ_NULL;
    1299         595 :   GEN CH, D, U, U2, H, cycD, dv, dchi, cyc = NULL;
    1300             : 
    1301         595 :   if (checkbnr_i(bnr)) { t = typ_BNR; cyc = bnr_get_cyc(bnr); }
    1302          14 :   else if (checkznstar_i(bnr)) { t = typ_BIDZ; cyc = znstar_get_cyc(bnr); }
    1303           0 :   else if (typ(bnr) == t_VEC && RgV_is_ZV(bnr)) cyc = bnr;
    1304           0 :   else pari_err_TYPE("bnrchar", bnr);
    1305         595 :   switch(typ(g))
    1306             :   {
    1307             :     GEN G;
    1308          28 :     case t_VEC:
    1309          28 :       G = cgetg(l, t_MAT);
    1310          28 :       if (t == typ_BNR)
    1311             :       {
    1312          49 :         for (i = 1; i < l; i++) gel(G,i) = isprincipalray(bnr, gel(g,i));
    1313          14 :         cyc = bnr_get_cyc(bnr);
    1314             :       }
    1315             :       else
    1316          35 :         for (i = 1; i < l; i++) gel(G,i) = Zideallog(bnr, gel(g,i));
    1317          28 :       g = G; break;
    1318         567 :     case t_MAT:
    1319         567 :       if (RgM_is_ZM(g)) break;
    1320             :     default:
    1321           0 :       pari_err_TYPE("bnrchar",g);
    1322             :   }
    1323         595 :   H = ZM_hnfall_i(shallowconcat(g,diagonal_shallow(cyc)), v? &U: NULL, 1);
    1324         595 :   dv = NULL;
    1325         595 :   if (v)
    1326             :   {
    1327          42 :     GEN w = Q_remove_denom(v, &dv);
    1328          42 :     if (typ(v)!=t_VEC || lg(v)!=l || !RgV_is_ZV(w)) pari_err_TYPE("bnrchar",v);
    1329          42 :     if (!dv) v = NULL;
    1330             :     else
    1331             :     {
    1332          42 :       U = rowslice(U, 1, l-1);
    1333          42 :       w = FpV_red(ZV_ZM_mul(w, U), dv);
    1334         140 :       for (i = 1; i < l; i++)
    1335         105 :         if (signe(gel(w,i))) pari_err_TYPE("bnrchar [inconsistent values]",v);
    1336          35 :       v = vecslice(w,l,lg(w)-1);
    1337             :     }
    1338             :   }
    1339             :   /* chi defined on subgroup H, chi(H[i]) = e(v[i] / dv)
    1340             :    * unless v = NULL: chi|H = 1*/
    1341         588 :   h = itos( ZM_det_triangular(H) ); /* #(clgp/H) = number of chars */
    1342         588 :   if (h == 1) /* unique character, H = Id */
    1343             :   {
    1344          14 :     if (v)
    1345          14 :       v = char_denormalize(cyc,dv,v);
    1346             :     else
    1347           0 :       v = zerovec(lg(cyc)-1); /* trivial char */
    1348          14 :     return mkvec(v);
    1349             :   }
    1350             : 
    1351             :   /* chi defined on a subgroup of index h > 1; U H V = D diagonal,
    1352             :    * Z^#H / (H) = Z^#H / (D) ~ \oplus (Z/diZ) */
    1353         574 :   D = ZM_snfall_i(H, &U, NULL, 1);
    1354         574 :   cycD = cyc_normalize(D); gel(cycD,1) = gen_1; /* cycD[i] = d1/di */
    1355         574 :   dchi = gel(D,1);
    1356         574 :   U2 = ZM_diag_mul(cycD, U);
    1357         574 :   if (v)
    1358             :   {
    1359          21 :     GEN Ui = ZM_inv(U, NULL);
    1360          21 :     GEN Z = hnf_solve(H, ZM_mul_diag(Ui, D));
    1361          21 :     v = ZV_ZM_mul(ZV_ZM_mul(v, Z), U2);
    1362          21 :     dchi = mulii(dchi, dv);
    1363          21 :     U2 = ZM_Z_mul(U2, dv);
    1364             :   }
    1365         574 :   CH = cyc2elts(D);
    1366        2310 :   for (i = 1; i <= h; i++)
    1367             :   {
    1368        1736 :     GEN c = zv_ZM_mul(gel(CH,i), U2);
    1369        1736 :     if (v) c = ZC_add(c, v);
    1370        1736 :     gel(CH,i) = char_denormalize(cyc, dchi, c);
    1371             :   }
    1372         574 :   return CH;
    1373             : }
    1374             : GEN
    1375         595 : bnrchar(GEN bnr, GEN g, GEN v)
    1376             : {
    1377         595 :   pari_sp av = avma;
    1378         595 :   return gerepilecopy(av, bnrchar_i(bnr,g,v));
    1379             : }
    1380             : 
    1381             : /* Let bnr1, bnr2 be such that mod(bnr2) | mod(bnr1), compute surjective map
    1382             :  *   p: Cl(bnr1) ->> Cl(bnr2).
    1383             :  * Write (bnr gens) for the concatenation of the bnf [corrected by El] and bid
    1384             :  * generators; and bnr.gen for the SNF generators. Then
    1385             :  *   bnr.gen = (bnf.gen*bnr.El | bid.gen) bnr.Ui
    1386             :  *  (bnf.gen*bnr.El | bid.gen) = bnr.gen * bnr.U */
    1387             : GEN
    1388        2709 : bnrsurjection(GEN bnr1, GEN bnr2)
    1389             : {
    1390        2709 :   GEN bnf = bnr_get_bnf(bnr2), nf = bnf_get_nf(bnf);
    1391        2709 :   GEN M, U = bnr_get_U(bnr2), bid2 = bnr_get_bid(bnr2);
    1392        2709 :   GEN gen1 = bid_get_gen(bnr_get_bid(bnr1));
    1393        2709 :   GEN cyc2 = bnr_get_cyc(bnr2), e2 = cyc_get_expo(cyc2);
    1394        2709 :   long i, l = lg(bnf_get_cyc(bnf)), lb = lg(gen1);
    1395             :   /* p(bnr1.gen) = p(bnr1 gens) * bnr1.Ui
    1396             :    *             = (bnr2 gens) * P * bnr1.Ui
    1397             :    *             = bnr2.gen * (bnr2.U * P * bnr1.Ui) */
    1398             : 
    1399             :   /* p(bid1.gen) on bid2.gen */
    1400        2709 :   M = cgetg(lb, t_MAT);
    1401       11816 :   for (i = 1; i < lb; i++) gel(M,i) = ideallogmod(nf, gel(gen1,i), bid2, e2);
    1402             :   /* [U[1], U[2]] * [Id, 0; N, M] = [U[1] + U[2]*N, U[2]*M] */
    1403        2709 :   M = ZM_mul(gel(U,2), M);
    1404        2709 :   if (l > 1)
    1405             :   { /* non trivial class group */
    1406             :     /* p(bnf.gen * bnr1.El) in terms of bnf.gen * bnr2.El and bid2.gen */
    1407         882 :     GEN El2 = bnr_get_El(bnr2), El1 = bnr_get_El(bnr1);
    1408         882 :     long ngen2 = lg(bid_get_gen(bid2))-1;
    1409         882 :     if (!ngen2)
    1410         595 :       M = gel(U,1);
    1411             :     else
    1412             :     {
    1413         287 :       GEN U1 = gel(U,1), U2 = gel(U,2), T = cgetg(l, t_MAT);
    1414             :       /* T = U1 + U2 log(El2/El1) */
    1415         595 :       for (i = 1; i < l; i++)
    1416             :       { /* bnf gen in bnr1 is bnf.gen * El1 = bnf gen in bnr 2 * El1/El2 */
    1417         308 :         GEN c = gel(U1,i);
    1418         308 :         if (typ(gel(El1,i)) != t_INT) /* else El1[i] = 1 => El2[i] = 1 */
    1419             :         {
    1420         119 :           GEN z = nfdiv(nf,gel(El1,i),gel(El2,i));
    1421         119 :           c = ZC_add(c, ZM_ZC_mul(U2, ideallogmod(nf, z, bid2, e2)));
    1422             :         }
    1423         308 :         gel(T,i) = c;
    1424             :       }
    1425         287 :       M = shallowconcat(T, M);
    1426             :     }
    1427             :   }
    1428        2709 :   M = ZM_ZV_mod(ZM_mul(M, bnr_get_Ui(bnr1)), cyc2);
    1429        2709 :   return mkvec3(M, bnr_get_cyc(bnr1), cyc2);
    1430             : }
    1431             : 
    1432             : /* nchi a normalized character, S a surjective map ; return S(nchi)
    1433             :  * still normalized wrt the original cyclic structure (S[2]) */
    1434             : static GEN
    1435         903 : abmap_nchar_image(GEN S, GEN nchi)
    1436             : {
    1437         903 :   GEN U, M = gel(S,1), Mc = diagonal_shallow(gel(S,3));
    1438         903 :   long l = lg(M);
    1439             : 
    1440         903 :   (void)ZM_hnfall_i(shallowconcat(M, Mc), &U, 1); /* identity */
    1441         903 :   U = matslice(U,1,l-1, l,lg(U)-1);
    1442         903 :   return char_simplify(gel(nchi,1), ZV_ZM_mul(gel(nchi,2), U));
    1443             : }
    1444             : static GEN
    1445         686 : abmap_char_image(GEN S, GEN chi)
    1446             : {
    1447         686 :   GEN nchi = char_normalize(chi, cyc_normalize(gel(S,2)));
    1448         686 :   GEN DC = abmap_nchar_image(S, nchi);
    1449         686 :   return char_denormalize(gel(S,3), gel(DC,1), gel(DC,2));
    1450             : }
    1451             : 
    1452             : GEN
    1453         616 : bnrmap(GEN A, GEN B)
    1454             : {
    1455         616 :   pari_sp av = avma;
    1456             :   GEN KA, KB, M, c, C;
    1457         616 :   if ((KA = checkbnf_i(A)))
    1458             :   {
    1459         168 :     checkbnr(A); checkbnr(B); KB = bnr_get_bnf(B);
    1460         168 :     if (!gidentical(KA, KB))
    1461           0 :       pari_err_TYPE("bnrmap [different fields]", mkvec2(KA,KB));
    1462         168 :     return gerepilecopy(av, bnrsurjection(A,B));
    1463             :   }
    1464         448 :   if (lg(A) != 4 || typ(A) != t_VEC) pari_err_TYPE("bnrmap [not a map]", A);
    1465         441 :   M = gel(A,1); c = gel(A,2); C = gel(A,3);
    1466         441 :   if (typ(M) != t_MAT || !RgM_is_ZM(M) || typ(c) != t_VEC ||
    1467         441 :       typ(C) != t_VEC || lg(c) != lg(M) || (lg(M) > 1 && lgcols(M) != lg(C)))
    1468           0 :         pari_err_TYPE("bnrmap [not a map]", A);
    1469         441 :   switch(typ(B))
    1470             :   {
    1471           7 :     case t_INT: /* subgroup */
    1472           7 :       B = scalarmat_shallow(B, lg(C)-1);
    1473           7 :       B = ZM_hnfmodid(B, C); break;
    1474         392 :     case t_MAT: /* subgroup */
    1475         392 :       if (!RgM_is_ZM(B)) pari_err_TYPE("bnrmap [not a subgroup]", B);
    1476         385 :       B = ZM_hnfmodid(B, c); B = abmap_subgroup_image(A, B); break;
    1477          21 :     case t_VEC: /* character */
    1478          21 :       if (!char_check(c, B))
    1479          14 :         pari_err_TYPE("bnrmap [not a character mod mA]", B);
    1480           7 :       B = abmap_char_image(A, B); break;
    1481          21 :     case t_COL: /* discrete log mod mA */
    1482          21 :       if (lg(B) != lg(c) || !RgV_is_ZV(B))
    1483          14 :         pari_err_TYPE("bnrmap [not a discrete log]", B);
    1484           7 :       B = ZV_ZV_mod(ZM_ZC_mul(M, B), C);
    1485           7 :       return gerepileupto(av, B);
    1486             :   }
    1487         392 :   return gerepilecopy(av, B);
    1488             : }
    1489             : 
    1490             : /* Given normalized chi on bnr.clgp of conductor bnrc.mod,
    1491             :  * compute primitive character chic on bnrc.clgp equivalent to chi,
    1492             :  * still normalized wrt. bnr:
    1493             :  *   chic(genc[i]) = zeta_C^chic[i]), C = cyc_normalize(bnr.cyc)[1] */
    1494             : GEN
    1495         217 : bnrchar_primitive(GEN bnr, GEN nchi, GEN bnrc)
    1496         217 : { return abmap_nchar_image(bnrsurjection(bnr, bnrc), nchi); }
    1497             : 
    1498             : /* s: <gen> = Cl_f -> Cl_f2 -> 0, H subgroup of Cl_f (generators given as
    1499             :  * HNF on [gen]). Return subgroup s(H) in Cl_f2 */
    1500             : static GEN
    1501        1960 : imageofgroup(GEN bnr, GEN bnr2, GEN H)
    1502             : {
    1503        1960 :   if (!H) return diagonal_shallow(bnr_get_cyc(bnr2));
    1504        1078 :   return abmap_subgroup_image(bnrsurjection(bnr, bnr2), H);
    1505             : }
    1506             : GEN
    1507         679 : bnrchar_primitive_raw(GEN bnr, GEN bnrc, GEN chi)
    1508         679 : { return abmap_char_image(bnrsurjection(bnr, bnrc), chi); }
    1509             : 
    1510             : /* convert A,B,C to [bnr, H] */
    1511             : GEN
    1512         273 : ABC_to_bnr(GEN A, GEN B, GEN C, GEN *H, int gen)
    1513             : {
    1514         273 :   if (typ(A) == t_VEC)
    1515         273 :     switch(lg(A))
    1516             :     {
    1517         119 :       case 7: /* bnr */
    1518         119 :         *H = B; return A;
    1519         154 :       case 11: /* bnf */
    1520         154 :         if (!B) pari_err_TYPE("ABC_to_bnr [bnf+missing conductor]",A);
    1521         154 :         *H = C; return Buchray(A,B, gen? nf_INIT | nf_GEN: nf_INIT);
    1522             :     }
    1523           0 :   pari_err_TYPE("ABC_to_bnr",A);
    1524             :   *H = NULL; return NULL; /* LCOV_EXCL_LINE */
    1525             : }
    1526             : 
    1527             : /* OBSOLETE */
    1528             : GEN
    1529          63 : bnrconductor0(GEN A, GEN B, GEN C, long flag)
    1530             : {
    1531          63 :   pari_sp av = avma;
    1532          63 :   GEN H, bnr = ABC_to_bnr(A,B,C,&H, 0);
    1533          63 :   return gerepilecopy(av, bnrconductor(bnr, H, flag));
    1534             : }
    1535             : 
    1536             : long
    1537          35 : bnrisconductor0(GEN A,GEN B,GEN C)
    1538             : {
    1539          35 :   GEN H, bnr = ABC_to_bnr(A,B,C,&H, 0);
    1540          35 :   return bnrisconductor(bnr, H);
    1541             : }
    1542             : 
    1543             : static GEN
    1544      515878 : ideallog_to_bnr_i(GEN Ubid, GEN cyc, GEN z)
    1545      515878 : { return (lg(Ubid)==1)? zerocol(lg(cyc)-1): ZV_ZV_mod(ZM_ZC_mul(Ubid,z), cyc); }
    1546             : /* return bnrisprincipal(bnr, (x)), assuming z = ideallog(x); allow a
    1547             :  * t_MAT for z, understood as a collection of ideallog(x_i) */
    1548             : static GEN
    1549      499540 : ideallog_to_bnr(GEN bnr, GEN z)
    1550             : {
    1551      499540 :   GEN U = gel(bnr_get_U(bnr), 2); /* bid part */
    1552      499538 :   GEN y, cyc = bnr_get_cyc(bnr);
    1553             :   long i, l;
    1554      499545 :   if (typ(z) == t_COL) return ideallog_to_bnr_i(U, cyc, z);
    1555      413441 :   y = cgetg_copy(z, &l);
    1556      843156 :   for (i = 1; i < l; i++) gel(y,i) = ideallog_to_bnr_i(U, cyc, gel(z,i));
    1557      413374 :   return y;
    1558             : }
    1559             : static GEN
    1560      413436 : bnr_log_gen_pr(GEN bnr, zlog_S *S, long e, long index)
    1561      413436 : { return ideallog_to_bnr(bnr, log_gen_pr(S, index, bnr_get_nf(bnr), e)); }
    1562             : static GEN
    1563       86103 : bnr_log_gen_arch(GEN bnr, zlog_S *S, long index)
    1564       86103 : { return ideallog_to_bnr(bnr, log_gen_arch(S, index)); }
    1565             : 
    1566             : /* A \subset H ? Allow H = NULL = trivial subgroup */
    1567             : static int
    1568      402255 : contains(GEN H, GEN A)
    1569      402255 : { return H? (hnf_solve(H, A) != NULL): gequal0(A); }
    1570             : 
    1571             : /* finite part of the conductor of H is S.P^e2*/
    1572             : static GEN
    1573       47067 : cond0_e(GEN bnr, GEN H, zlog_S *S)
    1574             : {
    1575       47067 :   long j, k, l = lg(S->k), iscond0 = S->no2;
    1576       47067 :   GEN e = S->k, e2 = cgetg(l, t_COL);
    1577      121364 :   for (k = 1; k < l; k++)
    1578             :   {
    1579       81276 :     for (j = itos(gel(e,k)); j > 0; j--)
    1580             :     {
    1581       77272 :       if (!contains(H, bnr_log_gen_pr(bnr, S, j, k))) break;
    1582        6979 :       iscond0 = 0;
    1583             :     }
    1584       74293 :     gel(e2,k) = utoi(j);
    1585             :   }
    1586       47067 :   return iscond0? NULL: e2;
    1587             : }
    1588             : /* infinite part of the conductor of H in archp form */
    1589             : static GEN
    1590       47068 : condoo_archp(GEN bnr, GEN H, zlog_S *S)
    1591             : {
    1592       47068 :   GEN archp = S->archp, archp2 = leafcopy(archp);
    1593       47068 :   long j, k, l = lg(archp);
    1594       65317 :   for (k = j = 1; k < l; k++)
    1595             :   {
    1596       18249 :     if (!contains(H, bnr_log_gen_arch(bnr, S, k)))
    1597             :     {
    1598       14574 :       archp2[j++] = archp[k];
    1599       14574 :       continue;
    1600             :     }
    1601             :   }
    1602       47068 :   if (j == l) return S->archp;
    1603        2744 :   setlg(archp2, j); return archp2;
    1604             : }
    1605             : /* MOD useless in this function */
    1606             : static GEN
    1607        5236 : bnrconductor_factored_i(GEN bnr, GEN H, long raw)
    1608             : {
    1609        5236 :   GEN nf, bid, ideal, arch, archp, e, fa, cond = NULL;
    1610             :   zlog_S S;
    1611             : 
    1612        5236 :   checkbnr(bnr);
    1613        5236 :   bid = bnr_get_bid(bnr); init_zlog(&S, bid);
    1614        5236 :   nf = bnr_get_nf(bnr);
    1615        5236 :   H = bnr_subgroup_check(bnr, H, NULL);
    1616        5236 :   e = cond0_e(bnr, H, &S); /* in terms of S.P */
    1617        5236 :   archp = condoo_archp(bnr, H, &S);
    1618        5236 :   ideal = e? factorbackprime(nf, S.P, e): bid_get_ideal(bid);
    1619        5236 :   if (archp == S.archp)
    1620             :   {
    1621        3423 :     if (!e) cond = bnr_get_mod(bnr);
    1622        3423 :     arch = bid_get_arch(bid);
    1623             :   }
    1624             :   else
    1625        1813 :     arch = indices_to_vec01(archp, nf_get_r1(nf));
    1626        5236 :   if (!cond) cond = mkvec2(ideal, arch);
    1627        5236 :   if (raw) return cond;
    1628         616 :   fa = e? famat_remove_trivial(mkmat2(S.P, e)): bid_get_fact(bid);
    1629         616 :   return mkvec2(cond, fa);
    1630             : }
    1631             : GEN
    1632         616 : bnrconductor_factored(GEN bnr, GEN H)
    1633         616 : { return bnrconductor_factored_i(bnr, H, 0); }
    1634             : GEN
    1635        4620 : bnrconductor_raw(GEN bnr, GEN H)
    1636        4620 : { return bnrconductor_factored_i(bnr, H, 1); }
    1637             : 
    1638             : /* (see bnrdisc_i). Given a bnr, and a subgroup
    1639             :  * H0 (possibly given as a character chi, in which case H0 = ker chi) of the
    1640             :  * ray class group, compute the conductor of H if flag=0. If flag > 0, compute
    1641             :  * also the corresponding H' and output
    1642             :  * if flag = 1: [[ideal,arch],[hm,cyc,gen],H']
    1643             :  * if flag = 2: [[ideal,arch],newbnr,H'] */
    1644             : GEN
    1645       41832 : bnrconductormod(GEN bnr, GEN H0, GEN MOD)
    1646             : {
    1647       41832 :   GEN nf, bid, arch, archp, bnrc, e, H, cond = NULL;
    1648             :   int ischi;
    1649             :   zlog_S S;
    1650             : 
    1651       41832 :   checkbnr(bnr);
    1652       41832 :   bid = bnr_get_bid(bnr); init_zlog(&S, bid);
    1653       41832 :   nf = bnr_get_nf(bnr);
    1654       41832 :   H = bnr_subgroup_check(bnr, H0, NULL);
    1655       41831 :   e = cond0_e(bnr, H, &S);
    1656       41832 :   archp = condoo_archp(bnr, H, &S);
    1657       41832 :   if (archp == S.archp)
    1658             :   {
    1659       40901 :     if (!e) cond = bnr_get_mod(bnr);
    1660       40901 :     arch = gel(bnr_get_mod(bnr), 2);
    1661             :   }
    1662             :   else
    1663         931 :     arch = indices_to_vec01(archp, nf_get_r1(nf));
    1664             : 
    1665             :   /* character or subgroup ? */
    1666       41832 :   ischi = H0 && typ(H0) == t_VEC;
    1667       41832 :   if (cond)
    1668             :   { /* same conductor */
    1669       39214 :     bnrc = bnr;
    1670       39214 :     if (ischi)
    1671         728 :       H = H0;
    1672       38486 :     else if (!H)
    1673       26887 :       H = diagonal_shallow(bnr_get_cyc(bnr));
    1674             :   }
    1675             :   else
    1676             :   {
    1677        2618 :     long fl = lg(bnr_get_clgp(bnr)) == 4? nf_INIT | nf_GEN: nf_INIT;
    1678        2618 :     GEN fa = famat_remove_trivial(mkmat2(S.P, e? e: S.k)), bid;
    1679        2618 :     bid = Idealstarmod(nf, mkvec2(fa, arch), nf_INIT | nf_GEN, MOD);
    1680        2618 :     bnrc = Buchraymod_i(bnr, bid, fl, MOD);
    1681        2618 :     cond = bnr_get_mod(bnrc);
    1682        2618 :     if (ischi)
    1683         658 :       H = bnrchar_primitive_raw(bnr, bnrc, H0);
    1684             :     else
    1685        1960 :       H = imageofgroup(bnr, bnrc, H);
    1686             :   }
    1687       41832 :   return mkvec3(cond, bnrc, H);
    1688             : }
    1689             : /* OBSOLETE */
    1690             : GEN
    1691         602 : bnrconductor_i(GEN bnr, GEN H, long flag)
    1692             : {
    1693             :   GEN v;
    1694         602 :   if (flag == 0) return bnrconductor_raw(bnr, H);
    1695           0 :   v = bnrconductormod(bnr, H, NULL);
    1696           0 :   if (flag == 1) gel(v,2) = bnr_get_clgp(gel(v,2));
    1697           0 :   return v;
    1698             : }
    1699             : /* OBSOLETE */
    1700             : GEN
    1701         602 : bnrconductor(GEN bnr, GEN H, long flag)
    1702             : {
    1703         602 :   pari_sp av = avma;
    1704         602 :   if (flag > 2 || flag < 0) pari_err_FLAG("bnrconductor");
    1705         602 :   return gerepilecopy(av, bnrconductor_i(bnr, H, flag));
    1706             : }
    1707             : 
    1708             : long
    1709      274942 : bnrisconductor(GEN bnr, GEN H0)
    1710             : {
    1711      274942 :   pari_sp av = avma;
    1712             :   long j, k, l;
    1713             :   GEN archp, e, H;
    1714             :   zlog_S S;
    1715             : 
    1716      274942 :   checkbnr(bnr);
    1717      274940 :   init_zlog(&S, bnr_get_bid(bnr));
    1718      274944 :   if (!S.no2) return 0;
    1719      231600 :   H = bnr_subgroup_check(bnr, H0, NULL);
    1720             : 
    1721      231593 :   archp = S.archp;
    1722      231593 :   e     = S.k; l = lg(e);
    1723      369030 :   for (k = 1; k < l; k++)
    1724             :   {
    1725      261565 :     j = itos(gel(e,k));
    1726      261566 :     if (contains(H, bnr_log_gen_pr(bnr, &S, j, k))) return gc_long(av,0);
    1727             :   }
    1728      107465 :   l = lg(archp);
    1729      136487 :   for (k = 1; k < l; k++)
    1730       44917 :     if (contains(H, bnr_log_gen_arch(bnr, &S, k))) return gc_long(av,0);
    1731       91570 :   return gc_long(av,1);
    1732             : }
    1733             : 
    1734             : /* return the norm group corresponding to the relative extension given by
    1735             :  * polrel over bnr.bnf, assuming it is abelian and the modulus of bnr is a
    1736             :  * multiple of the conductor */
    1737             : static GEN
    1738         805 : rnfnormgroup_i(GEN bnr, GEN polrel)
    1739             : {
    1740             :   long i, j, degrel, degnf, k;
    1741             :   GEN bnf, index, discnf, nf, G, detG, fa, gdegrel;
    1742             :   GEN fac, col, cnd;
    1743             :   forprime_t S;
    1744             :   ulong p;
    1745             : 
    1746         805 :   checkbnr(bnr); bnf = bnr_get_bnf(bnr);
    1747         805 :   nf = bnf_get_nf(bnf);
    1748         805 :   cnd = gel(bnr_get_mod(bnr), 1);
    1749         805 :   polrel = RgX_nffix("rnfnormgroup", nf_get_pol(nf),polrel,1);
    1750         805 :   if (!gequal1(leading_coeff(polrel)))
    1751           0 :     pari_err_IMPL("rnfnormgroup for nonmonic polynomials");
    1752             : 
    1753         805 :   degrel = degpol(polrel);
    1754         805 :   if (umodiu(bnr_get_no(bnr), degrel)) return NULL;
    1755             :   /* degrel-th powers are in norm group */
    1756         791 :   gdegrel = utoipos(degrel);
    1757         791 :   G = ZV_snf_gcd(bnr_get_cyc(bnr), gdegrel);
    1758         791 :   detG = ZV_prod(G);
    1759         791 :   k = abscmpiu(detG,degrel);
    1760         791 :   if (k < 0) return NULL;
    1761         791 :   if (!k) return diagonal(G);
    1762             : 
    1763         245 :   G = diagonal_shallow(G);
    1764         245 :   discnf = nf_get_disc(nf);
    1765         245 :   index  = nf_get_index(nf);
    1766         245 :   degnf = nf_get_degree(nf);
    1767         245 :   u_forprime_init(&S, 2, ULONG_MAX);
    1768        1344 :   while ( (p = u_forprime_next(&S)) )
    1769             :   {
    1770             :     long oldf, nfa;
    1771             :     /* If all pr are unramified and have the same residue degree, p =prod pr
    1772             :      * and including last pr^f or p^f is the same, but the last isprincipal
    1773             :      * is much easier! oldf is used to track this */
    1774             : 
    1775        1344 :     if (!umodiu(index, p)) continue; /* can't be treated efficiently */
    1776             : 
    1777             :     /* primes of degree 1 are enough, and simpler */
    1778        1344 :     fa = idealprimedec_limit_f(nf, utoipos(p), 1);
    1779        1344 :     nfa = lg(fa)-1;
    1780        1344 :     if (!nfa) continue;
    1781             :     /* all primes above p included ? */
    1782        1127 :     oldf = (nfa == degnf)? -1: 0;
    1783        2107 :     for (i=1; i<=nfa; i++)
    1784             :     {
    1785        1225 :       GEN pr = gel(fa,i), pp, T, polr, modpr;
    1786             :       long f, nfac;
    1787             :       /* if pr (probably) ramified, we have to use all (unramified) P | pr */
    1788        1680 :       if (idealval(nf,cnd,pr)) { oldf = 0; continue; }
    1789         910 :       modpr = zk_to_Fq_init(nf, &pr, &T, &pp); /* T = NULL, pp ignored */
    1790         910 :       polr = nfX_to_FqX(polrel, nf, modpr); /* in Fp[X] */
    1791         910 :       polr = ZX_to_Flx(polr, p);
    1792         910 :       if (!Flx_is_squarefree(polr, p)) { oldf = 0; continue; }
    1793             : 
    1794         854 :       fac = gel(Flx_factor(polr, p), 1);
    1795         854 :       f = degpol(gel(fac,1));
    1796         854 :       if (f == degrel) continue; /* degrel-th powers already included */
    1797         455 :       nfac = lg(fac)-1;
    1798             :       /* check decomposition of pr has Galois type */
    1799        1176 :       for (j=2; j<=nfac; j++)
    1800         966 :         if (degpol(gel(fac,j)) != f) return NULL;
    1801         448 :       if (oldf < 0) oldf = f; else if (oldf != f) oldf = 0;
    1802             : 
    1803             :       /* last prime & all pr^f, pr | p, included. Include p^f instead */
    1804         448 :       if (oldf && i == nfa && degrel == nfa*f && !umodiu(discnf, p))
    1805           0 :         pr = utoipos(p);
    1806             : 
    1807             :       /* pr^f = N P, P | pr, hence is in norm group */
    1808         448 :       col = bnrisprincipalmod(bnr,pr,gdegrel,0);
    1809         448 :       if (f > 1) col = ZC_z_mul(col, f);
    1810         448 :       G = ZM_hnf(shallowconcat(G, col));
    1811         448 :       detG = ZM_det_triangular(G);
    1812         448 :       k = abscmpiu(detG,degrel);
    1813         448 :       if (k < 0) return NULL;
    1814         448 :       if (!k) { cgiv(detG); return G; }
    1815             :     }
    1816             :   }
    1817           0 :   return NULL;
    1818             : }
    1819             : GEN
    1820          14 : rnfnormgroup(GEN bnr, GEN polrel)
    1821             : {
    1822          14 :   pari_sp av = avma;
    1823          14 :   GEN G = rnfnormgroup_i(bnr, polrel);
    1824          14 :   if (!G) { set_avma(av); return cgetg(1,t_MAT); }
    1825           7 :   return gerepileupto(av, G);
    1826             : }
    1827             : 
    1828             : GEN
    1829           0 : nf_deg1_prime(GEN nf)
    1830             : {
    1831           0 :   GEN z, T = nf_get_pol(nf), D = nf_get_disc(nf), f = nf_get_index(nf);
    1832           0 :   long degnf = degpol(T);
    1833             :   forprime_t S;
    1834             :   pari_sp av;
    1835             :   ulong p;
    1836           0 :   u_forprime_init(&S, degnf, ULONG_MAX);
    1837           0 :   av = avma;
    1838           0 :   while ( (p = u_forprime_next(&S)) )
    1839             :   {
    1840             :     ulong r;
    1841           0 :     if (!umodiu(D, p) || !umodiu(f, p)) continue;
    1842           0 :     r = Flx_oneroot(ZX_to_Flx(T,p), p);
    1843           0 :     if (r != p)
    1844             :     {
    1845           0 :       z = utoi(Fl_neg(r, p));
    1846           0 :       z = deg1pol_shallow(gen_1, z, varn(T));
    1847           0 :       return idealprimedec_kummer(nf, z, 1, utoipos(p));
    1848             :     }
    1849           0 :     set_avma(av);
    1850             :   }
    1851           0 :   return NULL;
    1852             : }
    1853             : 
    1854             : /* Given bnf and T defining an abelian relative extension, compute the
    1855             :  * corresponding conductor and congruence subgroup. Return
    1856             :  * [cond,bnr(cond),H] where cond=[ideal,arch] is the conductor. */
    1857             : GEN
    1858         805 : rnfconductor0(GEN bnf, GEN T, long flag)
    1859             : {
    1860         805 :   pari_sp av = avma;
    1861             :   GEN P, E, D, nf, module, bnr, H, lim, Tr, MOD;
    1862         805 :   long i, l, degT = degpol(T);
    1863             : 
    1864         805 :   if (flag < 0 || flag > 2) pari_err_FLAG("rnfconductor");
    1865         805 :   bnf = checkbnf(bnf); nf = bnf_get_nf(bnf);
    1866         791 :   Tr = rnfdisc_get_T(nf, T, &lim);
    1867         791 :   T = nfX_to_monic(nf, Tr, NULL);
    1868         791 :   if (!lim)
    1869         777 :     D = rnfdisc_factored(nf, T, NULL);
    1870             :   else
    1871             :   {
    1872          14 :     D = nfX_disc(nf, Q_primpart(Tr));
    1873          14 :     if (gequal0(D))
    1874           0 :       pari_err_DOMAIN("rnfconductor","issquarefree(pol)","=",gen_0, Tr);
    1875          14 :     D = idealfactor_partial(nf, D, lim);
    1876             :   }
    1877         791 :   P = gel(D,1); l = lg(P);
    1878         791 :   E = gel(D,2);
    1879        1743 :   for (i = 1; i < l; i++) /* cheaply update tame primes */
    1880             :   { /* v_pr(f) = 1 + \sum_{0 < i < l} g_i/g_0
    1881             :                <= 1 + max_{i>0} g_i/(g_i-1) \sum_{0 < i < l} g_i -1
    1882             :                <= 1 + (p/(p-1)) * v_P(e(L/K, pr)), P | pr | p */
    1883         952 :     GEN pr = gel(P,i), p = pr_get_p(pr), e = gen_1;
    1884         952 :     ulong q, e0 = itou(gel(E,i));
    1885         952 :     if (e0 > 1 && cmpiu(p, degT) <= 0)
    1886             :     {
    1887         385 :       long v, pp = itou(p);
    1888         385 :       if ((v = u_lvalrem(degT, pp, &q)))
    1889             :       { /* e = e_tame * e_wild, e_wild | p^v */
    1890         315 :         ulong t = ugcd(umodiu(subiu(pr_norm(pr),1), q), q); /* e_tame | t */
    1891             :         /* upper bound for 1 + p/(p-1) * v * e(L/Q,p) */
    1892         315 :         e0 = minuu(e0, 1 + (pp * v * pr_get_e(pr) * upowuu(pp,v) * t) / (pp-1));
    1893         315 :         e = utoipos(e0);
    1894             :       }
    1895             :     }
    1896         952 :     gel(E,i) = e;
    1897             :   }
    1898         791 :   module = mkvec2(D, identity_perm(nf_get_r1(nf)));
    1899         791 :   MOD = flag? utoipos(degpol(T)): NULL;
    1900         791 :   bnr = Buchraymod_i(bnf, module, nf_INIT|nf_GEN, MOD);
    1901         791 :   H = rnfnormgroup_i(bnr,T); if (!H) return gc_const(av,gen_0);
    1902        1295 :   return gerepilecopy(av, flag == 2? bnrconductor_factored(bnr, H)
    1903         518 :                                    : bnrconductormod(bnr, H, MOD));
    1904             : }
    1905             : GEN
    1906          35 : rnfconductor(GEN bnf, GEN T) { return rnfconductor0(bnf, T, 0); }
    1907             : 
    1908             : static GEN
    1909        1554 : prV_norms(GEN v)
    1910             : {
    1911             :   long i, l;
    1912        1554 :   GEN w = cgetg_copy(v, &l);
    1913        2835 :   for (i = 1; i < l; i++) gel(w,i) = pr_norm(gel(v,i));
    1914        1554 :   return w;
    1915             : }
    1916             : 
    1917             : /* Given a number field bnf=bnr[1], a ray class group structure bnr, and a
    1918             :  * subgroup H (HNF form) of the ray class group, compute [n, r1, dk]
    1919             :  * attached to H. If flag & rnf_COND, abort (return NULL) if module is not the
    1920             :  * conductor. If flag & rnf_REL, return relative data, else absolute */
    1921             : static GEN
    1922        1631 : bnrdisc_i(GEN bnr, GEN H, long flag)
    1923             : {
    1924        1631 :   const long flcond = flag & rnf_COND;
    1925             :   GEN nf, clhray, E, ED, dk;
    1926             :   long k, d, l, n, r1;
    1927             :   zlog_S S;
    1928             : 
    1929        1631 :   checkbnr(bnr);
    1930        1631 :   init_zlog(&S, bnr_get_bid(bnr));
    1931        1631 :   nf = bnr_get_nf(bnr);
    1932        1631 :   H = bnr_subgroup_check(bnr, H, &clhray);
    1933        1631 :   d = itos(clhray);
    1934        1631 :   if (!H) H = diagonal_shallow(bnr_get_cyc(bnr));
    1935        1631 :   E = S.k; ED = cgetg_copy(E, &l);
    1936        2954 :   for (k = 1; k < l; k++)
    1937             :   {
    1938        1337 :     long j, e = itos(gel(E,k)), eD = e*d;
    1939        1337 :     GEN H2 = H;
    1940        1477 :     for (j = e; j > 0; j--)
    1941             :     {
    1942        1379 :       GEN z = bnr_log_gen_pr(bnr, &S, j, k);
    1943             :       long d2;
    1944        1379 :       H2 = ZM_hnf(shallowconcat(H2, z));
    1945        1379 :       d2 = itos( ZM_det_triangular(H2) );
    1946        1379 :       if (flcond && j==e && d2 == d) return NULL;
    1947        1365 :       if (d2 == 1) { eD -= j; break; }
    1948         140 :       eD -= d2;
    1949             :     }
    1950        1323 :     gel(ED,k) = utoi(eD); /* v_{P[k]}(relative discriminant) */
    1951             :   }
    1952        1617 :   l = lg(S.archp); r1 = nf_get_r1(nf);
    1953        1904 :   for (k = 1; k < l; k++)
    1954             :   {
    1955         315 :     if (!contains(H, bnr_log_gen_arch(bnr, &S, k))) { r1--; continue; }
    1956          98 :     if (flcond) return NULL;
    1957             :   }
    1958             :   /* d = relative degree
    1959             :    * r1 = number of unramified real places;
    1960             :    * [P,ED] = factorization of relative discriminant */
    1961        1589 :   if (flag & rnf_REL)
    1962             :   {
    1963          35 :     n  = d;
    1964          35 :     dk = factorbackprime(nf, S.P, ED);
    1965             :   }
    1966             :   else
    1967             :   {
    1968        1554 :     n = d * nf_get_degree(nf);
    1969        1554 :     r1= d * r1;
    1970        1554 :     dk = factorback2(prV_norms(S.P), ED);
    1971        1554 :     if (((n-r1)&3) == 2) dk = negi(dk); /* (2r2) mod 4 = 2: r2(relext) is odd */
    1972        1554 :     dk = mulii(dk, powiu(absi_shallow(nf_get_disc(nf)), d));
    1973             :   }
    1974        1589 :   return mkvec3(utoipos(n), utoi(r1), dk);
    1975             : }
    1976             : GEN
    1977        1631 : bnrdisc(GEN bnr, GEN H, long flag)
    1978             : {
    1979        1631 :   pari_sp av = avma;
    1980        1631 :   GEN D = bnrdisc_i(bnr, H, flag);
    1981        1631 :   return D? gerepilecopy(av, D): gc_const(av, gen_0);
    1982             : }
    1983             : GEN
    1984         175 : bnrdisc0(GEN A, GEN B, GEN C, long flag)
    1985             : {
    1986         175 :   GEN H, bnr = ABC_to_bnr(A,B,C,&H, 0);
    1987         175 :   return bnrdisc(bnr,H,flag);
    1988             : }
    1989             : 
    1990             : /* Given a number field bnf=bnr[1], a ray class group structure bnr and a
    1991             :  * vector chi representing a character on the generators bnr[2][3], compute
    1992             :  * the conductor of chi. */
    1993             : GEN
    1994           7 : bnrconductorofchar(GEN bnr, GEN chi)
    1995             : {
    1996           7 :   pari_sp av = avma;
    1997           7 :   return gerepilecopy(av, bnrconductor_raw(bnr, chi));
    1998             : }
    1999             : 
    2000             : /* \sum U[i]*y[i], U[i],y[i] ZM, we allow lg(y) > lg(U). */
    2001             : static GEN
    2002         910 : ZMV_mul(GEN U, GEN y)
    2003             : {
    2004         910 :   long i, l = lg(U);
    2005         910 :   GEN z = NULL;
    2006         910 :   if (l == 1) return cgetg(1,t_MAT);
    2007        2324 :   for (i = 1; i < l; i++)
    2008             :   {
    2009        1442 :     GEN u = ZM_mul(gel(U,i), gel(y,i));
    2010        1442 :     z = z? ZM_add(z, u): u;
    2011             :   }
    2012         882 :   return z;
    2013             : }
    2014             : 
    2015             : /* t = [bid,U], h = #Cl(K) */
    2016             : static GEN
    2017         910 : get_classno(GEN t, GEN h)
    2018             : {
    2019         910 :   GEN bid = gel(t,1), m = gel(t,2), cyc = bid_get_cyc(bid), U = bid_get_U(bid);
    2020         910 :   return mulii(h, ZM_det_triangular(ZM_hnfmodid(ZMV_mul(U,m), cyc)));
    2021             : }
    2022             : 
    2023             : static void
    2024          28 : chk_listBU(GEN L, const char *s) {
    2025          28 :   if (typ(L) != t_VEC) pari_err_TYPE(s,L);
    2026          28 :   if (lg(L) > 1) {
    2027          28 :     GEN z = gel(L,1);
    2028          28 :     if (typ(z) != t_VEC) pari_err_TYPE(s,z);
    2029          28 :     if (lg(z) == 1) return;
    2030          28 :     z = gel(z,1); /* [bid,U] */
    2031          28 :     if (typ(z) != t_VEC || lg(z) != 3) pari_err_TYPE(s,z);
    2032          28 :     checkbid(gel(z,1));
    2033             :   }
    2034             : }
    2035             : 
    2036             : /* Given lists of [bid, unit ideallogs], return lists of ray class numbers */
    2037             : GEN
    2038           7 : bnrclassnolist(GEN bnf,GEN L)
    2039             : {
    2040           7 :   pari_sp av = avma;
    2041           7 :   long i, l = lg(L);
    2042             :   GEN V, h;
    2043             : 
    2044           7 :   chk_listBU(L, "bnrclassnolist");
    2045           7 :   if (l == 1) return cgetg(1, t_VEC);
    2046           7 :   bnf = checkbnf(bnf);
    2047           7 :   h = bnf_get_no(bnf);
    2048           7 :   V = cgetg(l,t_VEC);
    2049         392 :   for (i = 1; i < l; i++)
    2050             :   {
    2051         385 :     GEN v, z = gel(L,i);
    2052         385 :     long j, lz = lg(z);
    2053         385 :     gel(V,i) = v = cgetg(lz,t_VEC);
    2054         826 :     for (j=1; j<lz; j++) gel(v,j) = get_classno(gel(z,j), h);
    2055             :   }
    2056           7 :   return gerepilecopy(av, V);
    2057             : }
    2058             : 
    2059             : static GEN
    2060        1484 : Lbnrclassno(GEN L, GEN fac)
    2061             : {
    2062        1484 :   long i, l = lg(L);
    2063        2184 :   for (i=1; i<l; i++)
    2064        2184 :     if (gequal(gmael(L,i,1),fac)) return gmael(L,i,2);
    2065           0 :   pari_err_BUG("Lbnrclassno");
    2066             :   return NULL; /* LCOV_EXCL_LINE */
    2067             : }
    2068             : 
    2069             : static GEN
    2070         406 : factordivexact(GEN fa1,GEN fa2)
    2071             : {
    2072             :   long i, j, k, c, l;
    2073             :   GEN P, E, P1, E1, P2, E2, p1;
    2074             : 
    2075         406 :   P1 = gel(fa1,1); E1 = gel(fa1,2); l = lg(P1);
    2076         406 :   P2 = gel(fa2,1); E2 = gel(fa2,2);
    2077         406 :   P = cgetg(l,t_COL);
    2078         406 :   E = cgetg(l,t_COL);
    2079         903 :   for (c = i = 1; i < l; i++)
    2080             :   {
    2081         497 :     j = RgV_isin(P2,gel(P1,i));
    2082         497 :     if (!j) { gel(P,c) = gel(P1,i); gel(E,c) = gel(E1,i); c++; }
    2083             :     else
    2084             :     {
    2085         497 :       p1 = subii(gel(E1,i), gel(E2,j)); k = signe(p1);
    2086         497 :       if (k < 0) pari_err_BUG("factordivexact [not exact]");
    2087         497 :       if (k > 0) { gel(P,c) = gel(P1,i); gel(E,c) = p1; c++; }
    2088             :     }
    2089             :   }
    2090         406 :   setlg(P, c);
    2091         406 :   setlg(E, c); return mkmat2(P, E);
    2092             : }
    2093             : /* remove index k */
    2094             : static GEN
    2095        1169 : factorsplice(GEN fa, long k)
    2096             : {
    2097        1169 :   GEN p = gel(fa,1), e = gel(fa,2), P, E;
    2098        1169 :   long i, l = lg(p) - 1;
    2099        1169 :   P = cgetg(l, typ(p));
    2100        1169 :   E = cgetg(l, typ(e));
    2101        1344 :   for (i=1; i<k; i++) { P[i] = p[i]; E[i] = e[i]; }
    2102        1169 :   p++; e++;
    2103        1694 :   for (   ; i<l; i++) { P[i] = p[i]; E[i] = e[i]; }
    2104        1169 :   return mkvec2(P,E);
    2105             : }
    2106             : static GEN
    2107         812 : factorpow(GEN fa, long n)
    2108             : {
    2109         812 :   if (!n) return trivial_fact();
    2110         812 :   return mkmat2(gel(fa,1), gmulsg(n, gel(fa,2)));
    2111             : }
    2112             : static GEN
    2113        1043 : factormul(GEN fa1,GEN fa2)
    2114             : {
    2115        1043 :   GEN p, pnew, e, enew, v, P, y = famat_mul_shallow(fa1,fa2);
    2116             :   long i, c, lx;
    2117             : 
    2118        1043 :   p = gel(y,1); v = indexsort(p); lx = lg(p);
    2119        1043 :   e = gel(y,2);
    2120        1043 :   pnew = vecpermute(p, v);
    2121        1043 :   enew = vecpermute(e, v);
    2122        1043 :   P = gen_0; c = 0;
    2123        2933 :   for (i=1; i<lx; i++)
    2124             :   {
    2125        1890 :     if (gequal(gel(pnew,i),P))
    2126          49 :       gel(e,c) = addii(gel(e,c),gel(enew,i));
    2127             :     else
    2128             :     {
    2129        1841 :       c++; P = gel(pnew,i);
    2130        1841 :       gel(p,c) = P;
    2131        1841 :       gel(e,c) = gel(enew,i);
    2132             :     }
    2133             :   }
    2134        1043 :   setlg(p, c+1);
    2135        1043 :   setlg(e, c+1); return y;
    2136             : }
    2137             : 
    2138             : static long
    2139         168 : get_nz(GEN bnf, GEN ideal, GEN arch, long clhray)
    2140             : {
    2141             :   GEN arch2, mod;
    2142         168 :   long nz = 0, l = lg(arch), k, clhss;
    2143         168 :   if (typ(arch) == t_VECSMALL)
    2144          14 :     arch2 = indices_to_vec01(arch,nf_get_r1(bnf_get_nf(bnf)));
    2145             :   else
    2146         154 :     arch2 = leafcopy(arch);
    2147         168 :   mod = mkvec2(ideal, arch2);
    2148         448 :   for (k = 1; k < l; k++)
    2149             :   { /* FIXME: this is wasteful. Use the same algorithm as bnrconductor */
    2150         301 :     if (signe(gel(arch2,k)))
    2151             :     {
    2152          28 :       gel(arch2,k) = gen_0; clhss = itos(bnrclassno(bnf,mod));
    2153          28 :       gel(arch2,k) = gen_1;
    2154          28 :       if (clhss == clhray) return -1;
    2155             :     }
    2156         273 :     else nz++;
    2157             :   }
    2158         147 :   return nz;
    2159             : }
    2160             : 
    2161             : static GEN
    2162         427 : get_NR1D(long Nf, long clhray, long degk, long nz, GEN fadkabs, GEN idealrel)
    2163             : {
    2164             :   long n, R1;
    2165             :   GEN dlk;
    2166         427 :   if (nz < 0) return mkvec3(gen_0,gen_0,gen_0); /*EMPTY*/
    2167         406 :   n  = clhray * degk;
    2168         406 :   R1 = clhray * nz;
    2169         406 :   dlk = factordivexact(factorpow(Z_factor(utoipos(Nf)),clhray), idealrel);
    2170             :   /* r2 odd, set dlk = -dlk */
    2171         406 :   if (((n-R1)&3)==2) dlk = factormul(to_famat_shallow(gen_m1,gen_1), dlk);
    2172         406 :   return mkvec3(utoipos(n),
    2173             :                 stoi(R1),
    2174             :                 factormul(dlk,factorpow(fadkabs,clhray)));
    2175             : }
    2176             : 
    2177             : /* t = [bid,U], h = #Cl(K) */
    2178             : static GEN
    2179         469 : get_discdata(GEN t, GEN h)
    2180             : {
    2181         469 :   GEN bid = gel(t,1), fa = bid_get_fact(bid);
    2182         469 :   GEN P = gel(fa,1), E = vec_to_vecsmall(gel(fa,2));
    2183         469 :   return mkvec3(mkvec2(P, E), (GEN)itou(get_classno(t, h)), bid_get_mod(bid));
    2184             : }
    2185             : typedef struct _disc_data {
    2186             :   long degk;
    2187             :   GEN bnf, fadk, idealrelinit, V;
    2188             : } disc_data;
    2189             : 
    2190             : static GEN
    2191         469 : get_discray(disc_data *D, GEN V, GEN z, long N)
    2192             : {
    2193         469 :   GEN idealrel = D->idealrelinit;
    2194         469 :   GEN mod = gel(z,3), Fa = gel(z,1);
    2195         469 :   GEN P = gel(Fa,1), E = gel(Fa,2);
    2196         469 :   long k, nz, clhray = z[2], lP = lg(P);
    2197         700 :   for (k=1; k<lP; k++)
    2198             :   {
    2199         546 :     GEN pr = gel(P,k), p = pr_get_p(pr);
    2200         546 :     long e, ep = E[k], f = pr_get_f(pr);
    2201         546 :     long S = 0, norm = N, Npr = upowuu(p[2],f), clhss;
    2202         798 :     for (e=1; e<=ep; e++)
    2203             :     {
    2204             :       GEN fad;
    2205         574 :       if (e < ep) { E[k] = ep-e; fad = Fa; }
    2206         462 :       else fad = factorsplice(Fa, k);
    2207         574 :       norm /= Npr;
    2208         574 :       clhss = (long)Lbnrclassno(gel(V,norm), fad);
    2209         574 :       if (e==1 && clhss==clhray) { E[k] = ep; return cgetg(1, t_VEC); }
    2210         259 :       if (clhss == 1) { S += ep-e+1; break; }
    2211         252 :       S += clhss;
    2212             :     }
    2213         231 :     E[k] = ep;
    2214         231 :     idealrel = factormul(idealrel, to_famat_shallow(p, utoi(f * S)));
    2215             :   }
    2216         154 :   nz = get_nz(D->bnf, gel(mod,1), gel(mod,2), clhray);
    2217         154 :   return get_NR1D(N, clhray, D->degk, nz, D->fadk, idealrel);
    2218             : }
    2219             : 
    2220             : /* Given a list of bids and attached unit log matrices, return the
    2221             :  * list of discrayabs. Only keep moduli which are conductors. */
    2222             : GEN
    2223          21 : discrayabslist(GEN bnf, GEN L)
    2224             : {
    2225          21 :   pari_sp av = avma;
    2226          21 :   long i, l = lg(L);
    2227             :   GEN nf, V, D, h;
    2228             :   disc_data ID;
    2229             : 
    2230          21 :   chk_listBU(L, "discrayabslist");
    2231          21 :   if (l == 1) return cgetg(1, t_VEC);
    2232          21 :   ID.bnf = bnf = checkbnf(bnf);
    2233          21 :   nf = bnf_get_nf(bnf);
    2234          21 :   h = bnf_get_no(bnf);
    2235          21 :   ID.degk = nf_get_degree(nf);
    2236          21 :   ID.fadk = absZ_factor(nf_get_disc(nf));
    2237          21 :   ID.idealrelinit = trivial_fact();
    2238          21 :   V = cgetg(l, t_VEC);
    2239          21 :   D = cgetg(l, t_VEC);
    2240         448 :   for (i = 1; i < l; i++)
    2241             :   {
    2242         427 :     GEN z = gel(L,i), v, d;
    2243         427 :     long j, lz = lg(z);
    2244         427 :     gel(V,i) = v = cgetg(lz,t_VEC);
    2245         427 :     gel(D,i) = d = cgetg(lz,t_VEC);
    2246         896 :     for (j=1; j<lz; j++) {
    2247         469 :       gel(d,j) = get_discdata(gel(z,j), h);
    2248         469 :       gel(v,j) = get_discray(&ID, D, gel(d,j), i);
    2249             :     }
    2250             :   }
    2251          21 :   return gerepilecopy(av, V);
    2252             : }
    2253             : 
    2254             : /* a zsimp is [fa, cyc, v]
    2255             :  * fa: vecsmall factorisation,
    2256             :  * cyc: ZV (concatenation of (Z_K/pr^k)^* SNFs), the generators
    2257             :  * are positive at all real places [defined implicitly by weak approximation]
    2258             :  * v: ZC (log of units on (Z_K/pr^k)^* components) */
    2259             : static GEN
    2260          28 : zsimp(void)
    2261             : {
    2262          28 :   GEN empty = cgetg(1, t_VECSMALL);
    2263          28 :   return mkvec3(mkvec2(empty,empty), cgetg(1,t_VEC), cgetg(1,t_MAT));
    2264             : }
    2265             : 
    2266             : /* fa a vecsmall factorization, append p^e */
    2267             : static GEN
    2268         175 : fasmall_append(GEN fa, long p, long e)
    2269             : {
    2270         175 :   GEN P = gel(fa,1), E = gel(fa,2);
    2271         175 :   retmkvec2(vecsmall_append(P,p), vecsmall_append(E,e));
    2272             : }
    2273             : 
    2274             : /* sprk = sprkinit(pr,k), b zsimp with modulus coprime to pr */
    2275             : static GEN
    2276         518 : zsimpjoin(GEN b, GEN sprk, GEN U_pr, long prcode, long e)
    2277             : {
    2278         518 :   GEN fa, cyc = sprk_get_cyc(sprk);
    2279         518 :   if (lg(gel(b,2)) == 1) /* trivial group */
    2280         343 :     fa = mkvec2(mkvecsmall(prcode),mkvecsmall(e));
    2281             :   else
    2282             :   {
    2283         175 :     fa = fasmall_append(gel(b,1), prcode, e);
    2284         175 :     cyc = shallowconcat(gel(b,2), cyc); /* no SNF ! */
    2285         175 :     U_pr = vconcat(gel(b,3),U_pr);
    2286             :   }
    2287         518 :   return mkvec3(fa, cyc, U_pr);
    2288             : }
    2289             : /* B a zsimp, sgnU = [cyc[f_oo], sgn_{f_oo}(units)] */
    2290             : static GEN
    2291          28 : bnrclassno_1(GEN B, ulong h, GEN sgnU)
    2292             : {
    2293          28 :   long lx = lg(B), j;
    2294          28 :   GEN L = cgetg(lx,t_VEC);
    2295          56 :   for (j=1; j<lx; j++)
    2296             :   {
    2297          28 :     pari_sp av = avma;
    2298          28 :     GEN b = gel(B,j), cyc = gel(b,2), qm = gel(b,3);
    2299             :     ulong z;
    2300          28 :     cyc = shallowconcat(cyc, gel(sgnU,1));
    2301          28 :     qm = vconcat(qm, gel(sgnU,2));
    2302          28 :     z = itou( mului(h, ZM_det_triangular(ZM_hnfmodid(qm, cyc))) );
    2303          28 :     set_avma(av);
    2304          28 :     gel(L,j) = mkvec2(gel(b,1), mkvecsmall(z));
    2305             :   }
    2306          28 :   return L;
    2307             : }
    2308             : 
    2309             : static void
    2310        1344 : vecselect_p(GEN A, GEN B, GEN p, long init, long lB)
    2311             : {
    2312        1344 :   long i; setlg(B, lB);
    2313        2688 :   for (i=init; i<lB; i++) B[i] = A[p[i]];
    2314        1344 : }
    2315             : /* B := p . A = row selection according to permutation p. Treat only lower
    2316             :  * right corner init x init */
    2317             : static void
    2318        1022 : rowselect_p(GEN A, GEN B, GEN p, long init)
    2319             : {
    2320        1022 :   long i, lB = lg(A), lp = lg(p);
    2321        2436 :   for (i=1; i<init; i++) setlg(B[i],lp);
    2322        2366 :   for (   ; i<lB;   i++) vecselect_p(gel(A,i),gel(B,i),p,init,lp);
    2323        1022 : }
    2324             : static ulong
    2325        1022 : hdet(ulong h, GEN m)
    2326             : {
    2327        1022 :   pari_sp av = avma;
    2328        1022 :   GEN z = mului(h, ZM_det_triangular(ZM_hnf(m)));
    2329        1022 :   return gc_ulong(av, itou(z));
    2330             : }
    2331             : static GEN
    2332        1106 : bnrclassno_all(GEN B, ulong h, GEN sgnU)
    2333             : {
    2334             :   long lx, k, kk, j, r1, jj, nba, nbarch;
    2335             :   GEN _2, L, m, H, mm, rowsel;
    2336             : 
    2337        1106 :   if (typ(sgnU) == t_VEC) return bnrclassno_1(B,h,sgnU);
    2338        1078 :   lx = lg(B); if (lx == 1) return B;
    2339             : 
    2340         371 :   r1 = nbrows(sgnU); _2 = const_vec(r1, gen_2);
    2341         371 :   L = cgetg(lx,t_VEC); nbarch = 1L<<r1;
    2342         889 :   for (j=1; j<lx; j++)
    2343             :   {
    2344         518 :     pari_sp av = avma;
    2345         518 :     GEN b = gel(B,j), cyc = gel(b,2), qm = gel(b,3);
    2346         518 :     long nc = lg(cyc)-1;
    2347             :     /* [ qm   cyc 0 ]
    2348             :      * [ sgnU  0  2 ] */
    2349         518 :     m = ZM_hnfmodid(vconcat(qm, sgnU), shallowconcat(cyc,_2));
    2350         518 :     mm = RgM_shallowcopy(m);
    2351         518 :     rowsel = cgetg(nc+r1+1,t_VECSMALL);
    2352         518 :     H = cgetg(nbarch+1,t_VECSMALL);
    2353        1540 :     for (k = 0; k < nbarch; k++)
    2354             :     {
    2355        1022 :       nba = nc+1;
    2356        2366 :       for (kk=k,jj=1; jj<=r1; jj++,kk>>=1)
    2357        1344 :         if (kk&1) rowsel[nba++] = nc + jj;
    2358        1022 :       setlg(rowsel, nba);
    2359        1022 :       rowselect_p(m, mm, rowsel, nc+1);
    2360        1022 :       H[k+1] = hdet(h, mm);
    2361             :     }
    2362         518 :     H = gerepileuptoleaf(av, H);
    2363         518 :     gel(L,j) = mkvec2(gel(b,1), H);
    2364             :   }
    2365         371 :   return L;
    2366             : }
    2367             : 
    2368             : static int
    2369          21 : is_module(GEN v)
    2370             : {
    2371          21 :   if (lg(v) != 3 || (typ(v) != t_MAT && typ(v) != t_VEC)) return 0;
    2372          21 :   return typ(gel(v,1)) == t_VECSMALL && typ(gel(v,2)) == t_VECSMALL;
    2373             : }
    2374             : GEN
    2375          21 : decodemodule(GEN nf, GEN fa)
    2376             : {
    2377             :   long n, nn, k;
    2378          21 :   pari_sp av = avma;
    2379             :   GEN G, E, id, pr;
    2380             : 
    2381          21 :   nf = checknf(nf);
    2382          21 :   if (!is_module(fa)) pari_err_TYPE("decodemodule [not a factorization]", fa);
    2383          21 :   n = nf_get_degree(nf); nn = n*n; id = NULL;
    2384          21 :   G = gel(fa,1);
    2385          21 :   E = gel(fa,2);
    2386          35 :   for (k=1; k<lg(G); k++)
    2387             :   {
    2388          14 :     long code = G[k], p = code / nn, j = (code%n)+1;
    2389          14 :     GEN P = idealprimedec(nf, utoipos(p)), e = stoi(E[k]);
    2390          14 :     if (lg(P) <= j) pari_err_BUG("decodemodule [incorrect hash code]");
    2391          14 :     pr = gel(P,j);
    2392          14 :     id = id? idealmulpowprime(nf,id, pr,e)
    2393          14 :            : idealpow(nf, pr,e);
    2394             :   }
    2395          21 :   if (!id) { set_avma(av); return matid(n); }
    2396          14 :   return gerepileupto(av,id);
    2397             : }
    2398             : 
    2399             : /* List of ray class fields. Do all from scratch, bound < 2^30. No subgroups.
    2400             :  *
    2401             :  * Output: a vector V, V[k] contains the ideals of norm k. Given such an ideal
    2402             :  * m, the component is as follows:
    2403             :  *
    2404             :  * + if arch = NULL, run through all possible archimedean parts; archs are
    2405             :  * ordered using inverse lexicographic order, [0,..,0], [1,0,..,0], [0,1,..,0],
    2406             :  * Component is [m,V] where V is a vector with 2^r1 entries, giving for each
    2407             :  * arch the triple [N,R1,D], with N, R1, D as in discrayabs; D is in factored
    2408             :  * form.
    2409             :  *
    2410             :  * + otherwise [m,N,R1,D] */
    2411             : GEN
    2412          28 : discrayabslistarch(GEN bnf, GEN arch, ulong bound)
    2413             : {
    2414          28 :   int allarch = (arch==NULL), flbou = 0;
    2415             :   long degk, j, k, l, nba, nbarch, r1, c, sqbou;
    2416          28 :   pari_sp av0 = avma,  av,  av1;
    2417             :   GEN nf, p, Z, fa, Disc, U, sgnU, EMPTY, empty, archp;
    2418             :   GEN res, Ray, discall, idealrel, idealrelinit, fadkabs, BOUND;
    2419             :   ulong i, h;
    2420             :   forprime_t S;
    2421             : 
    2422          28 :   if (bound == 0)
    2423           0 :     pari_err_DOMAIN("discrayabslistarch","bound","==",gen_0,utoi(bound));
    2424          28 :   res = discall = NULL; /* -Wall */
    2425             : 
    2426          28 :   bnf = checkbnf(bnf);
    2427          28 :   nf = bnf_get_nf(bnf);
    2428          28 :   r1 = nf_get_r1(nf);
    2429          28 :   degk = nf_get_degree(nf);
    2430          28 :   fadkabs = absZ_factor(nf_get_disc(nf));
    2431          28 :   h = itou(bnf_get_no(bnf));
    2432             : 
    2433          28 :   if (allarch)
    2434             :   {
    2435          21 :     if (r1>15) pari_err_IMPL("r1>15 in discrayabslistarch");
    2436          21 :     arch = const_vec(r1, gen_1);
    2437             :   }
    2438           7 :   else if (lg(arch)-1 != r1)
    2439           0 :     pari_err_TYPE("Idealstar [incorrect archimedean component]",arch);
    2440          28 :   U = log_prk_units_init(bnf);
    2441          28 :   archp = vec01_to_indices(arch);
    2442          28 :   nba = lg(archp)-1;
    2443          28 :   sgnU = zm_to_ZM( nfsign_units(bnf, archp, 1) );
    2444          28 :   if (!allarch) sgnU = mkvec2(const_vec(nba,gen_2), sgnU);
    2445             : 
    2446          28 :   empty = cgetg(1,t_VEC);
    2447             :   /* what follows was rewritten from Ideallist */
    2448          28 :   BOUND = utoipos(bound);
    2449          28 :   p = cgetipos(3);
    2450          28 :   u_forprime_init(&S, 2, bound);
    2451          28 :   av = avma;
    2452          28 :   sqbou = (long)sqrt((double)bound) + 1;
    2453          28 :   Z = const_vec(bound, empty);
    2454          28 :   gel(Z,1) = mkvec(zsimp());
    2455          28 :   if (DEBUGLEVEL>1) err_printf("Starting zidealstarunits computations\n");
    2456             :   /* The goal is to compute Ray (lists of bnrclassno). Z contains "zsimps",
    2457             :    * simplified bid, from which bnrclassno is easy to compute.
    2458             :    * Once p > sqbou, delete Z[i] for i > sqbou and compute directly Ray */
    2459          28 :   Ray = Z;
    2460         294 :   while ((p[2] = u_forprime_next(&S)))
    2461             :   {
    2462         266 :     if (!flbou && p[2] > sqbou)
    2463             :     {
    2464          21 :       flbou = 1;
    2465          21 :       if (DEBUGLEVEL>1) err_printf("\nStarting bnrclassno computations\n");
    2466          21 :       Z = gerepilecopy(av,Z);
    2467          21 :       Ray = cgetg(bound+1, t_VEC);
    2468         889 :       for (i=1; i<=bound; i++) gel(Ray,i) = bnrclassno_all(gel(Z,i),h,sgnU);
    2469          21 :       Z = vecslice(Z, 1, sqbou);
    2470             :     }
    2471         266 :     fa = idealprimedec_limit_norm(nf,p,BOUND);
    2472         504 :     for (j=1; j<lg(fa); j++)
    2473             :     {
    2474         238 :       GEN pr = gel(fa,j);
    2475         238 :       long prcode, f = pr_get_f(pr);
    2476         238 :       ulong q, Q = upowuu(p[2], f);
    2477             : 
    2478             :       /* p, f-1, j-1 as a single integer in "base degk" (f,j <= degk)*/
    2479         238 :       prcode = (p[2]*degk + f-1)*degk + j-1;
    2480         238 :       q = Q;
    2481             :       /* FIXME: if Q = 2, should start at l = 2 */
    2482         238 :       for (l = 1;; l++) /* Q <= bound */
    2483         105 :       {
    2484             :         ulong iQ;
    2485         343 :         GEN sprk = log_prk_init(nf, pr, l, NULL);
    2486         343 :         GEN U_pr = log_prk_units(nf, U, sprk);
    2487        1582 :         for (iQ = Q, i = 1; iQ <= bound; iQ += Q, i++)
    2488             :         {
    2489        1239 :           GEN pz, p2, p1 = gel(Z,i);
    2490        1239 :           long lz = lg(p1);
    2491        1239 :           if (lz == 1) continue;
    2492             : 
    2493         595 :           p2 = cgetg(lz,t_VEC); c = 0;
    2494        1113 :           for (k=1; k<lz; k++)
    2495             :           {
    2496         658 :             GEN z = gel(p1,k), v = gmael(z,1,1); /* primes in zsimp's fact. */
    2497         658 :             long lv = lg(v);
    2498             :             /* If z has a power of pr in its modulus, skip it */
    2499         658 :             if (i != 1 && lv > 1 && v[lv-1] == prcode) break;
    2500         518 :             gel(p2,++c) = zsimpjoin(z,sprk,U_pr,prcode,l);
    2501             :           }
    2502         595 :           setlg(p2, c+1);
    2503         595 :           pz = gel(Ray,iQ);
    2504         595 :           if (flbou) p2 = bnrclassno_all(p2,h,sgnU);
    2505         595 :           if (lg(pz) > 1) p2 = shallowconcat(pz,p2);
    2506         595 :           gel(Ray,iQ) = p2;
    2507             :         }
    2508         343 :         Q = itou_or_0( muluu(Q, q) );
    2509         343 :         if (!Q || Q > bound) break;
    2510             :       }
    2511             :     }
    2512         266 :     if (gc_needed(av,1))
    2513             :     {
    2514           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"[1]: discrayabslistarch");
    2515           0 :       gerepileall(av, flbou? 2: 1, &Z, &Ray);
    2516             :     }
    2517             :   }
    2518          28 :   if (!flbou) /* occurs iff bound = 1,2,4 */
    2519             :   {
    2520           7 :     if (DEBUGLEVEL>1) err_printf("\nStarting bnrclassno computations\n");
    2521           7 :     Ray = cgetg(bound+1, t_VEC);
    2522          35 :     for (i=1; i<=bound; i++) gel(Ray,i) = bnrclassno_all(gel(Z,i),h,sgnU);
    2523             :   }
    2524          28 :   Ray = gerepilecopy(av, Ray);
    2525             : 
    2526          28 :   if (DEBUGLEVEL>1) err_printf("Starting discrayabs computations\n");
    2527          28 :   if (allarch) nbarch = 1L<<r1;
    2528             :   else
    2529             :   {
    2530           7 :     nbarch = 1;
    2531           7 :     discall = cgetg(2,t_VEC);
    2532             :   }
    2533          28 :   EMPTY = mkvec3(gen_0,gen_0,gen_0);
    2534          28 :   idealrelinit = trivial_fact();
    2535          28 :   av1 = avma;
    2536          28 :   Disc = const_vec(bound, empty);
    2537         924 :   for (i=1; i<=bound; i++)
    2538             :   {
    2539         896 :     GEN sousdisc, sous = gel(Ray,i);
    2540         896 :     long ls = lg(sous);
    2541         896 :     gel(Disc,i) = sousdisc = cgetg(ls,t_VEC);
    2542        1442 :     for (j=1; j<ls; j++)
    2543             :     {
    2544         546 :       GEN b = gel(sous,j), clhrayall = gel(b,2), Fa = gel(b,1);
    2545         546 :       GEN P = gel(Fa,1), E = gel(Fa,2);
    2546         546 :       long lP = lg(P), karch;
    2547             : 
    2548         546 :       if (allarch) discall = cgetg(nbarch+1,t_VEC);
    2549        1596 :       for (karch=0; karch<nbarch; karch++)
    2550             :       {
    2551        1050 :         long nz, clhray = clhrayall[karch+1];
    2552        1050 :         if (allarch)
    2553             :         {
    2554             :           long ka, k2;
    2555        1022 :           nba = 0;
    2556        2366 :           for (ka=karch,k=1; k<=r1; k++,ka>>=1)
    2557        1344 :             if (ka & 1) nba++;
    2558        1918 :           for (k2=1,k=1; k<=r1; k++,k2<<=1)
    2559        1190 :             if (karch&k2 && clhrayall[karch-k2+1] == clhray)
    2560         294 :               { res = EMPTY; goto STORE; }
    2561             :         }
    2562         756 :         idealrel = idealrelinit;
    2563        1078 :         for (k=1; k<lP; k++) /* cf get_discray */
    2564             :         {
    2565         805 :           long e, ep = E[k], pf = P[k] / degk, f = (pf%degk) + 1, S = 0;
    2566         805 :           ulong normi = i, Npr;
    2567         805 :           p = utoipos(pf / degk);
    2568         805 :           Npr = upowuu(p[2],f);
    2569        1204 :           for (e=1; e<=ep; e++)
    2570             :           {
    2571             :             long clhss;
    2572             :             GEN fad;
    2573         910 :             if (e < ep) { E[k] = ep-e; fad = Fa; }
    2574         707 :             else fad = factorsplice(Fa, k);
    2575         910 :             normi /= Npr;
    2576         910 :             clhss = Lbnrclassno(gel(Ray,normi),fad)[karch+1];
    2577         910 :             if (e==1 && clhss==clhray) { E[k] = ep; res = EMPTY; goto STORE; }
    2578         427 :             if (clhss == 1) { S += ep-e+1; break; }
    2579         399 :             S += clhss;
    2580             :           }
    2581         322 :           E[k] = ep;
    2582         322 :           idealrel = factormul(idealrel, to_famat_shallow(p, utoi(f * S)));
    2583             :         }
    2584         273 :         if (!allarch && nba)
    2585          14 :           nz = get_nz(bnf, decodemodule(nf,Fa), arch, clhray);
    2586             :         else
    2587         259 :           nz = r1 - nba;
    2588         273 :         res = get_NR1D(i, clhray, degk, nz, fadkabs, idealrel);
    2589        1050 : STORE:  gel(discall,karch+1) = res;
    2590             :       }
    2591         518 :       res = allarch? mkvec2(Fa, discall)
    2592         546 :                    : mkvec4(Fa, gel(res,1), gel(res,2), gel(res,3));
    2593         546 :       gel(sousdisc,j) = res;
    2594         546 :       if (gc_needed(av1,1))
    2595             :       {
    2596             :         long jj;
    2597           0 :         if(DEBUGMEM>1) pari_warn(warnmem,"[2]: discrayabslistarch");
    2598           0 :         for (jj=j+1; jj<ls; jj++) gel(sousdisc,jj) = gen_0; /* dummy */
    2599           0 :         Disc = gerepilecopy(av1, Disc);
    2600           0 :         sousdisc = gel(Disc,i);
    2601             :       }
    2602             :     }
    2603             :   }
    2604          28 :   return gerepilecopy(av0, Disc);
    2605             : }
    2606             : 
    2607             : int
    2608       95185 : subgroup_conductor_ok(GEN H, GEN L)
    2609             : { /* test conductor */
    2610       95185 :   long i, l = lg(L);
    2611      222338 :   for (i = 1; i < l; i++)
    2612      180654 :     if ( hnf_solve(H, gel(L,i)) ) return 0;
    2613       41684 :   return 1;
    2614             : }
    2615             : static GEN
    2616      182899 : conductor_elts(GEN bnr)
    2617             : {
    2618             :   long le, la, i, k;
    2619             :   GEN e, L;
    2620             :   zlog_S S;
    2621             : 
    2622      182899 :   if (!bnrisconductor(bnr, NULL)) return NULL;
    2623       56283 :   init_zlog(&S, bnr_get_bid(bnr));
    2624       56286 :   e = S.k; le = lg(e); la = lg(S.archp);
    2625       56286 :   L = cgetg(le + la - 1, t_VEC);
    2626       56286 :   i = 1;
    2627      129525 :   for (k = 1; k < le; k++)
    2628       73238 :     gel(L,i++) = bnr_log_gen_pr(bnr, &S, itos(gel(e,k)), k);
    2629       78910 :   for (k = 1; k < la; k++)
    2630       22623 :     gel(L,i++) = bnr_log_gen_arch(bnr, &S, k);
    2631       56287 :   return L;
    2632             : }
    2633             : 
    2634             : /* Let C a congruence group in bnr, compute its subgroups whose index is
    2635             :  * described by bound (see subgrouplist) as subgroups of Clk(bnr).
    2636             :  * Restrict to subgroups having the same conductor as bnr */
    2637             : GEN
    2638         448 : subgrouplist_cond_sub(GEN bnr, GEN C, GEN bound)
    2639             : {
    2640         448 :   pari_sp av = avma;
    2641             :   long l, i, j;
    2642         448 :   GEN D, Mr, U, T, subgrp, L, cyc = bnr_get_cyc(bnr);
    2643             : 
    2644         448 :   L = conductor_elts(bnr); if (!L) return cgetg(1,t_VEC);
    2645         448 :   Mr = diagonal_shallow(cyc);
    2646         448 :   D = ZM_snfall_i(hnf_solve(C, Mr), &U, NULL, 1);
    2647         448 :   T = ZM_mul(C, RgM_inv(U));
    2648         448 :   subgrp  = subgrouplist(D, bound);
    2649         448 :   l = lg(subgrp);
    2650         952 :   for (i = j = 1; i < l; i++)
    2651             :   {
    2652         504 :     GEN H = ZM_hnfmodid(ZM_mul(T, gel(subgrp,i)), cyc);
    2653         504 :     if (subgroup_conductor_ok(H, L)) gel(subgrp, j++) = H;
    2654             :   }
    2655         448 :   setlg(subgrp, j);
    2656         448 :   return gerepilecopy(av, subgrp);
    2657             : }
    2658             : 
    2659             : static GEN
    2660      182451 : subgroupcond(GEN bnr, GEN indexbound)
    2661             : {
    2662      182451 :   pari_sp av = avma;
    2663      182451 :   GEN L = conductor_elts(bnr);
    2664             : 
    2665      182438 :   if (!L) return cgetg(1, t_VEC);
    2666       55824 :   L = subgroupcondlist(bnr_get_cyc(bnr), indexbound, L);
    2667       55839 :   if (indexbound && typ(indexbound) != t_VEC)
    2668             :   { /* sort by increasing index if not single value */
    2669          14 :     long i, l = lg(L);
    2670          14 :     GEN D = cgetg(l,t_VEC);
    2671         245 :     for (i=1; i<l; i++) gel(D,i) = ZM_det_triangular(gel(L,i));
    2672          14 :     L = vecreverse( vecpermute(L, indexsort(D)) );
    2673             :   }
    2674       55839 :   return gerepilecopy(av, L);
    2675             : }
    2676             : 
    2677             : GEN
    2678      184658 : subgrouplist0(GEN cyc, GEN indexbound, long all)
    2679             : {
    2680      184658 :   if (!all && checkbnr_i(cyc)) return subgroupcond(cyc,indexbound);
    2681        2205 :   if (typ(cyc) != t_VEC || !RgV_is_ZV(cyc)) cyc = member_cyc(cyc);
    2682        2198 :   return subgrouplist(cyc,indexbound);
    2683             : }
    2684             : 
    2685             : GEN
    2686          49 : bnrdisclist0(GEN bnf, GEN L, GEN arch)
    2687             : {
    2688          49 :   if (typ(L)!=t_INT) return discrayabslist(bnf,L);
    2689          28 :   return discrayabslistarch(bnf,arch,itos(L));
    2690             : }
    2691             : 
    2692             : /****************************************************************************/
    2693             : /*                                Galois action on a BNR                    */
    2694             : /****************************************************************************/
    2695             : GEN
    2696        3087 : bnrautmatrix(GEN bnr, GEN aut)
    2697             : {
    2698        3087 :   pari_sp av = avma;
    2699        3087 :   GEN bnf = bnr_get_bnf(bnr), nf = bnf_get_nf(bnf), bid = bnr_get_bid(bnr);
    2700        3087 :   GEN M, Gen = get_Gen(bnf, bid, bnr_get_El(bnr)), cyc = bnr_get_cyc(bnr);
    2701        3087 :   long i, l = lg(Gen);
    2702             : 
    2703        3087 :   M = cgetg(l, t_MAT); aut = nfgaloismatrix(nf, aut);
    2704             :   /* Gen = clg.gen*U, clg.gen = Gen*Ui */
    2705       11662 :   for (i = 1; i < l; i++)
    2706        8575 :     gel(M,i) = isprincipalray(bnr, nfgaloismatrixapply(nf, aut, gel(Gen,i)));
    2707        3087 :   M = ZM_mul(M, bnr_get_Ui(bnr));
    2708        3087 :   return gerepilecopy(av, ZM_ZV_mod(M, cyc));
    2709             : }
    2710             : 
    2711             : GEN
    2712         231 : bnrgaloismatrix(GEN bnr, GEN aut)
    2713             : {
    2714         231 :   checkbnr(bnr);
    2715         231 :   switch (typ(aut))
    2716             :   {
    2717           0 :     case t_POL:
    2718             :     case t_COL:
    2719           0 :       return bnrautmatrix(bnr, aut);
    2720         231 :     case t_VEC:
    2721             :     {
    2722         231 :       pari_sp av = avma;
    2723         231 :       long i, l = lg(aut);
    2724             :       GEN v;
    2725         231 :       if (l == 9)
    2726             :       {
    2727           7 :         GEN g = gal_get_gen(aut);
    2728           7 :         if (typ(g) == t_VEC) { aut = galoispermtopol(aut, g); l = lg(aut); }
    2729             :       }
    2730         231 :       v = cgetg(l, t_VEC);
    2731         693 :       for(i = 1; i < l; i++) gel(v,i) = bnrautmatrix(bnr, gel(aut,i));
    2732         231 :       return gerepileupto(av, v);
    2733             :     }
    2734           0 :     default:
    2735           0 :       pari_err_TYPE("bnrgaloismatrix", aut);
    2736             :       return NULL; /*LCOV_EXCL_LINE*/
    2737             :   }
    2738             : }
    2739             : 
    2740             : GEN
    2741        3577 : bnrgaloisapply(GEN bnr, GEN mat, GEN x)
    2742             : {
    2743        3577 :   pari_sp av=avma;
    2744             :   GEN cyc;
    2745        3577 :   checkbnr(bnr);
    2746        3577 :   cyc = bnr_get_cyc(bnr);
    2747        3577 :   if (typ(mat)!=t_MAT || !RgM_is_ZM(mat))
    2748           0 :     pari_err_TYPE("bnrgaloisapply",mat);
    2749        3577 :   if (typ(x)!=t_MAT || !RgM_is_ZM(x))
    2750           0 :     pari_err_TYPE("bnrgaloisapply",x);
    2751        3577 :   return gerepileupto(av, ZM_hnfmodid(ZM_mul(mat, x), cyc));
    2752             : }
    2753             : 
    2754             : static GEN
    2755         448 : check_bnrgal(GEN bnr, GEN M)
    2756             : {
    2757         448 :   checkbnr(bnr);
    2758         448 :   if (typ(M)==t_MAT)
    2759           0 :     return mkvec(M);
    2760         448 :   else if (typ(M)==t_VEC && lg(M)==9 && typ(gal_get_gen(M))==t_VEC)
    2761             :   {
    2762         224 :     pari_sp av = avma;
    2763         224 :     GEN V = galoispermtopol(M, gal_get_gen(M));
    2764         224 :     return gerepileupto(av, bnrgaloismatrix(bnr, V));
    2765             :   }
    2766         224 :   else if (!is_vec_t(typ(M)))
    2767           0 :     pari_err_TYPE("bnrisgalois",M);
    2768         224 :   return M;
    2769             : }
    2770             : 
    2771             : long
    2772         448 : bnrisgalois(GEN bnr, GEN M, GEN H)
    2773             : {
    2774         448 :   pari_sp av = avma;
    2775             :   long i, l;
    2776         448 :   if (typ(H)!=t_MAT || !RgM_is_ZM(H))
    2777           0 :     pari_err_TYPE("bnrisgalois",H);
    2778         448 :   M = check_bnrgal(bnr, M); l = lg(M);
    2779         616 :   for (i=1; i<l; i++)
    2780             :   {
    2781         560 :     long res = ZM_equal(bnrgaloisapply(bnr,gel(M,i), H), H);
    2782         560 :     if (!res) return gc_long(av,0);
    2783             :   }
    2784          56 :   return gc_long(av,1);
    2785             : }
    2786             : 
    2787             : static GEN
    2788          14 : bnrlcmcond(GEN bnr1, GEN bnr2)
    2789             : {
    2790          14 :   GEN I1 = bnr_get_bid(bnr1), f1 = bid_get_fact(I1), a1 = bid_get_arch(I1);
    2791          14 :   GEN I2 = bnr_get_bid(bnr2), f2 = bid_get_fact(I2), a2 = bid_get_arch(I2);
    2792             :   GEN f, a;
    2793             :   long i, l;
    2794          14 :   if (!gidentical(bnr_get_nf(bnr1), bnr_get_nf(bnr2)))
    2795           0 :     pari_err_TYPE("bnrcompositum[different fields]", mkvec2(bnr1,bnr2));
    2796          14 :   f = merge_factor(f1, f2, (void*)&cmp_prime_ideal, &cmp_nodata);
    2797          14 :   a = cgetg_copy(a1, &l);
    2798          28 :   for (i = 1; i < l; i++)
    2799          14 :     gel(a,i) = (signe(gel(a1,i)) || signe(gel(a2,i)))? gen_1: gen_0;
    2800          14 :   return mkvec2(f, a);
    2801             : }
    2802             : /* H subgroup (of bnr.clgp) in HNF; lift to BNR */
    2803             : static GEN
    2804          28 : bnrliftsubgroup(GEN BNR, GEN bnr, GEN H)
    2805             : {
    2806          28 :   GEN E = gel(bnrsurjection(BNR, bnr), 1), K = kerint(shallowconcat(E, H));
    2807          28 :   return ZM_hnfmodid(rowslice(K, 1, lg(E)-1), bnr_get_cyc(BNR));
    2808             : }
    2809             : static GEN
    2810          14 : ZM_intersect(GEN A, GEN B)
    2811             : {
    2812          14 :   GEN K = kerint(shallowconcat(A, B));
    2813          14 :   return ZM_mul(A, rowslice(K, 1, lg(A)-1));
    2814             : }
    2815             : GEN
    2816          14 : bnrcompositum(GEN fH1, GEN fH2)
    2817             : {
    2818          14 :   pari_sp av = avma;
    2819             :   GEN bnr1, bnr2, bnr, H1, H2, H, n1, n2;
    2820          14 :   if (typ(fH1) != t_VEC || lg(fH2) != 3) pari_err_TYPE("bnrcompositum", fH1);
    2821          14 :   if (typ(fH2) != t_VEC || lg(fH2) != 3) pari_err_TYPE("bnrcompositum", fH2);
    2822          14 :   bnr1 = gel(fH1,1); if (!checkbnr_i(bnr1)) pari_err_TYPE("bnrcompositum",bnr1);
    2823          14 :   bnr2 = gel(fH2,1); if (!checkbnr_i(bnr2)) pari_err_TYPE("bnrcompositum",bnr2);
    2824          14 :   H1 = bnr_subgroup_check(bnr1, gel(fH1,2), &n1);
    2825          14 :   if (!H1) H1 = diagonal_shallow(bnr_get_cyc(bnr1));
    2826          14 :   H2 = bnr_subgroup_check(bnr2, gel(fH2,2), &n2);
    2827          14 :   if (!H2) H2 = diagonal_shallow(bnr_get_cyc(bnr2));
    2828          14 :   bnr = bnrinitmod(bnr_get_bnf(bnr1), bnrlcmcond(bnr1, bnr2), 0, lcmii(n1,n2));
    2829          14 :   H1 = bnrliftsubgroup(bnr, bnr1, H1);
    2830          14 :   H2 = bnrliftsubgroup(bnr, bnr2, H2);
    2831          14 :   H = ZM_intersect(H1, H2);
    2832          14 :   return gerepilecopy(av, mkvec2(bnr, ZM_hnfmodid(H, bnr_get_cyc(bnr))));
    2833             : }

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