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 - polarit3.c (source / functions) Hit Total Coverage
Test: PARI/GP v2.18.1 lcov report (development 30316-0578a48613) Lines: 1780 1982 89.8 %
Date: 2025-05-31 09:20:01 Functions: 191 205 93.2 %
Legend: Lines: hit not hit

          Line data    Source code
       1             : /* Copyright (C) 2000-2005  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             : /**               ARITHMETIC OPERATIONS ON POLYNOMIALS                **/
      18             : /**                         (third part)                              **/
      19             : /**                                                                   **/
      20             : /***********************************************************************/
      21             : #include "pari.h"
      22             : #include "paripriv.h"
      23             : 
      24             : #define DEBUGLEVEL DEBUGLEVEL_pol
      25             : 
      26             : /************************************************************************
      27             :  **                                                                    **
      28             :  **                      Ring membership                               **
      29             :  **                                                                    **
      30             :  ************************************************************************/
      31             : struct charact {
      32             :   GEN q;
      33             :   int isprime;
      34             : };
      35             : static void
      36        1225 : char_update_prime(struct charact *S, GEN p)
      37             : {
      38        1225 :   if (!S->isprime) { S->isprime = 1; S->q = p; }
      39        1225 :   if (!equalii(p, S->q)) pari_err_MODULUS("characteristic", S->q, p);
      40        1218 : }
      41             : static void
      42        6594 : char_update_int(struct charact *S, GEN n)
      43             : {
      44        6594 :   if (S->isprime)
      45             :   {
      46           7 :     if (dvdii(n, S->q)) return;
      47           7 :     pari_err_MODULUS("characteristic", S->q, n);
      48             :   }
      49        6587 :   S->q = gcdii(S->q, n);
      50             : }
      51             : static void
      52      179046 : charact(struct charact *S, GEN x)
      53             : {
      54      179046 :   const long tx = typ(x);
      55             :   long i, l;
      56      179046 :   switch(tx)
      57             :   {
      58        5145 :     case t_INTMOD:char_update_int(S, gel(x,1)); break;
      59        1134 :     case t_FFELT: char_update_prime(S, gel(x,4)); break;
      60       26761 :     case t_COMPLEX: case t_QUAD:
      61             :     case t_POLMOD: case t_POL: case t_SER: case t_RFRAC:
      62             :     case t_VEC: case t_COL: case t_MAT:
      63       26761 :       l = lg(x);
      64      178171 :       for (i=lontyp[tx]; i < l; i++) charact(S,gel(x,i));
      65       26747 :       break;
      66           7 :     case t_LIST:
      67           7 :       x = list_data(x);
      68           7 :       if (x) charact(S, x);
      69           7 :       break;
      70             :   }
      71      179018 : }
      72             : static void
      73        4739 : charact_res(struct charact *S, GEN x)
      74             : {
      75        4739 :   const long tx = typ(x);
      76             :   long i, l;
      77        4739 :   switch(tx)
      78             :   {
      79        1449 :     case t_INTMOD:char_update_int(S, gel(x,1)); break;
      80           0 :     case t_FFELT: char_update_prime(S, gel(x,4)); break;
      81          91 :     case t_PADIC: char_update_prime(S, padic_p(x)); break;
      82        1722 :     case t_COMPLEX: case t_QUAD:
      83             :     case t_POLMOD: case t_POL: case t_SER: case t_RFRAC:
      84             :     case t_VEC: case t_COL: case t_MAT:
      85        1722 :       l = lg(x);
      86        6132 :       for (i=lontyp[tx]; i < l; i++) charact_res(S,gel(x,i));
      87        1722 :       break;
      88           0 :     case t_LIST:
      89           0 :       x = list_data(x);
      90           0 :       if (x) charact_res(S, x);
      91           0 :       break;
      92             :   }
      93        4739 : }
      94             : GEN
      95       27622 : characteristic(GEN x)
      96             : {
      97             :   struct charact S;
      98       27622 :   S.q = gen_0; S.isprime = 0;
      99       27622 :   charact(&S, x); return S.q;
     100             : }
     101             : GEN
     102         329 : residual_characteristic(GEN x)
     103             : {
     104             :   struct charact S;
     105         329 :   S.q = gen_0; S.isprime = 0;
     106         329 :   charact_res(&S, x); return S.q;
     107             : }
     108             : 
     109             : int
     110    71020556 : Rg_is_Fp(GEN x, GEN *pp)
     111             : {
     112             :   GEN mod;
     113    71020556 :   switch(typ(x))
     114             :   {
     115     2482676 :   case t_INTMOD:
     116     2482676 :     mod = gel(x,1);
     117     2482676 :     if (!*pp) *pp = mod;
     118     2341976 :     else if (mod != *pp && !equalii(mod, *pp))
     119             :     {
     120           0 :       if (DEBUGLEVEL) pari_warn(warner,"different moduli in Rg_is_Fp");
     121           0 :       return 0;
     122             :     }
     123     2482676 :     return 1;
     124    57129405 :   case t_INT:
     125    57129405 :     return 1;
     126    11408475 :   default: return 0;
     127             :   }
     128             : }
     129             : 
     130             : int
     131    28180284 : RgX_is_FpX(GEN x, GEN *pp)
     132             : {
     133    28180284 :   long i, lx = lg(x);
     134    87766228 :   for (i=2; i<lx; i++)
     135    70994422 :     if (!Rg_is_Fp(gel(x, i), pp))
     136    11408470 :       return 0;
     137    16771806 :   return 1;
     138             : }
     139             : 
     140             : int
     141           0 : RgV_is_FpV(GEN x, GEN *pp)
     142             : {
     143           0 :   long i, lx = lg(x);
     144           0 :   for (i=1; i<lx; i++)
     145           0 :     if (!Rg_is_Fp(gel(x,i), pp)) return 0;
     146           0 :   return 1;
     147             : }
     148             : 
     149             : int
     150           0 : RgM_is_FpM(GEN x, GEN *pp)
     151             : {
     152           0 :   long i, lx = lg(x);
     153           0 :   for (i=1; i<lx; i++)
     154           0 :     if (!RgV_is_FpV(gel(x, i), pp)) return 0;
     155           0 :   return 1;
     156             : }
     157             : 
     158             : int
     159       60802 : Rg_is_FpXQ(GEN x, GEN *pT, GEN *pp)
     160             : {
     161             :   GEN pol, mod, p;
     162       60802 :   switch(typ(x))
     163             :   {
     164       26131 :   case t_INTMOD:
     165       26131 :     return Rg_is_Fp(x, pp);
     166        8561 :   case t_INT:
     167        8561 :     return 1;
     168          21 :   case t_POL:
     169          21 :     return RgX_is_FpX(x, pp);
     170       21350 :   case t_FFELT:
     171       21350 :     mod = x; p = FF_p_i(x);
     172       21350 :     if (!*pp) *pp = p;
     173       21350 :     if (!*pT) *pT = mod;
     174       19824 :     else if (typ(*pT)!=t_FFELT || !FF_samefield(*pT,mod))
     175             :     {
     176          42 :       if (DEBUGLEVEL) pari_warn(warner,"different moduli in Rg_is_FpXQ");
     177          42 :       return 0;
     178             :     }
     179       21308 :     return 1;
     180        4585 :   case t_POLMOD:
     181        4585 :     mod = gel(x,1); pol = gel(x, 2);
     182        4585 :     if (!RgX_is_FpX(mod, pp)) return 0;
     183        4585 :     if (typ(pol)==t_POL)
     184             :     {
     185        4578 :       if (!RgX_is_FpX(pol, pp)) return 0;
     186             :     }
     187           7 :     else if (!Rg_is_Fp(pol, pp)) return 0;
     188        4585 :     if (!*pT) *pT = mod;
     189        4431 :     else if (mod != *pT && !gequal(mod, *pT))
     190             :     {
     191           0 :       if (DEBUGLEVEL) pari_warn(warner,"different moduli in Rg_is_FpXQ");
     192           0 :       return 0;
     193             :     }
     194        4585 :     return 1;
     195             : 
     196         154 :   default: return 0;
     197             :   }
     198             : }
     199             : 
     200             : int
     201        3381 : RgX_is_FpXQX(GEN x, GEN *pT, GEN *pp)
     202             : {
     203        3381 :   long i, lx = lg(x);
     204       63427 :   for (i = 2; i < lx; i++)
     205       60144 :     if (!Rg_is_FpXQ(gel(x,i), pT, pp)) return 0;
     206        3283 :   return 1;
     207             : }
     208             : 
     209             : /************************************************************************
     210             :  **                                                                    **
     211             :  **                      Ring conversion                               **
     212             :  **                                                                    **
     213             :  ************************************************************************/
     214             : 
     215             : /* p > 0 a t_INT, return lift(x * Mod(1,p)).
     216             :  * If x is an INTMOD, assume modulus is a multiple of p. */
     217             : GEN
     218    52285018 : Rg_to_Fp(GEN x, GEN p)
     219             : {
     220    52285018 :   if (lgefint(p) == 3) return utoi(Rg_to_Fl(x, uel(p,2)));
     221     4555004 :   switch(typ(x))
     222             :   {
     223      288479 :     case t_INT: return modii(x, p);
     224       18790 :     case t_FRAC: {
     225       18790 :       pari_sp av = avma;
     226       18790 :       GEN z = modii(gel(x,1), p);
     227       18790 :       if (z == gen_0) return gen_0;
     228       18785 :       return gc_INT(av, remii(mulii(z, Fp_inv(gel(x,2), p)), p));
     229             :     }
     230          70 :     case t_PADIC: return padic_to_Fp(x, p);
     231     4247668 :     case t_INTMOD: {
     232     4247668 :       GEN q = gel(x,1), a = gel(x,2);
     233     4247668 :       if (equalii(q, p)) return icopy(a);
     234          14 :       if (!dvdii(q,p)) pari_err_MODULUS("Rg_to_Fp", q, p);
     235           0 :       return remii(a, p);
     236             :     }
     237           0 :     default: pari_err_TYPE("Rg_to_Fp",x);
     238             :       return NULL; /* LCOV_EXCL_LINE */
     239             :   }
     240             : }
     241             : /* If x is a POLMOD, assume modulus is a multiple of T. */
     242             : GEN
     243     1291958 : Rg_to_FpXQ(GEN x, GEN T, GEN p)
     244             : {
     245     1291958 :   long ta, tx = typ(x), v = get_FpX_var(T);
     246             :   GEN a, b;
     247     1291958 :   if (is_const_t(tx))
     248             :   {
     249       59175 :     if (tx == t_FFELT)
     250             :     {
     251       17355 :       GEN z = FF_to_FpXQ(x);
     252       17355 :       setvarn(z, v);
     253       17355 :       return z;
     254             :     }
     255       41820 :     return scalar_ZX(degpol(T)? Rg_to_Fp(x, p): gen_0, v);
     256             :   }
     257     1232783 :   switch(tx)
     258             :   {
     259     1230676 :     case t_POLMOD:
     260     1230676 :       b = gel(x,1);
     261     1230676 :       a = gel(x,2); ta = typ(a);
     262     1230676 :       if (is_const_t(ta))
     263        3885 :         return scalar_ZX(degpol(T)? Rg_to_Fp(a, p): gen_0, v);
     264     1226791 :       b = RgX_to_FpX(b, p); if (varn(b) != v) break;
     265     1226791 :       a = RgX_to_FpX(a, p);
     266     1226791 :       if (ZX_equal(b,get_FpX_mod(T)) || signe(FpX_rem(b,T,p))==0)
     267     1226791 :         return FpX_rem(a, T, p);
     268           0 :       break;
     269        2107 :     case t_POL:
     270        2107 :       if (varn(x) != v) break;
     271        2100 :       return FpX_rem(RgX_to_FpX(x,p), T, p);
     272           0 :     case t_RFRAC:
     273           0 :       a = Rg_to_FpXQ(gel(x,1), T,p);
     274           0 :       b = Rg_to_FpXQ(gel(x,2), T,p);
     275           0 :       return FpXQ_div(a,b, T,p);
     276             :   }
     277           7 :   pari_err_TYPE("Rg_to_FpXQ",x);
     278             :   return NULL; /* LCOV_EXCL_LINE */
     279             : }
     280             : GEN
     281     3335006 : RgX_to_FpX(GEN x, GEN p)
     282             : {
     283             :   long i, l;
     284     3335006 :   GEN z = cgetg_copy(x, &l); z[1] = x[1];
     285    14762943 :   for (i = 2; i < l; i++) gel(z,i) = Rg_to_Fp(gel(x,i), p);
     286     3335006 :   return FpX_renormalize(z, l);
     287             : }
     288             : 
     289             : GEN
     290         140 : RgV_to_FpV(GEN x, GEN p)
     291         483 : { pari_APPLY_type(t_VEC, Rg_to_Fp(gel(x,i), p)) }
     292             : 
     293             : GEN
     294     1751090 : RgC_to_FpC(GEN x, GEN p)
     295    28499485 : { pari_APPLY_type(t_COL, Rg_to_Fp(gel(x,i), p)) }
     296             : 
     297             : GEN
     298      222349 : RgM_to_FpM(GEN x, GEN p)
     299     1973397 : { pari_APPLY_same(RgC_to_FpC(gel(x,i), p)) }
     300             : 
     301             : GEN
     302      369001 : RgV_to_Flv(GEN x, ulong p)
     303     1676894 : { pari_APPLY_ulong(Rg_to_Fl(gel(x,i), p)) }
     304             : 
     305             : GEN
     306      118296 : RgM_to_Flm(GEN x, ulong p)
     307      422998 : { pari_APPLY_same(RgV_to_Flv(gel(x,i), p)) }
     308             : 
     309             : GEN
     310        5098 : RgX_to_FpXQX(GEN x, GEN T, GEN p)
     311             : {
     312        5098 :   long i, l = lg(x);
     313        5098 :   GEN z = cgetg(l, t_POL); z[1] = x[1];
     314       43366 :   for (i = 2; i < l; i++) gel(z,i) = Rg_to_FpXQ(gel(x,i), T,p);
     315        5098 :   return FpXQX_renormalize(z, l);
     316             : }
     317             : GEN
     318       49186 : RgX_to_FqX(GEN x, GEN T, GEN p)
     319             : {
     320       49186 :   long i, l = lg(x);
     321       49186 :   GEN z = cgetg(l, t_POL); z[1] = x[1];
     322       49186 :   if (T)
     323       10990 :     for (i = 2; i < l; i++) gel(z,i) = Rg_to_FpXQ(gel(x,i), T, p);
     324             :   else
     325      791394 :     for (i = 2; i < l; i++) gel(z,i) = Rg_to_Fp(gel(x,i), p);
     326       49186 :   return FpXQX_renormalize(z, l);
     327             : }
     328             : 
     329             : GEN
     330      219128 : RgC_to_FqC(GEN x, GEN T, GEN p)
     331             : {
     332      219128 :   long i, l = lg(x);
     333      219128 :   GEN z = cgetg(l, t_COL);
     334      219128 :   if (T)
     335     1430310 :     for (i = 1; i < l; i++) gel(z,i) = Rg_to_FpXQ(gel(x,i), T, p);
     336             :   else
     337           0 :     for (i = 1; i < l; i++) gel(z,i) = Rg_to_Fp(gel(x,i), p);
     338      219128 :   return z;
     339             : }
     340             : 
     341             : GEN
     342       52325 : RgM_to_FqM(GEN x, GEN T, GEN p)
     343      271418 : { pari_APPLY_same(RgC_to_FqC(gel(x, i), T, p)) }
     344             : 
     345             : /* lg(V) > 1 */
     346             : GEN
     347      851487 : FpXV_FpC_mul(GEN V, GEN W, GEN p)
     348             : {
     349      851487 :   pari_sp av = avma;
     350      851487 :   long i, l = lg(V);
     351      851487 :   GEN z = ZX_Z_mul(gel(V,1),gel(W,1));
     352     4201029 :   for(i=2; i<l; i++)
     353             :   {
     354     3349542 :     z = ZX_add(z, ZX_Z_mul(gel(V,i),gel(W,i)));
     355     3349542 :     if ((i & 7) == 0) z = gc_upto(av, z);
     356             :   }
     357      851487 :   return gc_upto(av, FpX_red(z,p));
     358             : }
     359             : 
     360             : GEN
     361       55832 : FqX_Fq_add(GEN y, GEN x, GEN T, GEN p)
     362             : {
     363       55832 :   long i, lz = lg(y);
     364             :   GEN z;
     365       55832 :   if (!T) return FpX_Fp_add(y, x, p);
     366        8666 :   if (lz == 2) return scalarpol(x, varn(y));
     367        7952 :   z = cgetg(lz,t_POL); z[1] = y[1];
     368        7952 :   gel(z,2) = Fq_add(gel(y,2),x, T, p);
     369        7952 :   if (lz == 3) z = FpXX_renormalize(z,lz);
     370             :   else
     371       33145 :     for(i=3;i<lz;i++) gel(z,i) = gcopy(gel(y,i));
     372        7952 :   return z;
     373             : }
     374             : 
     375             : GEN
     376        1059 : FqX_Fq_sub(GEN y, GEN x, GEN T, GEN p)
     377             : {
     378        1059 :   long i, lz = lg(y);
     379             :   GEN z;
     380        1059 :   if (!T) return FpX_Fp_sub(y, x, p);
     381        1059 :   if (lz == 2) return scalarpol(x, varn(y));
     382        1059 :   z = cgetg(lz,t_POL); z[1] = y[1];
     383        1059 :   gel(z,2) = Fq_sub(gel(y,2), x, T, p);
     384        1059 :   if (lz == 3) z = FpXX_renormalize(z,lz);
     385             :   else
     386       10278 :     for(i=3;i<lz;i++) gel(z,i) = gcopy(gel(y,i));
     387        1059 :   return z;
     388             : }
     389             : 
     390             : GEN
     391      149052 : FqX_Fq_mul_to_monic(GEN P, GEN U, GEN T, GEN p)
     392             : {
     393             :   long i, lP;
     394      149052 :   GEN res = cgetg_copy(P, &lP); res[1] = P[1];
     395      918799 :   for(i=2; i<lP-1; i++) gel(res,i) = Fq_mul(U,gel(P,i), T,p);
     396      149052 :   gel(res,lP-1) = gen_1; return res;
     397             : }
     398             : 
     399             : GEN
     400       38189 : FpXQX_normalize(GEN z, GEN T, GEN p)
     401             : {
     402             :   GEN lc;
     403       38189 :   if (lg(z) == 2) return z;
     404       38175 :   lc = leading_coeff(z);
     405       38175 :   if (typ(lc) == t_POL)
     406             :   {
     407        2167 :     if (lg(lc) > 3) /* nonconstant */
     408        1902 :       return FqX_Fq_mul_to_monic(z, Fq_inv(lc,T,p), T,p);
     409             :     /* constant */
     410         265 :     lc = gel(lc,2);
     411         265 :     z = shallowcopy(z);
     412         265 :     gel(z, lg(z)-1) = lc;
     413             :   }
     414             :   /* lc a t_INT */
     415       36273 :   if (equali1(lc)) return z;
     416          87 :   return FqX_Fq_mul_to_monic(z, Fp_inv(lc,p), T,p);
     417             : }
     418             : 
     419             : GEN
     420      390935 : FqX_eval(GEN x, GEN y, GEN T, GEN p)
     421             : {
     422             :   pari_sp av;
     423             :   GEN p1, r;
     424      390935 :   long j, i=lg(x)-1;
     425      390935 :   if (i<=2)
     426       45107 :     return (i==2)? Fq_red(gel(x,2), T, p): gen_0;
     427      345828 :   av=avma; p1=gel(x,i);
     428             :   /* specific attention to sparse polynomials (see poleval)*/
     429             :   /*You've guessed it! It's a copy-paste(tm)*/
     430     1150444 :   for (i--; i>=2; i=j-1)
     431             :   {
     432      805304 :     for (j=i; !signe(gel(x,j)); j--)
     433         686 :       if (j==2)
     434             :       {
     435         490 :         if (i!=j) y = Fq_pow(y,utoipos(i-j+1), T, p);
     436         490 :         return gc_upto(av, Fq_mul(p1,y, T, p));
     437             :       }
     438      804618 :     r = (i==j)? y: Fq_pow(y, utoipos(i-j+1), T, p);
     439      804618 :     p1 = Fq_add(Fq_mul(p1,r,T,p), gel(x,j), T, p);
     440             :   }
     441      345336 :   return gc_upto(av, p1);
     442             : }
     443             : 
     444             : GEN
     445       97321 : FqXY_evalx(GEN Q, GEN x, GEN T, GEN p)
     446             : {
     447       97321 :   long i, lb = lg(Q);
     448             :   GEN z;
     449       97321 :   if (!T) return FpXY_evalx(Q, x, p);
     450       86961 :   z = cgetg(lb, t_POL); z[1] = Q[1];
     451      462945 :   for (i=2; i<lb; i++)
     452             :   {
     453      375984 :     GEN q = gel(Q,i);
     454      375984 :     gel(z,i) = typ(q) == t_INT? modii(q,p): FqX_eval(q, x, T, p);
     455             :   }
     456       86961 :   return FpXQX_renormalize(z, lb);
     457             : }
     458             : 
     459             : /* Q an FpXY, evaluate at (X,Y) = (x,y) */
     460             : GEN
     461       14623 : FqXY_eval(GEN Q, GEN y, GEN x, GEN T, GEN p)
     462             : {
     463       14623 :   pari_sp av = avma;
     464       14623 :   if (!T) return FpXY_eval(Q, y, x, p);
     465         966 :   return gc_upto(av, FqX_eval(FqXY_evalx(Q, x, T, p), y, T, p));
     466             : }
     467             : 
     468             : /* a X^d */
     469             : GEN
     470    13104914 : monomial(GEN a, long d, long v)
     471             : {
     472             :   long i, n;
     473             :   GEN P;
     474    13104914 :   if (d < 0) {
     475          14 :     if (isrationalzero(a)) return pol_0(v);
     476          14 :     retmkrfrac(a, pol_xn(-d, v));
     477             :   }
     478    13104900 :   if (gequal0(a))
     479             :   {
     480       93989 :     if (isexactzero(a)) return scalarpol_shallow(a,v);
     481           0 :     n = d+2; P = cgetg(n+1, t_POL);
     482           0 :     P[1] = evalsigne(0) | evalvarn(v);
     483             :   }
     484             :   else
     485             :   {
     486    13010909 :     n = d+2; P = cgetg(n+1, t_POL);
     487    13010911 :     P[1] = evalsigne(1) | evalvarn(v);
     488             :   }
     489    32179365 :   for (i = 2; i < n; i++) gel(P,i) = gen_0;
     490    13010911 :   gel(P,i) = a; return P;
     491             : }
     492             : GEN
     493      157969 : monomialcopy(GEN a, long d, long v)
     494             : {
     495             :   long i, n;
     496             :   GEN P;
     497      157969 :   if (d < 0) {
     498          14 :     if (isrationalzero(a)) return pol_0(v);
     499          14 :     retmkrfrac(gcopy(a), pol_xn(-d, v));
     500             :   }
     501      157955 :   if (gequal0(a))
     502             :   {
     503          14 :     if (isexactzero(a)) return scalarpol(a,v);
     504           7 :     n = d+2; P = cgetg(n+1, t_POL);
     505           7 :     P[1] = evalsigne(0) | evalvarn(v);
     506             :   }
     507             :   else
     508             :   {
     509      157941 :     n = d+2; P = cgetg(n+1, t_POL);
     510      157941 :     P[1] = evalsigne(1) | evalvarn(v);
     511             :   }
     512      314678 :   for (i = 2; i < n; i++) gel(P,i) = gen_0;
     513      157948 :   gel(P,i) = gcopy(a); return P;
     514             : }
     515             : GEN
     516      325824 : pol_x_powers(long N, long v)
     517             : {
     518      325824 :   GEN L = cgetg(N+1,t_VEC);
     519             :   long i;
     520      788717 :   for (i=1; i<=N; i++) gel(L,i) = pol_xn(i-1, v);
     521      325827 :   return L;
     522             : }
     523             : 
     524             : GEN
     525           0 : FqXQ_powers(GEN x, long l, GEN S, GEN T, GEN p)
     526             : {
     527           0 :   return T ? FpXQXQ_powers(x, l, S, T, p): FpXQ_powers(x, l, S, p);
     528             : }
     529             : 
     530             : GEN
     531           0 : FqXQ_matrix_pow(GEN y, long n, long m, GEN S, GEN T, GEN p)
     532             : {
     533           0 :   return T ? FpXQXQ_matrix_pow(y, n, m, S, T, p): FpXQ_matrix_pow(y, n, m, S, p);
     534             : }
     535             : 
     536             : /*******************************************************************/
     537             : /*                                                                 */
     538             : /*                             Fq                                  */
     539             : /*                                                                 */
     540             : /*******************************************************************/
     541             : 
     542             : GEN
     543    11592874 : Fq_add(GEN x, GEN y, GEN T/*unused*/, GEN p)
     544             : {
     545             :   (void)T;
     546    11592874 :   switch((typ(x)==t_POL)|((typ(y)==t_POL)<<1))
     547             :   {
     548     1143687 :     case 0: return Fp_add(x,y,p);
     549      748136 :     case 1: return FpX_Fp_add(x,y,p);
     550       91991 :     case 2: return FpX_Fp_add(y,x,p);
     551     9609060 :     case 3: return FpX_add(x,y,p);
     552             :   }
     553             :   return NULL;/*LCOV_EXCL_LINE*/
     554             : }
     555             : 
     556             : GEN
     557     8562688 : Fq_sub(GEN x, GEN y, GEN T/*unused*/, GEN p)
     558             : {
     559             :   (void)T;
     560     8562688 :   switch((typ(x)==t_POL)|((typ(y)==t_POL)<<1))
     561             :   {
     562      255995 :     case 0: return Fp_sub(x,y,p);
     563       24540 :     case 1: return FpX_Fp_sub(x,y,p);
     564       23896 :     case 2: return Fp_FpX_sub(x,y,p);
     565     8258257 :     case 3: return FpX_sub(x,y,p);
     566             :   }
     567             :   return NULL;/*LCOV_EXCL_LINE*/
     568             : }
     569             : 
     570             : GEN
     571     1079556 : Fq_neg(GEN x, GEN T/*unused*/, GEN p)
     572             : {
     573             :   (void)T;
     574     1079556 :   return (typ(x)==t_POL)? FpX_neg(x,p): Fp_neg(x,p);
     575             : }
     576             : 
     577             : GEN
     578       81354 : Fq_halve(GEN x, GEN T/*unused*/, GEN p)
     579             : {
     580             :   (void)T;
     581       81354 :   return (typ(x)==t_POL)? FpX_halve(x,p): Fp_halve(x,p);
     582             : }
     583             : 
     584             : /* If T==NULL do not reduce*/
     585             : GEN
     586     8608648 : Fq_mul(GEN x, GEN y, GEN T, GEN p)
     587             : {
     588     8608648 :   switch((typ(x)==t_POL)|((typ(y)==t_POL)<<1))
     589             :   {
     590     1037917 :     case 0: return Fp_mul(x,y,p);
     591      128565 :     case 1: return FpX_Fp_mul(x,y,p);
     592      394686 :     case 2: return FpX_Fp_mul(y,x,p);
     593     7047481 :     case 3: if (T) return FpXQ_mul(x,y,T,p);
     594     4478770 :             else return FpX_mul(x,y,p);
     595             :   }
     596             :   return NULL;/*LCOV_EXCL_LINE*/
     597             : }
     598             : 
     599             : /* If T==NULL do not reduce*/
     600             : GEN
     601      490555 : Fq_mulu(GEN x, ulong y, /*unused*/GEN T, GEN p)
     602             : {
     603             :   (void) T;
     604      490555 :   return typ(x)==t_POL ? FpX_Fp_mul(x,utoi(y),p): Fp_mulu(x, y, p);
     605             : }
     606             : 
     607             : /* y t_INT */
     608             : GEN
     609       43929 : Fq_Fp_mul(GEN x, GEN y, GEN T/*unused*/, GEN p)
     610             : {
     611             :   (void)T;
     612        6822 :   return (typ(x) == t_POL)? FpX_Fp_mul(x,y,p)
     613       50751 :                           : Fp_mul(x,y,p);
     614             : }
     615             : /* If T==NULL do not reduce*/
     616             : GEN
     617      611173 : Fq_sqr(GEN x, GEN T, GEN p)
     618             : {
     619      611173 :   if (typ(x) == t_POL)
     620             :   {
     621       70585 :     if (T) return FpXQ_sqr(x,T,p);
     622           0 :     else return FpX_sqr(x,p);
     623             :   }
     624             :   else
     625      540588 :     return Fp_sqr(x,p);
     626             : }
     627             : 
     628             : GEN
     629           0 : Fq_neg_inv(GEN x, GEN T, GEN p)
     630             : {
     631           0 :   if (typ(x) == t_INT) return Fp_inv(Fp_neg(x,p),p);
     632           0 :   return FpXQ_inv(FpX_neg(x,p),T,p);
     633             : }
     634             : 
     635             : GEN
     636           0 : Fq_invsafe(GEN x, GEN pol, GEN p)
     637             : {
     638           0 :   if (typ(x) == t_INT) return Fp_invsafe(x,p);
     639           0 :   return FpXQ_invsafe(x,pol,p);
     640             : }
     641             : 
     642             : GEN
     643       89311 : Fq_inv(GEN x, GEN pol, GEN p)
     644             : {
     645       89311 :   if (typ(x) == t_INT) return Fp_inv(x,p);
     646       81545 :   return FpXQ_inv(x,pol,p);
     647             : }
     648             : 
     649             : GEN
     650      343791 : Fq_div(GEN x, GEN y, GEN pol, GEN p)
     651             : {
     652      343791 :   switch((typ(x)==t_POL)|((typ(y)==t_POL)<<1))
     653             :   {
     654      318402 :     case 0: return Fp_div(x,y,p);
     655       16702 :     case 1: return FpX_Fp_div(x,y,p);
     656         406 :     case 2: return FpX_Fp_mul(FpXQ_inv(y,pol,p),x,p);
     657        8281 :     case 3: return FpXQ_div(x,y,pol,p);
     658             :   }
     659             :   return NULL;/*LCOV_EXCL_LINE*/
     660             : }
     661             : 
     662             : GEN
     663      795544 : Fq_pow(GEN x, GEN n, GEN pol, GEN p)
     664             : {
     665      795544 :   if (typ(x) == t_INT) return Fp_pow(x,n,p);
     666      136711 :   return FpXQ_pow(x,n,pol,p);
     667             : }
     668             : 
     669             : GEN
     670       15050 : Fq_powu(GEN x, ulong n, GEN pol, GEN p)
     671             : {
     672       15050 :   if (typ(x) == t_INT) return Fp_powu(x,n,p);
     673        1267 :   return FpXQ_powu(x,n,pol,p);
     674             : }
     675             : 
     676             : GEN
     677     1892926 : Fq_sqrt(GEN x, GEN T, GEN p)
     678             : {
     679     1892926 :   if (typ(x) == t_INT)
     680             :   {
     681     1825064 :     if (!T || odd(get_FpX_degree(T))) return Fp_sqrt(x,p);
     682        9621 :     x = scalarpol_shallow(x, get_FpX_var(T));
     683             :   }
     684       77483 :   return FpXQ_sqrt(x,T,p);
     685             : }
     686             : GEN
     687      170786 : Fq_sqrtn(GEN x, GEN n, GEN T, GEN p, GEN *zeta)
     688             : {
     689      170786 :   if (typ(x) == t_INT)
     690             :   {
     691             :     long d;
     692      170415 :     if (!T) return Fp_sqrtn(x,n,p,zeta);
     693         126 :     d = get_FpX_degree(T);
     694         126 :     if (ugcdiu(n,d) == 1)
     695             :     {
     696          56 :       if (!zeta) return Fp_sqrtn(x,n,p,NULL);
     697             :       /* gcd(n,p-1)=gcd(n,q-1): same number of solutions in Fp and F_q */
     698          21 :       if (equalii(gcdii(subiu(p,1),n), gcdii(subiu(Fp_powu(p,d,n), 1), n)))
     699          14 :         return Fp_sqrtn(x,n,p,zeta);
     700             :     }
     701          77 :     x = scalarpol(x, get_FpX_var(T)); /* left on stack */
     702             :   }
     703         448 :   return FpXQ_sqrtn(x,n,T,p,zeta);
     704             : }
     705             : 
     706             : struct _Fq_field
     707             : {
     708             :   GEN T, p;
     709             : };
     710             : 
     711             : static GEN
     712      303247 : _Fq_red(void *E, GEN x)
     713      303247 : { struct _Fq_field *s = (struct _Fq_field *)E;
     714      303247 :   return Fq_red(x, s->T, s->p);
     715             : }
     716             : 
     717             : static GEN
     718      362523 : _Fq_add(void *E, GEN x, GEN y)
     719             : {
     720             :   (void) E;
     721      362523 :   switch((typ(x)==t_POL)|((typ(y)==t_POL)<<1))
     722             :   {
     723          14 :     case 0: return addii(x,y);
     724           0 :     case 1: return ZX_Z_add(x,y);
     725       15918 :     case 2: return ZX_Z_add(y,x);
     726      346591 :     default: return ZX_add(x,y);
     727             :   }
     728             : }
     729             : 
     730             : static GEN
     731      315028 : _Fq_neg(void *E, GEN x) { (void) E; return typ(x)==t_POL?ZX_neg(x):negi(x); }
     732             : 
     733             : static GEN
     734      243341 : _Fq_mul(void *E, GEN x, GEN y)
     735             : {
     736             :   (void) E;
     737      243341 :   switch((typ(x)==t_POL)|((typ(y)==t_POL)<<1))
     738             :   {
     739         679 :     case 0: return mulii(x,y);
     740        1085 :     case 1: return ZX_Z_mul(x,y);
     741        1043 :     case 2: return ZX_Z_mul(y,x);
     742      240534 :     default: return ZX_mul(x,y);
     743             :   }
     744             : }
     745             : 
     746             : static GEN
     747        9331 : _Fq_inv(void *E, GEN x)
     748        9331 : { struct _Fq_field *s = (struct _Fq_field *)E;
     749        9331 :   return Fq_inv(x,s->T,s->p);
     750             : }
     751             : 
     752             : static int
     753       38388 : _Fq_equal0(GEN x) { return signe(x)==0; }
     754             : 
     755             : static GEN
     756        4151 : _Fq_s(void *E, long x) { (void) E; return stoi(x); }
     757             : 
     758             : static const struct bb_field Fq_field={_Fq_red,_Fq_add,_Fq_mul,_Fq_neg,
     759             :                                        _Fq_inv,_Fq_equal0,_Fq_s};
     760             : 
     761        4725 : const struct bb_field *get_Fq_field(void **E, GEN T, GEN p)
     762             : {
     763        4725 :   if (!T)
     764           0 :     return get_Fp_field(E, p);
     765             :   else
     766             :   {
     767        4725 :     GEN z = new_chunk(sizeof(struct _Fq_field));
     768        4725 :     struct _Fq_field *e = (struct _Fq_field *) z;
     769        4725 :     e->T = T; e->p  = p; *E = (void*)e;
     770        4725 :     return &Fq_field;
     771             :   }
     772             : }
     773             : 
     774             : /*******************************************************************/
     775             : /*                                                                 */
     776             : /*                             Fq[X]                               */
     777             : /*                                                                 */
     778             : /*******************************************************************/
     779             : /* P(X + c) */
     780             : static GEN
     781         434 : Fp_XpN_powu(GEN u, long n, GEN p, long v)
     782             : {
     783             :   pari_sp av;
     784             :   long k;
     785             :   GEN B, C, V;
     786         434 :   if (!n) return pol_1(v);
     787         434 :   if (is_pm1(u))
     788         434 :     return Xpm1_powu(n, signe(u), v);
     789           0 :   av = avma;
     790           0 :   V = Fp_powers(u, n, p);
     791           0 :   B = FpV_red(vecbinomial(n), p);
     792           0 :   C = cgetg(n+3, t_POL);
     793           0 :   C[1] = evalsigne(1)| evalvarn(v);
     794           0 :   for (k=1; k <= n+1; k++)
     795           0 :     gel(C,k+1) = Fp_mul(gel(V,n+2-k), gel(B,k), p);
     796           0 :   return gc_upto(av, C);
     797             : }
     798             : 
     799             : static GEN
     800         700 : FpX_translate_basecase(GEN P, GEN c, GEN p)
     801             : {
     802         700 :   pari_sp av = avma;
     803             :   GEN Q, *R;
     804             :   long i, k, n;
     805             : 
     806         700 :   if (!signe(P) || !signe(c)) return ZX_copy(P);
     807         560 :   Q = leafcopy(P);
     808         560 :   R = (GEN*)(Q+2); n = degpol(P);
     809        1316 :   for (i=1; i<=n; i++)
     810             :   {
     811        2016 :     for (k=n-i; k<n; k++)
     812        1260 :       R[k] = Fp_add(R[k], Fp_mul(c, R[k+1], p), p);
     813             : 
     814         756 :     if (gc_needed(av,2))
     815             :     {
     816           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"FpX_translate, i = %ld/%ld", i,n);
     817           0 :       Q = gc_GEN(av, Q); R = (GEN*)Q+2;
     818             :     }
     819             :   }
     820         560 :   return gc_GEN(av, FpX_renormalize(Q, lg(Q)));
     821             : }
     822             : 
     823             : GEN
     824        1134 : FpX_translate(GEN P, GEN c, GEN p)
     825             : {
     826        1134 :   pari_sp av = avma;
     827        1134 :   long n = degpol(P);
     828        1134 :   if (n<=3 || 25*(n-3) < expi(p))
     829         700 :     return FpX_translate_basecase(P, c, p);
     830             :   else
     831             :   {
     832         434 :     long d = n >> 1;
     833         434 :     GEN Q = FpX_translate(RgX_shift_shallow(P, -d), c, p);
     834         434 :     GEN R = FpX_translate(RgXn_red_shallow(P, d), c, p);
     835         434 :     GEN S = Fp_XpN_powu(c, d, p, varn(P));
     836         434 :     return gc_upto(av, FpX_add(FpX_mul(Q, S, p), R, p));
     837             :   }
     838             : }
     839             : 
     840             : /* P(X + c), c an Fq */
     841             : GEN
     842       33880 : FqX_translate(GEN P, GEN c, GEN T, GEN p)
     843             : {
     844       33880 :   pari_sp av = avma;
     845             :   GEN Q, *R;
     846             :   long i, k, n;
     847             : 
     848             :   /* signe works for t_(INT|POL) */
     849       33880 :   if (!signe(P) || !signe(c)) return RgX_copy(P);
     850       33880 :   Q = leafcopy(P);
     851       33880 :   R = (GEN*)(Q+2); n = degpol(P);
     852      150059 :   for (i=1; i<=n; i++)
     853             :   {
     854      433559 :     for (k=n-i; k<n; k++)
     855      317380 :       R[k] = Fq_add(R[k], Fq_mul(c, R[k+1], T, p), T, p);
     856             : 
     857      116179 :     if (gc_needed(av,2))
     858             :     {
     859           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"FqX_translate, i = %ld/%ld", i,n);
     860           0 :       Q = gc_GEN(av, Q); R = (GEN*)Q+2;
     861             :     }
     862             :   }
     863       33880 :   return gc_GEN(av, FpXQX_renormalize(Q, lg(Q)));
     864             : }
     865             : 
     866             : GEN
     867       40452 : FqV_roots_to_pol(GEN V, GEN T, GEN p, long v)
     868             : {
     869       40452 :   pari_sp ltop = avma;
     870             :   long k;
     871             :   GEN W;
     872       40452 :   if (lgefint(p) == 3)
     873             :   {
     874       31741 :     ulong pp = p[2];
     875       31741 :     GEN Tl = ZX_to_Flx(T, pp);
     876       31744 :     GEN Vl = FqC_to_FlxqC(V, Tl, pp);
     877       31745 :     Tl = FlxqV_roots_to_pol(Vl, Tl, pp, v);
     878       31746 :     return gc_upto(ltop, FlxX_to_ZXX(Tl));
     879             :   }
     880        8711 :   W = cgetg(lg(V),t_VEC);
     881       78117 :   for(k=1; k < lg(V); k++)
     882       69406 :     gel(W,k) = deg1pol_shallow(gen_1,Fq_neg(gel(V,k),T,p),v);
     883        8711 :   return gc_upto(ltop, FpXQXV_prod(W, T, p));
     884             : }
     885             : 
     886             : GEN
     887      109459 : FqV_red(GEN x, GEN T, GEN p)
     888      778238 : { pari_APPLY_type(t_VEC, Fq_red(gel(x,i), T, p)) }
     889             : 
     890             : GEN
     891       24058 : FqC_red(GEN x, GEN T, GEN p)
     892      163384 : { pari_APPLY_type(t_COL, Fq_red(gel(x,i), T, p)) }
     893             : 
     894             : GEN
     895        1701 : FqM_red(GEN x, GEN T, GEN p)
     896        5411 : { pari_APPLY_same(FqC_red(gel(x,i), T, p)) }
     897             : 
     898             : GEN
     899           0 : FqC_add(GEN x, GEN y, GEN T, GEN p)
     900             : {
     901           0 :   if (!T) return FpC_add(x, y, p);
     902           0 :   pari_APPLY_type(t_COL, Fq_add(gel(x,i), gel(y,i), T, p))
     903             : }
     904             : 
     905             : GEN
     906           0 : FqC_sub(GEN x, GEN y, GEN T, GEN p)
     907             : {
     908           0 :   if (!T) return FpC_sub(x, y, p);
     909           0 :   pari_APPLY_type(t_COL, Fq_sub(gel(x,i), gel(y,i), T, p))
     910             : }
     911             : 
     912             : GEN
     913           0 : FqC_Fq_mul(GEN x, GEN y, GEN T, GEN p)
     914             : {
     915           0 :   if (!T) return FpC_Fp_mul(x, y, p);
     916           0 :   pari_APPLY_type(t_COL, Fq_mul(gel(x,i),y,T,p))
     917             : }
     918             : 
     919             : GEN
     920         105 : FqC_FqV_mul(GEN x, GEN y, GEN T, GEN p)
     921             : {
     922         105 :   long i,j, lx=lg(x), ly=lg(y);
     923             :   GEN z;
     924         105 :   if (ly==1) return cgetg(1,t_MAT);
     925         105 :   z = cgetg(ly,t_MAT);
     926         819 :   for (j=1; j < ly; j++)
     927             :   {
     928         714 :     GEN zj = cgetg(lx,t_COL);
     929        4200 :     for (i=1; i<lx; i++) gel(zj,i) = Fq_mul(gel(x,i),gel(y,j), T, p);
     930         714 :     gel(z, j) = zj;
     931             :   }
     932         105 :   return z;
     933             : }
     934             : 
     935             : GEN
     936        5467 : FpXC_center(GEN x, GEN p, GEN pov2)
     937       41476 : { pari_APPLY_type(t_COL, FpX_center(gel(x,i), p, pov2)) }
     938             : 
     939             : GEN
     940      109021 : FqC_to_FlxqC(GEN x, GEN T, ulong p)
     941      109021 : { long sv = get_Flx_var(T);
     942     4834755 :   pari_APPLY_type(t_COL,typ(gel(x,i))==t_INT ?
     943             :                   Z_to_Flx(gel(x,i), p, sv): ZX_to_Flx(gel(x,i), p)) }
     944             : 
     945             : GEN
     946        8708 : FqM_to_FlxqM(GEN x, GEN T, ulong p)
     947       85985 : { pari_APPLY_same(FqC_to_FlxqC(gel(x,i), T, p)) }
     948             : 
     949             : GEN
     950        1800 : FpXM_center(GEN x, GEN p, GEN pov2)
     951        7267 : { pari_APPLY_same(FpXC_center(gel(x,i), p, pov2)) }
     952             : 
     953             : /*******************************************************************/
     954             : /*                                                                 */
     955             : /*                          GENERIC CRT                            */
     956             : /*                                                                 */
     957             : /*******************************************************************/
     958             : static GEN
     959     8309555 : primelist(forprime_t *S, long n, GEN dB)
     960             : {
     961     8309555 :   GEN P = cgetg(n+1, t_VECSMALL);
     962     8309542 :   long i = 1;
     963             :   ulong p;
     964    20071949 :   while (i <= n && (p = u_forprime_next(S)))
     965    11762408 :     if (!dB || umodiu(dB, p)) P[i++] = p;
     966     8309540 :   return P;
     967             : }
     968             : 
     969             : void
     970     7726980 : gen_inccrt_i(const char *str, GEN worker, GEN dB, long n, long mmin,
     971             :              forprime_t *S, GEN *pH, GEN *pmod, GEN crt(GEN, GEN, GEN*),
     972             :              GEN center(GEN, GEN, GEN))
     973             : {
     974     7726980 :   long m = mmin? minss(mmin, n): usqrt(n);
     975             :   GEN  H, P, mod;
     976             :   pari_timer ti;
     977     7726977 :   if (DEBUGLEVEL > 4)
     978             :   {
     979           0 :     timer_start(&ti);
     980           0 :     err_printf("%s: nb primes: %ld\n",str, n);
     981             :   }
     982     7726976 :   if (m == 1)
     983             :   {
     984     7415914 :     GEN P = primelist(S, n, dB);
     985     7415894 :     GEN done = closure_callgen1(worker, P);
     986     7415890 :     H = gel(done,1);
     987     7415890 :     mod = gel(done,2);
     988     7415890 :     if (!*pH && center) H = center(H, mod, shifti(mod,-1));
     989     7415828 :     if (DEBUGLEVEL>4) timer_printf(&ti,"%s: modular", str);
     990             :   }
     991             :   else
     992             :   {
     993      311062 :     long i, s = (n+m-1)/m, r = m - (m*s-n), di = 0;
     994             :     struct pari_mt pt;
     995      311062 :     long pending = 0;
     996      311062 :     H = cgetg(m+1, t_VEC); P = cgetg(m+1, t_VEC);
     997      311062 :     mt_queue_start_lim(&pt, worker, m);
     998     1270306 :     for (i=1; i<=m || pending; i++)
     999             :     {
    1000             :       GEN done;
    1001      959242 :       GEN pr = i <= m ? mkvec(primelist(S, i<=r ? s: s-1, dB)): NULL;
    1002      959244 :       mt_queue_submit(&pt, i, pr);
    1003      959245 :       done = mt_queue_get(&pt, NULL, &pending);
    1004      959245 :       if (done)
    1005             :       {
    1006      893645 :         di++;
    1007      893645 :         gel(H, di) = gel(done,1);
    1008      893645 :         gel(P, di) = gel(done,2);
    1009      893645 :         if (DEBUGLEVEL>5) err_printf("%ld%% ",100*di/m);
    1010             :       }
    1011             :     }
    1012      311064 :     mt_queue_end(&pt);
    1013      311064 :     if (DEBUGLEVEL>5) err_printf("\n");
    1014      311064 :     if (DEBUGLEVEL>4) timer_printf(&ti,"%s: modular", str);
    1015      311064 :     H = crt(H, P, &mod);
    1016      311064 :     if (DEBUGLEVEL>4) timer_printf(&ti,"%s: chinese", str);
    1017             :   }
    1018     7726892 :   if (*pH) H = crt(mkvec2(*pH, H), mkvec2(*pmod, mod), &mod);
    1019     7726892 :   *pH = H; *pmod = mod;
    1020     7726892 : }
    1021             : void
    1022     2060066 : gen_inccrt(const char *str, GEN worker, GEN dB, long n, long mmin,
    1023             :            forprime_t *S, GEN *pH, GEN *pmod, GEN crt(GEN, GEN, GEN*),
    1024             :            GEN center(GEN, GEN, GEN))
    1025             : {
    1026     2060066 :   pari_sp av = avma;
    1027     2060066 :   gen_inccrt_i(str, worker, dB, n, mmin, S, pH, pmod, crt, center);
    1028     2060015 :   (void)gc_all(av, 2, pH, pmod);
    1029     2060168 : }
    1030             : 
    1031             : GEN
    1032     1273428 : gen_crt(const char *str, GEN worker, forprime_t *S, GEN dB, ulong bound, long mmin, GEN *pmod,
    1033             :         GEN crt(GEN, GEN, GEN*), GEN center(GEN, GEN, GEN))
    1034             : {
    1035     1273428 :   GEN mod = gen_1, H = NULL;
    1036             :   ulong e;
    1037             : 
    1038     1273428 :   bound++;
    1039     2546946 :   while (bound > (e = expi(mod)))
    1040             :   {
    1041     1273390 :     long n = (bound - e) / expu(S->p) + 1;
    1042     1273415 :     gen_inccrt(str, worker, dB, n, mmin, S, &H, &mod, crt, center);
    1043             :   }
    1044     1273501 :   if (pmod) *pmod = mod;
    1045     1273501 :   return H;
    1046             : }
    1047             : 
    1048             : /*******************************************************************/
    1049             : /*                                                                 */
    1050             : /*                          MODULAR GCD                            */
    1051             : /*                                                                 */
    1052             : /*******************************************************************/
    1053             : /* return z = a mod q, b mod p (p,q) = 1; qinv = 1/q mod p; a in ]-q,q] */
    1054             : static GEN
    1055     5155154 : Fl_chinese_coprime(GEN a, ulong b, GEN q, ulong p, ulong qinv, GEN pq, GEN pq2)
    1056             : {
    1057     5155154 :   ulong d, amod = umodiu(a, p);
    1058     5155174 :   pari_sp av = avma;
    1059             :   GEN ax;
    1060             : 
    1061     5155174 :   if (b == amod) return NULL;
    1062     2126315 :   d = Fl_mul(Fl_sub(b, amod, p), qinv, p); /* != 0 */
    1063     2126937 :   if (d >= 1 + (p>>1))
    1064     1037825 :     ax = subii(a, mului(p-d, q));
    1065             :   else
    1066             :   {
    1067     1089112 :     ax = addii(a, mului(d, q)); /* in ]0, pq[ assuming a in ]-q,q[ */
    1068     1088663 :     if (cmpii(ax,pq2) > 0) ax = subii(ax,pq);
    1069             :   }
    1070     2126024 :   return gc_INT(av, ax);
    1071             : }
    1072             : GEN
    1073         364 : Z_init_CRT(ulong Hp, ulong p) { return stoi(Fl_center(Hp, p, p>>1)); }
    1074             : GEN
    1075       31794 : ZX_init_CRT(GEN Hp, ulong p, long v)
    1076             : {
    1077       31794 :   long i, l = lg(Hp), lim = (long)(p>>1);
    1078       31794 :   GEN H = cgetg(l, t_POL);
    1079       31794 :   H[1] = evalsigne(1) | evalvarn(v);
    1080      796087 :   for (i=2; i<l; i++)
    1081      764294 :     gel(H,i) = stoi(Fl_center(Hp[i], p, lim));
    1082       31793 :   return ZX_renormalize(H,l);
    1083             : }
    1084             : 
    1085             : GEN
    1086        5789 : ZM_init_CRT(GEN Hp, ulong p)
    1087             : {
    1088        5789 :   long i,j, m, l = lg(Hp), lim = (long)(p>>1);
    1089        5789 :   GEN c, cp, H = cgetg(l, t_MAT);
    1090        5789 :   if (l==1) return H;
    1091        5789 :   m = lgcols(Hp);
    1092       18984 :   for (j=1; j<l; j++)
    1093             :   {
    1094       13195 :     cp = gel(Hp,j);
    1095       13195 :     c = cgetg(m, t_COL);
    1096       13195 :     gel(H,j) = c;
    1097      166166 :     for (i=1; i<m; i++) gel(c,i) = stoi(Fl_center(cp[i],p, lim));
    1098             :   }
    1099        5789 :   return H;
    1100             : }
    1101             : 
    1102             : int
    1103        7560 : Z_incremental_CRT(GEN *H, ulong Hp, GEN *ptq, ulong p)
    1104             : {
    1105        7560 :   GEN h, q = *ptq, qp = muliu(q,p);
    1106        7560 :   ulong qinv = Fl_inv(umodiu(q,p), p);
    1107        7560 :   int stable = 1;
    1108        7560 :   h = Fl_chinese_coprime(*H,Hp,q,p,qinv,qp,shifti(qp,-1));
    1109        7560 :   if (h) { *H = h; stable = 0; }
    1110        7560 :   *ptq = qp; return stable;
    1111             : }
    1112             : 
    1113             : static int
    1114      147611 : ZX_incremental_CRT_raw(GEN *ptH, GEN Hp, GEN q, GEN qp, ulong p)
    1115             : {
    1116      147611 :   GEN H = *ptH, h, qp2 = shifti(qp,-1);
    1117      147604 :   ulong qinv = Fl_inv(umodiu(q,p), p);
    1118      147612 :   long i, l = lg(H), lp = lg(Hp);
    1119      147612 :   int stable = 1;
    1120             : 
    1121      147612 :   if (l < lp)
    1122             :   { /* degree increases */
    1123           0 :     GEN x = cgetg(lp, t_POL);
    1124           0 :     for (i=1; i<l; i++)  x[i] = H[i];
    1125           0 :     for (   ; i<lp; i++) gel(x,i) = gen_0;
    1126           0 :     *ptH = H = x;
    1127           0 :     stable = 0;
    1128      147612 :   } else if (l > lp)
    1129             :   { /* degree decreases */
    1130           0 :     GEN x = cgetg(l, t_VECSMALL);
    1131           0 :     for (i=1; i<lp; i++)  x[i] = Hp[i];
    1132           0 :     for (   ; i<l; i++) x[i] = 0;
    1133           0 :     Hp = x; lp = l;
    1134             :   }
    1135     4933609 :   for (i=2; i<lp; i++)
    1136             :   {
    1137     4786108 :     h = Fl_chinese_coprime(gel(H,i),Hp[i],q,p,qinv,qp,qp2);
    1138     4785997 :     if (h) { gel(H,i) = h; stable = 0; }
    1139             :   }
    1140      147501 :   (void)ZX_renormalize(H,lp);
    1141      147615 :   return stable;
    1142             : }
    1143             : 
    1144             : int
    1145           0 : ZX_incremental_CRT(GEN *ptH, GEN Hp, GEN *ptq, ulong p)
    1146             : {
    1147           0 :   GEN q = *ptq, qp = muliu(q,p);
    1148           0 :   int stable = ZX_incremental_CRT_raw(ptH, Hp, q, qp, p);
    1149           0 :   *ptq = qp; return stable;
    1150             : }
    1151             : 
    1152             : int
    1153        7597 : ZM_incremental_CRT(GEN *pH, GEN Hp, GEN *ptq, ulong p)
    1154             : {
    1155        7597 :   GEN h, H = *pH, q = *ptq, qp = muliu(q, p), qp2 = shifti(qp,-1);
    1156        7597 :   ulong qinv = Fl_inv(umodiu(q,p), p);
    1157        7597 :   long i,j, l = lg(H), m = lgcols(H);
    1158        7597 :   int stable = 1;
    1159       26206 :   for (j=1; j<l; j++)
    1160      202351 :     for (i=1; i<m; i++)
    1161             :     {
    1162      183742 :       h = Fl_chinese_coprime(gcoeff(H,i,j), coeff(Hp,i,j),q,p,qinv,qp,qp2);
    1163      183742 :       if (h) { gcoeff(H,i,j) = h; stable = 0; }
    1164             :     }
    1165        7597 :   *ptq = qp; return stable;
    1166             : }
    1167             : 
    1168             : GEN
    1169         679 : ZXM_init_CRT(GEN Hp, long deg, ulong p)
    1170             : {
    1171             :   long i, j, k;
    1172             :   GEN H;
    1173         679 :   long m, l = lg(Hp), lim = (long)(p>>1), n;
    1174         679 :   H = cgetg(l, t_MAT);
    1175         679 :   if (l==1) return H;
    1176         679 :   m = lgcols(Hp);
    1177         679 :   n = deg + 3;
    1178        2268 :   for (j=1; j<l; j++)
    1179             :   {
    1180        1589 :     GEN cp = gel(Hp,j);
    1181        1589 :     GEN c = cgetg(m, t_COL);
    1182        1589 :     gel(H,j) = c;
    1183       24465 :     for (i=1; i<m; i++)
    1184             :     {
    1185       22876 :       GEN dp = gel(cp, i);
    1186       22876 :       long l = lg(dp);
    1187       22876 :       GEN d = cgetg(n, t_POL);
    1188       22876 :       gel(c, i) = d;
    1189       22876 :       d[1] = dp[1] | evalsigne(1);
    1190       46459 :       for (k=2; k<l; k++)
    1191       23583 :         gel(d,k) = stoi(Fl_center(dp[k], p, lim));
    1192       45493 :       for (   ; k<n; k++)
    1193       22617 :         gel(d,k) = gen_0;
    1194             :     }
    1195             :   }
    1196         679 :   return H;
    1197             : }
    1198             : 
    1199             : int
    1200         653 : ZXM_incremental_CRT(GEN *pH, GEN Hp, GEN *ptq, ulong p)
    1201             : {
    1202         653 :   GEN v, H = *pH, q = *ptq, qp = muliu(q, p), qp2 = shifti(qp,-1);
    1203         653 :   ulong qinv = Fl_inv(umodiu(q,p), p);
    1204         653 :   long i,j,k, l = lg(H), m = lgcols(H), n = lg(gmael(H,1,1));
    1205         653 :   int stable = 1;
    1206        2225 :   for (j=1; j<l; j++)
    1207       90418 :     for (i=1; i<m; i++)
    1208             :     {
    1209       88846 :       GEN h = gmael(H,j,i), hp = gmael(Hp,j,i);
    1210       88846 :       long lh = lg(hp);
    1211      246641 :       for (k=2; k<lh; k++)
    1212             :       {
    1213      157795 :         v = Fl_chinese_coprime(gel(h,k),uel(hp,k),q,p,qinv,qp,qp2);
    1214      157795 :         if (v) { gel(h,k) = v; stable = 0; }
    1215             :       }
    1216      108763 :       for (; k<n; k++)
    1217             :       {
    1218       19917 :         v = Fl_chinese_coprime(gel(h,k),0,q,p,qinv,qp,qp2);
    1219       19917 :         if (v) { gel(h,k) = v; stable = 0; }
    1220             :       }
    1221             :     }
    1222         653 :   *ptq = qp; return stable;
    1223             : }
    1224             : 
    1225             : /* record the degrees of Euclidean remainders (make them as large as
    1226             :  * possible : smaller values correspond to a degenerate sequence) */
    1227             : static void
    1228       23286 : Flx_resultant_set_dglist(GEN a, GEN b, GEN dglist, ulong p)
    1229             : {
    1230             :   long da,db,dc, ind;
    1231       23286 :   pari_sp av = avma;
    1232             : 
    1233       23286 :   if (lgpol(a)==0 || lgpol(b)==0) return;
    1234       22019 :   da = degpol(a);
    1235       22019 :   db = degpol(b);
    1236       22019 :   if (db > da)
    1237           0 :   { swapspec(a,b, da,db); }
    1238       22019 :   else if (!da) return;
    1239       22019 :   ind = 0;
    1240      144374 :   while (db)
    1241             :   {
    1242      122360 :     GEN c = Flx_rem(a,b, p);
    1243      122356 :     a = b; b = c; dc = degpol(c);
    1244      122355 :     if (dc < 0) break;
    1245             : 
    1246      122355 :     ind++;
    1247      122355 :     if (dc > dglist[ind]) dglist[ind] = dc;
    1248      122355 :     if (gc_needed(av,2))
    1249             :     {
    1250           0 :       if (DEBUGMEM>1) pari_warn(warnmem,"Flx_resultant_all");
    1251           0 :       (void)gc_all(av, 2, &a,&b);
    1252             :     }
    1253      122355 :     db = dc; /* = degpol(b) */
    1254             :   }
    1255       22014 :   if (ind+1 > lg(dglist)) setlg(dglist,ind+1);
    1256       22014 :   set_avma(av);
    1257             : }
    1258             : /* assuming the PRS finishes on a degree 1 polynomial C0 + C1X, with
    1259             :  * "generic" degree sequence as given by dglist, set *Ci and return
    1260             :  * resultant(a,b). Modular version of Collins's subresultant */
    1261             : static ulong
    1262     2085119 : Flx_resultant_all(GEN a, GEN b, long *C0, long *C1, GEN dglist, ulong p)
    1263             : {
    1264             :   long da,db,dc, ind;
    1265     2085119 :   ulong lb, res, g = 1UL, h = 1UL, ca = 1UL, cb = 1UL;
    1266     2085119 :   int s = 1;
    1267     2085119 :   pari_sp av = avma;
    1268             : 
    1269     2085119 :   *C0 = 1; *C1 = 0;
    1270     2085119 :   if (lgpol(a)==0 || lgpol(b)==0) return 0;
    1271     2075691 :   da = degpol(a);
    1272     2075719 :   db = degpol(b);
    1273     2075696 :   if (db > da)
    1274             :   {
    1275           0 :     swapspec(a,b, da,db);
    1276           0 :     if (both_odd(da,db)) s = -s;
    1277             :   }
    1278     2075696 :   else if (!da) return 1; /* = a[2] ^ db, since 0 <= db <= da = 0 */
    1279     2075696 :   ind = 0;
    1280    19802961 :   while (db)
    1281             :   { /* sub-resultant algo., applied to ca * a and cb * b, ca,cb scalars,
    1282             :      * da = deg a, db = deg b */
    1283    17731948 :     GEN c = Flx_rem(a,b, p);
    1284    17618931 :     long delta = da - db;
    1285             : 
    1286    17618931 :     if (both_odd(da,db)) s = -s;
    1287    17619125 :     lb = Fl_mul(b[db+2], cb, p);
    1288    17636554 :     a = b; b = c; dc = degpol(c);
    1289    17636294 :     ind++;
    1290    17636294 :     if (dc != dglist[ind]) return gc_ulong(av,0); /* degenerates */
    1291    17631345 :     if (g == h)
    1292             :     { /* frequent */
    1293    17571501 :       ulong cc = Fl_mul(ca, Fl_powu(Fl_div(lb,g,p), delta+1, p), p);
    1294    17668094 :       ca = cb;
    1295    17668094 :       cb = cc;
    1296             :     }
    1297             :     else
    1298             :     {
    1299       59844 :       ulong cc = Fl_mul(ca, Fl_powu(lb, delta+1, p), p);
    1300       59844 :       ulong ghdelta = Fl_mul(g, Fl_powu(h, delta, p), p);
    1301       59844 :       ca = cb;
    1302       59844 :       cb = Fl_div(cc, ghdelta, p);
    1303             :     }
    1304    17728723 :     da = db; /* = degpol(a) */
    1305    17728723 :     db = dc; /* = degpol(b) */
    1306             : 
    1307    17728723 :     g = lb;
    1308    17728723 :     if (delta == 1)
    1309    17628543 :       h = g; /* frequent */
    1310             :     else
    1311      100180 :       h = Fl_mul(h, Fl_powu(Fl_div(g,h,p), delta, p), p);
    1312             : 
    1313    17727435 :     if (gc_needed(av,2))
    1314             :     {
    1315           0 :       if (DEBUGMEM>1) pari_warn(warnmem,"Flx_resultant_all");
    1316           0 :       (void)gc_all(av, 2, &a,&b);
    1317             :     }
    1318             :   }
    1319     2071013 :   if (da > 1) return 0; /* Failure */
    1320             :   /* last nonconstant polynomial has degree 1 */
    1321     2071013 :   *C0 = Fl_mul(ca, a[2], p);
    1322     2070979 :   *C1 = Fl_mul(ca, a[3], p);
    1323     2070964 :   res = Fl_mul(cb, b[2], p);
    1324     2070933 :   if (s == -1) res = p - res;
    1325     2070933 :   return gc_ulong(av,res);
    1326             : }
    1327             : 
    1328             : /* Q a vector of polynomials representing B in Fp[X][Y], evaluate at X = x,
    1329             :  * Return 0 in case of degree drop. */
    1330             : static GEN
    1331     2108526 : FlxY_evalx_drop(GEN Q, ulong x, ulong p)
    1332             : {
    1333             :   GEN z;
    1334     2108526 :   long i, lb = lg(Q);
    1335     2108526 :   ulong leadz = Flx_eval(leading_coeff(Q), x, p);
    1336     2108378 :   long vs=mael(Q,2,1);
    1337     2108378 :   if (!leadz) return zero_Flx(vs);
    1338             : 
    1339     2097718 :   z = cgetg(lb, t_VECSMALL); z[1] = vs;
    1340    20069120 :   for (i=2; i<lb-1; i++) z[i] = Flx_eval(gel(Q,i), x, p);
    1341     2095857 :   z[i] = leadz; return z;
    1342             : }
    1343             : 
    1344             : GEN
    1345        2072 : FpXY_FpXQ_evaly(GEN Q, GEN y, GEN T, GEN p, long vx)
    1346             : {
    1347        2072 :   pari_sp av = avma;
    1348        2072 :   long i, lb = lg(Q);
    1349             :   GEN z;
    1350        2072 :   if (lb == 2) return pol_0(vx);
    1351        2072 :   z = gel(Q, lb-1);
    1352        2072 :   if (lb == 3 || !signe(y)) return typ(z)==t_INT? scalar_ZX(z, vx): ZX_copy(z);
    1353             : 
    1354        2072 :   if (typ(z) == t_INT) z = scalar_ZX_shallow(z, vx);
    1355       48636 :   for (i=lb-2; i>=2; i--)
    1356             :   {
    1357       46564 :     GEN c = gel(Q,i);
    1358       46564 :     z = FqX_Fq_mul(z, y, T, p);
    1359       46564 :     z = typ(c) == t_INT? FqX_Fq_add(z,c,T,p): FqX_add(z,c,T,p);
    1360             :   }
    1361        2072 :   return gc_upto(av, z);
    1362             : }
    1363             : 
    1364             : static GEN
    1365      291737 : ZX_norml1(GEN x)
    1366             : {
    1367      291737 :   long i, l = lg(x);
    1368             :   GEN s;
    1369             : 
    1370      291737 :   if (l == 2) return gen_0;
    1371      199183 :   s = gel(x, l-1); /* != 0 */
    1372      697188 :   for (i = l-2; i > 1; i--) {
    1373      498015 :     GEN xi = gel(x,i);
    1374      498015 :     if (!signe(xi)) continue;
    1375      259400 :     s = addii_sign(s,1, xi,1);
    1376             :   }
    1377      199173 :   return s;
    1378             : }
    1379             : /* x >= 0, y != 0, return x + |y| */
    1380             : static GEN
    1381       25552 : addii_abs(GEN x, GEN y)
    1382             : {
    1383       25552 :   if (!signe(x)) return absi_shallow(y);
    1384       16044 :   return addii_sign(x,1, y,1);
    1385             : }
    1386             : 
    1387             : /* x a ZX, return sum_{i >= k} |x[i]| binomial(i, k) */
    1388             : static GEN
    1389       31648 : ZX_norml1_1(GEN x, long k)
    1390             : {
    1391       31648 :   long i, d = degpol(x);
    1392             :   GEN s, C; /* = binomial(i, k) */
    1393             : 
    1394       31648 :   if (!d || k > d) return gen_0;
    1395       31648 :   s = absi_shallow(gel(x, k+2)); /* may be 0 */
    1396       31647 :   C = gen_1;
    1397       68049 :   for (i = k+1; i <= d; i++) {
    1398       36407 :     GEN xi = gel(x,i+2);
    1399       36407 :     if (k) C = diviuexact(muliu(C, i), i-k);
    1400       36409 :     if (signe(xi)) s = addii_abs(s, mulii(C, xi));
    1401             :   }
    1402       31642 :   return s;
    1403             : }
    1404             : /* x has non-negative real coefficients */
    1405             : static GEN
    1406        3283 : RgX_norml1_1(GEN x, long k)
    1407             : {
    1408        3283 :   long i, d = degpol(x);
    1409             :   GEN s, C; /* = binomial(i, k) */
    1410             : 
    1411        3283 :   if (!d || k > d) return gen_0;
    1412        3283 :   s = gel(x, k+2); /* may be 0 */
    1413        3283 :   C = gen_1;
    1414        9198 :   for (i = k+1; i <= d; i++) {
    1415        5915 :     GEN xi = gel(x,i+2);
    1416        5915 :     if (k) C = diviuexact(muliu(C, i), i-k);
    1417        5915 :     if (!gequal0(xi)) s = gadd(s, gmul(C, xi));
    1418             :   }
    1419        3283 :   return s;
    1420             : }
    1421             : 
    1422             : /* N_2(A)^2 */
    1423             : static GEN
    1424        8571 : sqrN2(GEN A, long prec)
    1425             : {
    1426        8571 :   pari_sp av = avma;
    1427        8571 :   long i, l = lg(A);
    1428        8571 :   GEN a = gen_0;
    1429       41935 :   for (i = 2; i < l; i++)
    1430             :   {
    1431       33364 :     a = gadd(a, gabs(gnorm(gel(A,i)), prec));
    1432       33364 :     if (gc_needed(av,1))
    1433             :     {
    1434           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"RgX_RgXY_ResBound i = %ld",i);
    1435           0 :       a = gc_upto(av, a);
    1436             :     }
    1437             :   }
    1438        8571 :   return a;
    1439             : }
    1440             : /* Interpolate at roots of 1 and use Hadamard bound for univariate resultant:
    1441             :  *   bound = N_2(A)^degpol B N_2(B)^degpol(A),  where
    1442             :  *     N_2(A) = sqrt(sum (N_1(Ai))^2)
    1443             :  * Return e such that Res(A, B) < 2^e */
    1444             : static GEN
    1445        7717 : RgX_RgXY_ResBound(GEN A, GEN B, long prec)
    1446             : {
    1447        7717 :   pari_sp av = avma;
    1448        7717 :   GEN b = gen_0, bnd;
    1449        7717 :   long i, lB = lg(B);
    1450       30403 :   for (i=2; i<lB; i++)
    1451             :   {
    1452       22686 :     GEN t = gel(B,i);
    1453       22686 :     if (typ(t) == t_POL) t = gnorml1(t, prec);
    1454       22686 :     b = gadd(b, gabs(gsqr(t), prec));
    1455       22686 :     if (gc_needed(av,1))
    1456             :     {
    1457           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"RgX_RgXY_ResBound i = %ld",i);
    1458           0 :       b = gc_upto(av, b);
    1459             :     }
    1460             :   }
    1461        7717 :   bnd = gsqrt(gmul(gpowgs(sqrN2(A,prec), degpol(B)),
    1462             :                    gpowgs(b, degpol(A))), prec);
    1463        7717 :   return gc_upto(av, bnd);
    1464             : }
    1465             : /* A,B in C[X] return RgX_RgXY_ResBound(A, B(x+y)) */
    1466             : static GEN
    1467         854 : RgX_RgXY_ResBound_1(GEN A, GEN B, long prec)
    1468             : {
    1469         854 :   pari_sp av = avma, av2;
    1470         854 :   GEN b = gen_0, bnd;
    1471         854 :   long i, lB = lg(B);
    1472         854 :   B = shallowcopy(B);
    1473        4137 :   for (i=2; i<lB; i++) gel(B,i) = gabs(gel(B,i), prec);
    1474         854 :   av2 = avma;
    1475        4137 :   for (i=2; i<lB; i++)
    1476             :   {
    1477        3283 :     b = gadd(b, gsqr(RgX_norml1_1(B, i-2)));
    1478        3283 :     if (gc_needed(av2,1))
    1479             :     {
    1480           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"RgX_RgXY_ResBound i = %ld",i);
    1481           0 :       b = gc_upto(av2, b);
    1482             :     }
    1483             :   }
    1484         854 :   bnd = gsqrt(gmul(gpowgs(sqrN2(A,prec), degpol(B)),
    1485             :                    gpowgs(b, degpol(A))), prec);
    1486         854 :   return gc_upto(av, bnd);
    1487             : }
    1488             : 
    1489             : /* log2 N_2(A)^2 */
    1490             : static double
    1491      176691 : log2N2(GEN A)
    1492             : {
    1493      176691 :   pari_sp av = avma;
    1494      176691 :   long i, l = lg(A);
    1495      176691 :   GEN a = gen_0;
    1496     1335190 :   for (i=2; i < l; i++)
    1497             :   {
    1498     1158495 :     a = addii(a, sqri(gel(A,i)));
    1499     1158501 :     if (gc_needed(av,1))
    1500             :     {
    1501           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"ZX_ZXY_ResBound i = %ld",i);
    1502           0 :       a = gc_upto(av, a);
    1503             :     }
    1504             :   }
    1505      176695 :   return gc_double(av, dbllog2(a));
    1506             : }
    1507             : /* Interpolate at roots of 1 and use Hadamard bound for univariate resultant:
    1508             :  *   bound = N_2(A)^degpol B N_2(B)^degpol(A),  where
    1509             :  *     N_2(A) = sqrt(sum (N_1(Ai))^2)
    1510             :  * Return e such that Res(A, B) < 2^e */
    1511             : ulong
    1512      166612 : ZX_ZXY_ResBound(GEN A, GEN B, GEN dB)
    1513             : {
    1514      166612 :   pari_sp av = avma;
    1515      166612 :   GEN b = gen_0;
    1516      166612 :   long i, lB = lg(B);
    1517             :   double logb;
    1518     1260638 :   for (i=2; i<lB; i++)
    1519             :   {
    1520     1094036 :     GEN t = gel(B,i);
    1521     1094036 :     if (typ(t) == t_POL) t = ZX_norml1(t);
    1522     1094031 :     b = addii(b, sqri(t));
    1523     1094027 :     if (gc_needed(av,1))
    1524             :     {
    1525           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"ZX_ZXY_ResBound i = %ld",i);
    1526           0 :       b = gc_upto(av, b);
    1527             :     }
    1528             :   }
    1529      166602 :   logb = dbllog2(b); if (dB) logb -= 2 * dbllog2(dB);
    1530      166607 :   i = (long)((degpol(B) * log2N2(A) + degpol(A) * logb) / 2);
    1531      166612 :   return gc_ulong(av, (i <= 0)? 1: 1 + (ulong)i);
    1532             : }
    1533             : /* A,B ZX. Return ZX_ZXY_ResBound(A(x), B(x+y)) */
    1534             : static ulong
    1535       10084 : ZX_ZXY_ResBound_1(GEN A, GEN B)
    1536             : {
    1537       10084 :   pari_sp av = avma;
    1538       10084 :   GEN b = gen_0;
    1539       10084 :   long i, lB = lg(B);
    1540       41735 :   for (i=2; i<lB; i++)
    1541             :   {
    1542       31648 :     b = addii(b, sqri(ZX_norml1_1(B, i-2)));
    1543       31651 :     if (gc_needed(av,1))
    1544             :     {
    1545           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"ZX_ZXY_ResBound i = %ld",i);
    1546           0 :       b = gc_upto(av, b);
    1547             :     }
    1548             :   }
    1549       10087 :   i = (long)((degpol(B) * log2N2(A) + degpol(A) * dbllog2(b)) / 2);
    1550       10086 :   return gc_ulong(av, (i <= 0)? 1: 1 + (ulong)i);
    1551             : }
    1552             : /* special case B = A' */
    1553             : static ulong
    1554     1134083 : ZX_discbound(GEN A)
    1555             : {
    1556     1134083 :   pari_sp av = avma;
    1557     1134083 :   GEN a = gen_0, b = gen_0;
    1558     1134083 :   long i , lA = lg(A), dA = degpol(A);
    1559             :   double loga, logb;
    1560     6767141 :   for (i = 2; i < lA; i++)
    1561             :   {
    1562     5633220 :     GEN c = sqri(gel(A,i));
    1563     5632895 :     a = addii(a, c);
    1564     5633033 :     if (i > 2) b = addii(b, mulii(c, sqru(i-2)));
    1565     5633063 :     if (gc_needed(av,1))
    1566             :     {
    1567           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"ZX_discbound i = %ld",i);
    1568           0 :       (void)gc_all(av, 2, &a, &b);
    1569             :     }
    1570             :   }
    1571     1133921 :   loga = dbllog2(a);
    1572     1133960 :   logb = dbllog2(b); set_avma(av);
    1573     1133981 :   i = (long)(((dA-1) * loga + dA * logb) / 2);
    1574     1133981 :   return (i <= 0)? 1: 1 + (ulong)i;
    1575             : }
    1576             : 
    1577             : /* return Res(a(Y), b(n,Y)) over Fp. la = leading_coeff(a) [for efficiency] */
    1578             : static ulong
    1579     5538186 : Flx_FlxY_eval_resultant(GEN a, GEN b, ulong n, ulong p, ulong pi, ulong la)
    1580             : {
    1581     5538186 :   GEN ev = FlxY_evalx_pre(b, n, p, pi);
    1582     5538496 :   long drop = lg(b) - lg(ev);
    1583     5538496 :   ulong r = Flx_resultant_pre(a, ev, p, pi);
    1584     5537976 :   if (drop && la != 1) r = Fl_mul(r, Fl_powu_pre(la, drop, p, pi), p);
    1585     5538004 :   return r;
    1586             : }
    1587             : static GEN
    1588         284 : FpX_FpXY_eval_resultant(GEN a, GEN b, GEN n, GEN p, GEN la, long db, long vX)
    1589             : {
    1590         284 :   GEN ev = FpXY_evaly(b, n, p, vX);
    1591         284 :   long drop = db-degpol(ev);
    1592         284 :   GEN r = FpX_resultant(a, ev, p);
    1593         284 :   if (drop && !gequal1(la)) r = Fp_mul(r, Fp_powu(la, drop,p),p);
    1594         284 :   return r;
    1595             : }
    1596             : 
    1597             : /* assume dres := deg(Res_X(a,b), Y) <= deg(a,X) * deg(b,Y) < p */
    1598             : /* Return a Fly */
    1599             : static GEN
    1600      368413 : Flx_FlxY_resultant_polint(GEN a, GEN b, ulong p, ulong pi, long dres, long sx)
    1601             : {
    1602             :   long i;
    1603      368413 :   ulong n, la = Flx_lead(a);
    1604      368410 :   GEN  x = cgetg(dres+2, t_VECSMALL);
    1605      368410 :   GEN  y = cgetg(dres+2, t_VECSMALL);
    1606             :  /* Evaluate at dres+ 1 points: 0 (if dres even) and +/- n, so that P_n(X) =
    1607             :   * P_{-n}(-X), where P_i is Lagrange polynomial: P_i(j) = delta_{i,j} */
    1608     2956738 :   for (i=0,n = 1; i < dres; n++)
    1609             :   {
    1610     2588325 :     x[++i] = n;   y[i] = Flx_FlxY_eval_resultant(a,b, x[i], p,pi,la);
    1611     2588263 :     x[++i] = p-n; y[i] = Flx_FlxY_eval_resultant(a,b, x[i], p,pi,la);
    1612             :   }
    1613      368413 :   if (i == dres)
    1614             :   {
    1615      362907 :     x[++i] = 0;   y[i] = Flx_FlxY_eval_resultant(a,b, x[i], p,pi,la);
    1616             :   }
    1617      368410 :   return Flv_polint(x,y, p, sx);
    1618             : }
    1619             : 
    1620             : static GEN
    1621        7497 : FlxX_pseudorem(GEN x, GEN y, ulong p, ulong pi)
    1622             : {
    1623        7497 :   long vx = varn(x), dx, dy, dz, i, lx, dp;
    1624        7497 :   pari_sp av = avma, av2;
    1625             : 
    1626        7497 :   if (!signe(y)) pari_err_INV("FlxX_pseudorem",y);
    1627        7497 :   (void)new_chunk(2);
    1628        7498 :   dx=degpol(x); x = RgX_recip_i(x)+2;
    1629        7500 :   dy=degpol(y); y = RgX_recip_i(y)+2; dz=dx-dy; dp = dz+1;
    1630        7499 :   av2 = avma;
    1631             :   for (;;)
    1632             :   {
    1633       61435 :     gel(x,0) = Flx_neg(gel(x,0), p); dp--;
    1634      230121 :     for (i=1; i<=dy; i++)
    1635      168438 :       gel(x,i) = Flx_add( Flx_mul_pre(gel(y,0), gel(x,i), p, pi),
    1636      168660 :                           Flx_mul_pre(gel(x,0), gel(y,i), p, pi), p );
    1637     1116835 :     for (   ; i<=dx; i++)
    1638     1056080 :       gel(x,i) = Flx_mul_pre(gel(y,0), gel(x,i), p, pi);
    1639       65327 :     do { x++; dx--; } while (dx >= 0 && lg(gel(x,0))==2);
    1640       60755 :     if (dx < dy) break;
    1641       53257 :     if (gc_needed(av2,1))
    1642             :     {
    1643           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"FlxX_pseudorem dx = %ld >= %ld",dx,dy);
    1644           0 :       gc_slice(av2,x,dx+1);
    1645             :     }
    1646             :   }
    1647        7498 :   if (dx < 0) return zero_Flx(0);
    1648        7498 :   lx = dx+3; x -= 2;
    1649        7498 :   x[0]=evaltyp(t_POL) | _evallg(lx);
    1650        7498 :   x[1]=evalsigne(1) | evalvarn(vx);
    1651        7498 :   x = RgX_recip_i(x);
    1652        7497 :   if (dp)
    1653             :   { /* multiply by y[0]^dp   [beware dummy vars from FpX_FpXY_resultant] */
    1654        1959 :     GEN t = Flx_powu_pre(gel(y,0), dp, p, pi);
    1655        7837 :     for (i=2; i<lx; i++) gel(x,i) = Flx_mul_pre(gel(x,i), t, p, pi);
    1656             :   }
    1657        7495 :   return gc_GEN(av, x);
    1658             : }
    1659             : 
    1660             : /* return a Flx */
    1661             : GEN
    1662        2508 : FlxX_resultant(GEN u, GEN v, ulong p, long sx)
    1663             : {
    1664        2508 :   pari_sp av = avma, av2;
    1665             :   long degq, dx, dy, du, dv, dr, signh;
    1666             :   ulong pi;
    1667             :   GEN z, g, h, r, p1;
    1668             : 
    1669        2508 :   dx = degpol(u); dy = degpol(v); signh = 1;
    1670        2508 :   if (dx < dy)
    1671             :   {
    1672           7 :     swap(u,v); lswap(dx,dy);
    1673           7 :     if (both_odd(dx, dy)) signh = -signh;
    1674             :   }
    1675        2508 :   if (dy < 0) return zero_Flx(sx);
    1676        2508 :   pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    1677        2508 :   if (dy==0) return gc_upto(av, Flx_powu_pre(gel(v,2),dx,p,pi));
    1678             : 
    1679        2508 :   g = h = pol1_Flx(sx); av2 = avma;
    1680             :   for(;;)
    1681             :   {
    1682        7497 :     r = FlxX_pseudorem(u,v,p,pi); dr = lg(r);
    1683        7501 :     if (dr == 2) { set_avma(av); return zero_Flx(sx); }
    1684        7501 :     du = degpol(u); dv = degpol(v); degq = du-dv;
    1685        7501 :     u = v; p1 = g; g = leading_coeff(u);
    1686        7501 :     switch(degq)
    1687             :     {
    1688           0 :       case 0: break;
    1689        5528 :       case 1:
    1690        5528 :         p1 = Flx_mul_pre(h,p1, p, pi); h = g; break;
    1691        1973 :       default:
    1692        1973 :         p1 = Flx_mul_pre(Flx_powu_pre(h,degq,p,pi), p1, p, pi);
    1693        1973 :         h = Flx_div_pre(Flx_powu_pre(g,degq,p,pi),
    1694        1972 :                         Flx_powu_pre(h,degq-1,p,pi), p, pi);
    1695             :     }
    1696        7497 :     if (both_odd(du,dv)) signh = -signh;
    1697        7496 :     v = FlxY_Flx_div(r, p1, p);
    1698        7496 :     if (dr==3) break;
    1699        4987 :     if (gc_needed(av2,1))
    1700             :     {
    1701           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"FlxX_resultant, dr = %ld",dr);
    1702           0 :       (void)gc_all(av2,4, &u, &v, &g, &h);
    1703             :     }
    1704             :   }
    1705        2509 :   z = gel(v,2);
    1706        2509 :   if (dv > 1) z = Flx_div_pre(Flx_powu_pre(z,dv,p,pi),
    1707           0 :                               Flx_powu_pre(h,dv-1,p,pi), p, pi);
    1708        2509 :   if (signh < 0) z = Flx_neg(z,p);
    1709        2509 :   return gc_upto(av, z);
    1710             : }
    1711             : 
    1712             : /* Warning:
    1713             :  * This function switches between valid and invalid variable ordering*/
    1714             : 
    1715             : static GEN
    1716        6118 : FlxY_to_FlyX(GEN b, long sv)
    1717             : {
    1718        6118 :   long i, n=-1;
    1719        6118 :   long sw = b[1]&VARNBITS;
    1720       20869 :   for(i=2;i<lg(b);i++) n = maxss(n,lgpol(gel(b,i)));
    1721        6118 :   return Flm_to_FlxX(Flm_transpose(FlxX_to_Flm(b,n)),sv,sw);
    1722             : }
    1723             : 
    1724             : /* Return a Fly*/
    1725             : GEN
    1726        6119 : Flx_FlxY_resultant(GEN a, GEN b, ulong p)
    1727             : {
    1728        6119 :   pari_sp ltop=avma;
    1729        6119 :   long dres = degpol(a)*degpol(b);
    1730        6118 :   long sx=a[1], sy=b[1]&VARNBITS;
    1731             :   GEN z;
    1732        6118 :   b = FlxY_to_FlyX(b,sx);
    1733        6116 :   if ((ulong)dres >= p)
    1734        2506 :     z = FlxX_resultant(Fly_to_FlxY(a, sy), b, p, sx);
    1735             :   else
    1736             :   {
    1737        3610 :     ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    1738        3610 :     z = Flx_FlxY_resultant_polint(a, b, p, pi, (ulong)dres, sy);
    1739             :   }
    1740        6120 :   return gc_upto(ltop,z);
    1741             : }
    1742             : 
    1743             : /* Return a t_POL in variable vc whose coeffs are the coeffs of b in
    1744             :  * variable v; vc must have higher priority than all variables occuring in b. */
    1745             : GEN
    1746      146016 : swap_vars(GEN b, long v, long vc)
    1747             : {
    1748      146016 :   long i, n = RgX_degree(b, v);
    1749             :   GEN c, x;
    1750      146014 :   if (n < 0) return pol_0(vc);
    1751      146014 :   c = cgetg(n+3, t_POL); x = c + 2;
    1752      146014 :   c[1] = evalsigne(1) | evalvarn(vc);
    1753      967844 :   for (i = 0; i <= n; i++) gel(x,i) = polcoef_i(b, i, v);
    1754      146010 :   return c;
    1755             : }
    1756             : 
    1757             : /* assume varn(b) << varn(a) */
    1758             : /* return a FpY*/
    1759             : GEN
    1760          15 : FpX_FpXY_resultant(GEN a, GEN b, GEN p)
    1761             : {
    1762          15 :   long i,n,dres, db, vY = varn(b), vX = varn(a);
    1763             :   GEN la,x,y;
    1764             : 
    1765          15 :   if (lgefint(p) == 3)
    1766             :   {
    1767           0 :     ulong pp = uel(p,2);
    1768           0 :     b = ZXX_to_FlxX(b, pp, vX);
    1769           0 :     a = ZX_to_Flx(a, pp);
    1770           0 :     x = Flx_FlxY_resultant(a, b, pp);
    1771           0 :     return Flx_to_ZX(x);
    1772             :   }
    1773          15 :   db = RgXY_degreex(b);
    1774          15 :   dres = degpol(a)*degpol(b);
    1775          15 :   la = leading_coeff(a);
    1776          15 :   x = cgetg(dres+2, t_VEC);
    1777          15 :   y = cgetg(dres+2, t_VEC);
    1778             :  /* Evaluate at dres+ 1 points: 0 (if dres even) and +/- n, so that P_n(X) =
    1779             :   * P_{-n}(-X), where P_i is Lagrange polynomial: P_i(j) = delta_{i,j} */
    1780         157 :   for (i=0,n = 1; i < dres; n++)
    1781             :   {
    1782         142 :     gel(x,++i) = utoipos(n);
    1783         142 :     gel(y,i) = FpX_FpXY_eval_resultant(a,b,gel(x,i),p,la,db,vY);
    1784         142 :     gel(x,++i) = subiu(p,n);
    1785         142 :     gel(y,i) = FpX_FpXY_eval_resultant(a,b,gel(x,i),p,la,db,vY);
    1786             :   }
    1787          15 :   if (i == dres)
    1788             :   {
    1789           0 :     gel(x,++i) = gen_0;
    1790           0 :     gel(y,i) = FpX_FpXY_eval_resultant(a,b, gel(x,i), p,la,db,vY);
    1791             :   }
    1792          15 :   return FpV_polint(x,y, p, vY);
    1793             : }
    1794             : 
    1795             : GEN
    1796         191 : FpX_composedsum(GEN P, GEN Q, GEN p)
    1797             : {
    1798         191 :   pari_sp av = avma;
    1799         191 :   if (lgefint(p)==3)
    1800             :   {
    1801           0 :     ulong pp = p[2];
    1802           0 :     GEN z = Flx_composedsum(ZX_to_Flx(P, pp), ZX_to_Flx(Q, pp), pp);
    1803           0 :     return gc_upto(av, Flx_to_ZX(z));
    1804             :   }
    1805             :   else
    1806             :   {
    1807         191 :     long n = 1+ degpol(P)*degpol(Q);
    1808         191 :     GEN Pl = FpX_invLaplace(FpX_Newton(P,n,p), p);
    1809         191 :     GEN Ql = FpX_invLaplace(FpX_Newton(Q,n,p), p);
    1810         191 :     GEN L = FpX_Laplace(FpXn_mul(Pl, Ql, n, p), p);
    1811         191 :     GEN lead = Fp_mul(Fp_powu(leading_coeff(P),degpol(Q), p),
    1812         191 :         Fp_powu(leading_coeff(Q),degpol(P), p), p);
    1813         191 :     GEN R = FpX_fromNewton(L, p);
    1814         191 :     return gc_upto(av, FpX_Fp_mul(R, lead, p));
    1815             :   }
    1816             : }
    1817             : 
    1818             : GEN
    1819           0 : FpX_composedprod(GEN P, GEN Q, GEN p)
    1820             : {
    1821           0 :   pari_sp av = avma;
    1822           0 :   if (lgefint(p)==3)
    1823             :   {
    1824           0 :     ulong pp = p[2];
    1825           0 :     GEN z = Flx_composedprod(ZX_to_Flx(P, pp), ZX_to_Flx(Q, pp), pp);
    1826           0 :     return gc_upto(av, Flx_to_ZX(z));
    1827             :   }
    1828             :   else
    1829             :   {
    1830           0 :     long n = 1+ degpol(P)*degpol(Q);
    1831           0 :     GEN L = FpX_convol(FpX_Newton(P,n,p), FpX_Newton(Q,n,p), p);
    1832           0 :     return gc_upto(av,FpX_fromNewton(L, p));
    1833             :   }
    1834             : }
    1835             : 
    1836             : static GEN
    1837         191 : _FpX_composedsum(void *E, GEN a, GEN b)
    1838         191 : { return FpX_composedsum(a,b, (GEN)E); }
    1839             : 
    1840             : GEN
    1841        1637 : FpXV_composedsum(GEN V, GEN p)
    1842             : {
    1843        1637 :   if (lgefint(p)==3)
    1844             :   {
    1845           0 :     ulong pp = p[2];
    1846           0 :     return Flx_to_ZX(FlxV_composedsum(ZXV_to_FlxV(V, pp), pp));
    1847             :   }
    1848        1637 :   return gen_product(V, (void *)p, &_FpX_composedsum);
    1849             : }
    1850             : 
    1851             : /* 0, 1, -1, 2, -2, ... */
    1852             : #define next_lambda(a) (a>0 ? -a : 1-a)
    1853             : 
    1854             : /* Assume A in Z[Y], B in Q[Y][X], B squarefree in (Q[Y]/(A))[X] and
    1855             :  * Res_Y(A, B) in Z[X]. Find a small lambda (start from *lambda, use
    1856             :  * next_lambda successively) such that C(X) = Res_Y(A(Y), B(X + lambda Y))
    1857             :  * is squarefree, reset *lambda to the chosen value and return C. Set LERS to
    1858             :  * the Last nonconstant polynomial in the Euclidean Remainder Sequence */
    1859             : static GEN
    1860       21847 : ZX_ZXY_resultant_LERS(GEN A, GEN B0, long *plambda, GEN *LERS)
    1861             : {
    1862             :   ulong bound, dp;
    1863       21847 :   pari_sp av = avma, av2 = 0;
    1864       21847 :   long lambda = *plambda, degA = degpol(A), dres = degA*degpol(B0);
    1865             :   long stable, checksqfree, i,n, cnt, degB;
    1866       21847 :   long v, vX = varn(B0), vY = varn(A); /* vY < vX */
    1867             :   GEN x, y, dglist, B, q, a, b, ev, H, H0, H1, Hp, H0p, H1p, C0, C1;
    1868             :   forprime_t S;
    1869             : 
    1870       21847 :   if (degA == 1)
    1871             :   {
    1872        1260 :     GEN a1 = gel(A,3), a0 = gel(A,2);
    1873        1260 :     B = lambda? RgX_translate(B0, monomial(stoi(lambda), 1, vY)): B0;
    1874        1260 :     H = gsubst(B, vY, gdiv(gneg(a0),a1));
    1875        1260 :    if (!equali1(a1)) H = RgX_Rg_mul(H, powiu(a1, poldegree(B,vY)));
    1876        1260 :     *LERS = mkvec2(scalarpol_shallow(a0,vX), scalarpol_shallow(a1,vX));
    1877        1260 :     return gc_all(av, 2, &H, LERS);
    1878             :   }
    1879             : 
    1880       20587 :   dglist = Hp = H0p = H1p = C0 = C1 = NULL; /* gcc -Wall */
    1881       20587 :   C0 = cgetg(dres+2, t_VECSMALL);
    1882       20587 :   C1 = cgetg(dres+2, t_VECSMALL);
    1883       20587 :   dglist = cgetg(dres+1, t_VECSMALL);
    1884       20587 :   x = cgetg(dres+2, t_VECSMALL);
    1885       20587 :   y = cgetg(dres+2, t_VECSMALL);
    1886       20587 :   B0 = leafcopy(B0);
    1887       20587 :   A = leafcopy(A);
    1888       20587 :   B = B0;
    1889       20587 :   v = fetch_var_higher(); setvarn(A,v);
    1890             :   /* make sure p large enough */
    1891       21473 : INIT:
    1892             :   /* always except the first time */
    1893       21473 :   if (av2) { set_avma(av2); lambda = next_lambda(lambda); }
    1894       21473 :   if (lambda) B = RgX_translate(B0, monomial(stoi(lambda), 1, vY));
    1895       21473 :   B = swap_vars(B, vY, v);
    1896             :   /* B0(lambda v + x, v) */
    1897       21473 :   if (DEBUGLEVEL>4) err_printf("Trying lambda = %ld\n", lambda);
    1898       21473 :   av2 = avma;
    1899             : 
    1900       21473 :   if (degA <= 3)
    1901             :   { /* sub-resultant faster for small degrees */
    1902       10752 :     H = RgX_resultant_all(A,B,&q);
    1903       10752 :     if (typ(q) != t_POL || degpol(q)!=1) goto INIT;
    1904       10031 :     H0 = gel(q,2);
    1905       10031 :     if (typ(H0) == t_POL) setvarn(H0,vX); else H0 = scalarpol(H0,vX);
    1906       10031 :     H1 = gel(q,3);
    1907       10031 :     if (typ(H1) == t_POL) setvarn(H1,vX); else H1 = scalarpol(H1,vX);
    1908       10031 :     if (!ZX_is_squarefree(H)) goto INIT;
    1909        9989 :     goto END;
    1910             :   }
    1911             : 
    1912       10721 :   H = H0 = H1 = NULL;
    1913       10721 :   degB = degpol(B);
    1914       10721 :   bound = ZX_ZXY_ResBound(A, B, NULL);
    1915       10720 :   if (DEBUGLEVEL>4) err_printf("bound for resultant coeffs: 2^%ld\n",bound);
    1916       10720 :   dp = 1;
    1917       10720 :   init_modular_big(&S);
    1918       10720 :   for(cnt = 0, checksqfree = 1;;)
    1919       49204 :   {
    1920       59924 :     ulong p = u_forprime_next(&S);
    1921             :     GEN Hi;
    1922       59924 :     a = ZX_to_Flx(A, p);
    1923       59926 :     b = ZXX_to_FlxX(B, p, varn(A));
    1924       59925 :     if (degpol(a) < degA || degpol(b) < degB) continue; /* p | lc(A)lc(B) */
    1925       59925 :     if (checksqfree)
    1926             :     { /* find degree list for generic Euclidean Remainder Sequence */
    1927       10721 :       long goal = minss(degpol(a), degpol(b)); /* longest possible */
    1928       73203 :       for (n=1; n <= goal; n++) dglist[n] = 0;
    1929       10721 :       setlg(dglist, 1);
    1930       23678 :       for (n=0; n <= dres; n++)
    1931             :       {
    1932       23286 :         ev = FlxY_evalx_drop(b, n, p);
    1933       23286 :         Flx_resultant_set_dglist(a, ev, dglist, p);
    1934       23285 :         if (lg(dglist)-1 == goal) break;
    1935             :       }
    1936             :       /* last pol in ERS has degree > 1 ? */
    1937       10720 :       goal = lg(dglist)-1;
    1938       10720 :       if (degpol(B) == 1) { if (!goal) goto INIT; }
    1939             :       else
    1940             :       {
    1941       10664 :         if (goal <= 1) goto INIT;
    1942       10601 :         if (dglist[goal] != 0 || dglist[goal-1] != 1) goto INIT;
    1943             :       }
    1944       10657 :       if (DEBUGLEVEL>4)
    1945           0 :         err_printf("Degree list for ERS (trials: %ld) = %Ps\n",n+1,dglist);
    1946             :     }
    1947             : 
    1948     2145116 :     for (i=0,n = 0; i <= dres; n++)
    1949             :     {
    1950     2085249 :       ev = FlxY_evalx_drop(b, n, p);
    1951     2085109 :       x[++i] = n; y[i] = Flx_resultant_all(a, ev, C0+i, C1+i, dglist, p);
    1952     2085254 :       if (!C1[i]) i--; /* C1(i) = 0. No way to recover C0(i) */
    1953             :     }
    1954       59867 :     Hi = Flv_Flm_polint(x, mkvec3(y,C0,C1), p, 0);
    1955       59863 :     Hp = gel(Hi,1); H0p = gel(Hi,2); H1p = gel(Hi,3);
    1956       59863 :     if (!H && degpol(Hp) != dres) continue;
    1957       59863 :     if (dp != 1) Hp = Flx_Fl_mul(Hp, Fl_powu(Fl_inv(dp,p), degA, p), p);
    1958       59863 :     if (checksqfree) {
    1959       10658 :       if (!Flx_is_squarefree(Hp, p)) goto INIT;
    1960       10598 :       if (DEBUGLEVEL>4) err_printf("Final lambda = %ld\n", lambda);
    1961       10598 :       checksqfree = 0;
    1962             :     }
    1963             : 
    1964       59803 :     if (!H)
    1965             :     { /* initialize */
    1966       10598 :       q = utoipos(p); stable = 0;
    1967       10598 :       H = ZX_init_CRT(Hp, p,vX);
    1968       10598 :       H0= ZX_init_CRT(H0p, p,vX);
    1969       10598 :       H1= ZX_init_CRT(H1p, p,vX);
    1970             :     }
    1971             :     else
    1972             :     {
    1973       49205 :       GEN qp = muliu(q,p);
    1974       49203 :       stable  = ZX_incremental_CRT_raw(&H, Hp, q,qp, p)
    1975       49205 :               & ZX_incremental_CRT_raw(&H0,H0p, q,qp, p)
    1976       49205 :               & ZX_incremental_CRT_raw(&H1,H1p, q,qp, p);
    1977       49205 :       q = qp;
    1978             :     }
    1979             :     /* could make it probabilistic for H ? [e.g if stable twice, etc]
    1980             :      * Probabilistic anyway for H0, H1 */
    1981       59803 :     if (DEBUGLEVEL>5 && (stable ||  ++cnt==100))
    1982           0 :     { cnt=0; err_printf("%ld%%%s ",100*expi(q)/bound,stable?"s":""); }
    1983       59802 :     if (stable && (ulong)expi(q) >= bound) break; /* DONE */
    1984       49204 :     if (gc_needed(av,2))
    1985             :     {
    1986           0 :       if (DEBUGMEM>1) pari_warn(warnmem,"ZX_ZXY_rnfequation");
    1987           0 :       (void)gc_all(av2, 4, &H, &q, &H0, &H1);
    1988             :     }
    1989             :   }
    1990       20587 : END:
    1991       20587 :   if (DEBUGLEVEL>5) err_printf(" done\n");
    1992       20587 :   setvarn(H, vX); (void)delete_var();
    1993       20587 :   *LERS = mkvec2(H0,H1);
    1994       20587 :   *plambda = lambda; return gc_all(av, 2, &H, LERS);
    1995             : }
    1996             : 
    1997             : GEN
    1998       59639 : ZX_ZXY_resultant_all(GEN A, GEN B, long *plambda, GEN *LERS)
    1999             : {
    2000       59639 :   if (LERS)
    2001             :   {
    2002       21847 :     if (!plambda)
    2003           0 :       pari_err_BUG("ZX_ZXY_resultant_all [LERS != NULL needs lambda]");
    2004       21847 :     return ZX_ZXY_resultant_LERS(A, B, plambda, LERS);
    2005             :   }
    2006       37792 :   return ZX_ZXY_rnfequation(A, B, plambda);
    2007             : }
    2008             : 
    2009             : /* If lambda = NULL, return caract(Mod(A, T)), T,A in Z[X].
    2010             :  * Otherwise find a small lambda such that caract (Mod(A + lambda X, T)) is
    2011             :  * squarefree */
    2012             : GEN
    2013       22594 : ZXQ_charpoly_sqf(GEN A, GEN T, long *lambda, long v)
    2014             : {
    2015       22594 :   pari_sp av = avma;
    2016             :   GEN R, a;
    2017             :   long dA;
    2018             :   int delvar;
    2019             : 
    2020       22594 :   if (v < 0) v = 0;
    2021       22594 :   switch (typ(A))
    2022             :   {
    2023       22594 :     case t_POL: dA = degpol(A); if (dA > 0) break;
    2024           0 :       A = constant_coeff(A);
    2025           0 :     default:
    2026           0 :       if (lambda) { A = scalar_ZX_shallow(A,varn(T)); dA = 0; break;}
    2027           0 :       return gc_upto(av, gpowgs(gsub(pol_x(v), A), degpol(T)));
    2028             :   }
    2029       22594 :   delvar = 0;
    2030       22594 :   if (varncmp(varn(T), 0) <= 0)
    2031             :   {
    2032        3681 :     long v0 = fetch_var(); delvar = 1;
    2033        3681 :     T = leafcopy(T); setvarn(T,v0);
    2034        3681 :     A = leafcopy(A); setvarn(A,v0);
    2035             :   }
    2036       22594 :   R = ZX_ZXY_rnfequation(T, deg1pol_shallow(gen_1, gneg_i(A), 0), lambda);
    2037       22594 :   if (delvar) (void)delete_var();
    2038       22594 :   setvarn(R, v); a = leading_coeff(T);
    2039       22594 :   if (!gequal1(a)) R = gdiv(R, powiu(a, dA));
    2040       22594 :   return gc_upto(av, R);
    2041             : }
    2042             : 
    2043             : /* charpoly(Mod(A,T)), A may be in Q[X], but assume T and result are integral */
    2044             : GEN
    2045      995251 : ZXQ_charpoly(GEN A, GEN T, long v)
    2046             : {
    2047      995251 :   return (degpol(T) < 16) ? RgXQ_charpoly_i(A,T,v): ZXQ_charpoly_sqf(A,T, NULL, v);
    2048             : }
    2049             : 
    2050             : GEN
    2051        9772 : QXQ_charpoly(GEN A, GEN T, long v)
    2052             : {
    2053        9772 :   pari_sp av = avma;
    2054        9772 :   GEN den, B = Q_remove_denom(A, &den);
    2055        9772 :   GEN P = ZXQ_charpoly(B, T, v);
    2056        9772 :   return gc_GEN(av, den ? RgX_rescale(P, ginv(den)): P);
    2057             : }
    2058             : 
    2059             : static ulong
    2060     3863839 : ZX_resultant_prime(GEN a, GEN b, GEN dB, long degA, long degB, ulong p)
    2061             : {
    2062     3863839 :   long dropa = degA - degpol(a), dropb = degB - degpol(b);
    2063             :   ulong H, dp;
    2064     3863721 :   if (dropa && dropb) return 0; /* p | lc(A), p | lc(B) */
    2065     3863721 :   H = Flx_resultant(a, b, p);
    2066     3863503 :   if (dropa)
    2067             :   { /* multiply by ((-1)^deg B lc(B))^(deg A - deg a) */
    2068           0 :     ulong c = b[degB+2]; /* lc(B) */
    2069           0 :     if (odd(degB)) c = p - c;
    2070           0 :     c = Fl_powu(c, dropa, p);
    2071           0 :     if (c != 1) H = Fl_mul(H, c, p);
    2072             :   }
    2073     3863503 :   else if (dropb)
    2074             :   { /* multiply by lc(A)^(deg B - deg b) */
    2075           0 :     ulong c = a[degA+2]; /* lc(A) */
    2076           0 :     c = Fl_powu(c, dropb, p);
    2077           0 :     if (c != 1) H = Fl_mul(H, c, p);
    2078             :   }
    2079     3863503 :   dp = dB ? umodiu(dB, p): 1;
    2080     3863502 :   if (dp != 1) H = Fl_mul(H, Fl_powu(Fl_inv(dp,p), degA, p), p);
    2081     3863504 :   return H;
    2082             : }
    2083             : 
    2084             : /* If B=NULL, assume B=A' */
    2085             : static GEN
    2086     1494401 : ZX_resultant_slice(GEN A, GEN B, GEN dB, GEN P, GEN *mod)
    2087             : {
    2088     1494401 :   pari_sp av = avma, av2;
    2089     1494401 :   long degA, degB, i, n = lg(P)-1;
    2090             :   GEN H, T;
    2091             : 
    2092     1494401 :   degA = degpol(A);
    2093     1494393 :   degB = B? degpol(B): degA - 1;
    2094     1494395 :   if (n == 1)
    2095             :   {
    2096      810594 :     ulong Hp, p = uel(P,1);
    2097      810594 :     GEN a = ZX_to_Flx(A, p), b = B? ZX_to_Flx(B, p): Flx_deriv(a, p);
    2098      810580 :     Hp = ZX_resultant_prime(a, b, dB, degA, degB, p);
    2099      810579 :     set_avma(av); *mod = utoipos(p); return utoi(Hp);
    2100             :   }
    2101      683801 :   T = ZV_producttree(P);
    2102      683802 :   A = ZX_nv_mod_tree(A, P, T);
    2103      683799 :   if (B) B = ZX_nv_mod_tree(B, P, T);
    2104      683799 :   H = cgetg(n+1, t_VECSMALL); av2 = avma;
    2105     3736767 :   for(i=1; i <= n; i++, set_avma(av2))
    2106             :   {
    2107     3052969 :     ulong p = P[i];
    2108     3052969 :     GEN a = gel(A,i), b = B? gel(B,i): Flx_deriv(a, p);
    2109     3053263 :     H[i] = ZX_resultant_prime(a, b, dB, degA, degB, p);
    2110             :   }
    2111      683798 :   H = ZV_chinese_tree(H, P, T, ZV_chinesetree(P,T));
    2112      683798 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2113             : }
    2114             : 
    2115             : GEN
    2116     1494401 : ZX_resultant_worker(GEN P, GEN A, GEN B, GEN dB)
    2117             : {
    2118     1494401 :   GEN V = cgetg(3, t_VEC);
    2119     1494402 :   if (typ(B) == t_INT) B = NULL;
    2120     1494402 :   if (!signe(dB)) dB = NULL;
    2121     1494402 :   gel(V,1) = ZX_resultant_slice(A, B, dB, P, &gel(V,2));
    2122     1494377 :   return V;
    2123             : }
    2124             : 
    2125             : /* Compute Res(A, B/dB) in Z, assuming A,B in Z[X], dB in Z or NULL (= 1)
    2126             :  * If B=NULL, take B = A' and assume deg A > 1 and 'bound' is set */
    2127             : GEN
    2128     1351019 : ZX_resultant_all(GEN A, GEN B, GEN dB, ulong bound)
    2129             : {
    2130     1351019 :   pari_sp av = avma;
    2131             :   forprime_t S;
    2132             :   GEN  H, worker;
    2133     1351019 :   if (!B && degpol(A)==2)
    2134             :   {
    2135      114020 :     GEN a = gel(A,4), b = gel(A,3), c = gel(A,2);
    2136      114020 :     H = mulii(a, subii(shifti(mulii(a, c), 2), sqri(b)));
    2137      114012 :     if (dB) H = diviiexact(H, sqri(dB));
    2138      114012 :     return gc_INT(av, H);
    2139             :   }
    2140     1236996 :   if (B)
    2141             :   {
    2142      155216 :     long a = degpol(A), b = degpol(B);
    2143      155216 :     if (a < 0 || b < 0) return gen_0;
    2144      155186 :     if (!a) return powiu(gel(A,2), b);
    2145      155186 :     if (!b) return powiu(gel(B,2), a);
    2146      153441 :     if (minss(a, b) <= 1)
    2147             :     {
    2148       76738 :       H = RgX_resultant_all(A, B, NULL);
    2149       76738 :       if (dB) H = diviiexact(H, powiu(dB, a));
    2150       76738 :       return gc_INT(av, H);
    2151             :     }
    2152       76703 :     if (!bound) bound = ZX_ZXY_ResBound(A, B, dB);
    2153             :   }
    2154     1158494 :   worker = snm_closure(is_entry("_ZX_resultant_worker"),
    2155             :                        mkvec3(A, B? B: gen_0, dB? dB: gen_0));
    2156     1158634 :   init_modular_big(&S);
    2157     1158586 :   H = gen_crt("ZX_resultant_all", worker, &S, dB, bound, 0, NULL,
    2158             :               ZV_chinese_center, Fp_center);
    2159     1158643 :   return gc_INT(av, H);
    2160             : }
    2161             : 
    2162             : /* A0 and B0 in Q[X] */
    2163             : GEN
    2164          56 : QX_resultant(GEN A0, GEN B0)
    2165             : {
    2166             :   GEN s, a, b, A, B;
    2167          56 :   pari_sp av = avma;
    2168             : 
    2169          56 :   A = Q_primitive_part(A0, &a);
    2170          56 :   B = Q_primitive_part(B0, &b);
    2171          56 :   s = ZX_resultant(A, B);
    2172          56 :   if (!signe(s)) { set_avma(av); return gen_0; }
    2173          56 :   if (a) s = gmul(s, gpowgs(a,degpol(B)));
    2174          56 :   if (b) s = gmul(s, gpowgs(b,degpol(A)));
    2175          56 :   return gc_upto(av, s);
    2176             : }
    2177             : 
    2178             : GEN
    2179       57309 : ZX_resultant(GEN A, GEN B) { return ZX_resultant_all(A,B,NULL,0); }
    2180             : 
    2181             : GEN
    2182           0 : QXQ_intnorm(GEN A, GEN B)
    2183             : {
    2184             :   GEN c, n, R, lB;
    2185           0 :   long dA = degpol(A), dB = degpol(B);
    2186           0 :   pari_sp av = avma;
    2187           0 :   if (dA < 0) return gen_0;
    2188           0 :   A = Q_primitive_part(A, &c);
    2189           0 :   if (!c || typ(c) == t_INT) {
    2190           0 :     n = c;
    2191           0 :     R = ZX_resultant(B, A);
    2192             :   } else {
    2193           0 :     n = gel(c,1);
    2194           0 :     R = ZX_resultant_all(B, A, gel(c,2), 0);
    2195             :   }
    2196           0 :   if (n && !equali1(n)) R = mulii(R, powiu(n, dB));
    2197           0 :   lB = leading_coeff(B);
    2198           0 :   if (!equali1(lB)) R = diviiexact(R, powiu(lB, dA));
    2199           0 :   return gc_INT(av, R);
    2200             : }
    2201             : 
    2202             : GEN
    2203       19418 : QXQ_norm(GEN A, GEN B)
    2204             : {
    2205             :   GEN c, R, lB;
    2206       19418 :   long dA = degpol(A), dB = degpol(B);
    2207       19418 :   pari_sp av = avma;
    2208       19418 :   if (dA < 0) return gen_0;
    2209       19418 :   A = Q_primitive_part(A, &c);
    2210       19418 :   R = ZX_resultant(B, A);
    2211       19418 :   if (c) R = gmul(R, gpowgs(c, dB));
    2212       19418 :   lB = leading_coeff(B);
    2213       19418 :   if (!equali1(lB)) R = gdiv(R, gpowgs(lB, dA));
    2214       19418 :   return gc_upto(av, R);
    2215             : }
    2216             : 
    2217             : /* assume x has integral coefficients */
    2218             : GEN
    2219     1199175 : ZX_disc_all(GEN x, ulong bound)
    2220             : {
    2221     1199175 :   pari_sp av = avma;
    2222     1199175 :   long s, d = degpol(x);
    2223             :   GEN l, R;
    2224             : 
    2225     1199172 :   if (d <= 1) return d == 1? gen_1: gen_0;
    2226     1195879 :   s = (d & 2) ? -1: 1;
    2227     1195879 :   l = leading_coeff(x);
    2228     1195871 :   if (!bound) bound = ZX_discbound(x);
    2229     1195772 :   R = ZX_resultant_all(x, NULL, NULL, bound);
    2230     1195919 :   if (is_pm1(l))
    2231     1016897 :   { if (signe(l) < 0) s = -s; }
    2232             :   else
    2233      179023 :     R = diviiexact(R,l);
    2234     1195920 :   if (s == -1) togglesign_safe(&R);
    2235     1195916 :   return gc_INT(av,R);
    2236             : }
    2237             : 
    2238             : GEN
    2239     1137331 : ZX_disc(GEN x) { return ZX_disc_all(x,0); }
    2240             : 
    2241             : static GEN
    2242       10784 : ZXQX_resultant_prime(GEN a, GEN b, GEN dB, long degA, long degB, GEN T, ulong p)
    2243             : {
    2244       10784 :   long dropa = degA - degpol(a), dropb = degB - degpol(b);
    2245             :   GEN H, dp;
    2246       10785 :   if (dropa && dropb) return pol0_Flx(T[1]); /* p | lc(A), p | lc(B) */
    2247       10785 :   H = FlxqX_saferesultant(a, b, T, p);
    2248       10784 :   if (!H) return NULL;
    2249       10784 :   if (dropa)
    2250             :   { /* multiply by ((-1)^deg B lc(B))^(deg A - deg a) */
    2251           0 :     GEN c = gel(b,degB+2); /* lc(B) */
    2252           0 :     if (odd(degB)) c = Flx_neg(c, p);
    2253           0 :     c = Flxq_powu(c, dropa, T, p);
    2254           0 :     if (!Flx_equal1(c)) H = Flxq_mul(H, c, T, p);
    2255             :   }
    2256       10784 :   else if (dropb)
    2257             :   { /* multiply by lc(A)^(deg B - deg b) */
    2258           0 :     GEN c = gel(a,degA+2); /* lc(A) */
    2259           0 :     c = Flxq_powu(c, dropb, T, p);
    2260           0 :     if (!Flx_equal1(c)) H = Flxq_mul(H, c, T, p);
    2261             :   }
    2262       10784 :   dp = dB ? ZX_to_Flx(dB, p): pol1_Flx(T[1]);
    2263       10785 :   if (!Flx_equal1(dp))
    2264             :   {
    2265           0 :     GEN idp = Flxq_invsafe(dp, T, p);
    2266           0 :     if (!idp) return NULL;
    2267           0 :     H = Flxq_mul(H, Flxq_powu(idp, degA, T, p), T, p);
    2268             :   }
    2269       10785 :   return H;
    2270             : }
    2271             : 
    2272             : /* If B=NULL, assume B=A' */
    2273             : static GEN
    2274        4687 : ZXQX_resultant_slice(GEN A, GEN B, GEN U, GEN dB, GEN P, GEN *mod)
    2275             : {
    2276        4687 :   pari_sp av = avma;
    2277        4687 :   long degA, degB, i, n = lg(P)-1;
    2278             :   GEN H, T;
    2279        4687 :   long v = varn(U), redo = 0;
    2280             : 
    2281        4687 :   degA = degpol(A);
    2282        4687 :   degB = B? degpol(B): degA - 1;
    2283        4687 :   if (n == 1)
    2284             :   {
    2285        2953 :     ulong p = uel(P,1);
    2286        2953 :     GEN a = ZXX_to_FlxX(A, p, v), b = B? ZXX_to_FlxX(B, p, v): FlxX_deriv(a, p);
    2287        2953 :     GEN u = ZX_to_Flx(U, p);
    2288        2953 :     GEN Hp = ZXQX_resultant_prime(a, b, dB, degA, degB, u, p);
    2289        2953 :     if (!Hp) { set_avma(av); *mod = gen_1; return pol_0(v); }
    2290        2953 :     Hp = gc_upto(av, Flx_to_ZX(Hp)); *mod = utoipos(p); return Hp;
    2291             :   }
    2292        1734 :   T = ZV_producttree(P);
    2293        1734 :   A = ZXX_nv_mod_tree(A, P, T, v);
    2294        1734 :   if (B) B = ZXX_nv_mod_tree(B, P, T, v);
    2295        1734 :   U = ZX_nv_mod_tree(U, P, T);
    2296        1734 :   H = cgetg(n+1, t_VEC);
    2297        9567 :   for(i=1; i <= n; i++)
    2298             :   {
    2299        7833 :     ulong p = P[i];
    2300        7833 :     GEN a = gel(A,i), b = B? gel(B,i): FlxX_deriv(a, p), u = gel(U, i);
    2301        7831 :     GEN h = ZXQX_resultant_prime(a, b, dB, degA, degB, u, p);
    2302        7832 :     if (!h)
    2303             :     {
    2304           0 :       gel(H,i) = pol_0(v);
    2305           0 :       P[i] = 1; redo = 1;
    2306             :     }
    2307             :     else
    2308        7832 :       gel(H,i) = h;
    2309             :   }
    2310        1734 :   if (redo) T = ZV_producttree(P);
    2311        1734 :   H = nxV_chinese_center_tree(H, P, T, ZV_chinesetree(P, T));
    2312        1734 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2313             : }
    2314             : 
    2315             : GEN
    2316        4687 : ZXQX_resultant_worker(GEN P, GEN A, GEN B, GEN T, GEN dB)
    2317             : {
    2318        4687 :   GEN V = cgetg(3, t_VEC);
    2319        4687 :   if (isintzero(B)) B = NULL;
    2320        4687 :   if (!signe(dB)) dB = NULL;
    2321        4687 :   gel(V,1) = ZXQX_resultant_slice(A, B, T, dB, P, &gel(V,2));
    2322        4687 :   return V;
    2323             : }
    2324             : 
    2325             : static ulong
    2326        4091 : ZXQX_resultant_bound_i(GEN nf, GEN A, GEN B, GEN (*f)(GEN,GEN,long))
    2327             : {
    2328        4091 :   pari_sp av = avma;
    2329        4091 :   GEN r, M = nf_L2_bound(nf, NULL, &r);
    2330        4091 :   long v = nf_get_varn(nf), i, l = lg(r);
    2331        4091 :   GEN a = cgetg(l, t_COL);
    2332       12662 :   for (i = 1; i < l; i++)
    2333        8571 :     gel(a, i) = f(gsubst(A, v, gel(r,i)), gsubst(B, v, gel(r,i)), DEFAULTPREC);
    2334        4091 :   return gc_ulong(av, (ulong) dbllog2(gmul(M,RgC_fpnorml2(a, DEFAULTPREC))));
    2335             : }
    2336             : static ulong
    2337        3776 : ZXQX_resultant_bound(GEN nf, GEN A, GEN B)
    2338        3776 : { return ZXQX_resultant_bound_i(nf, A, B, &RgX_RgXY_ResBound); }
    2339             : 
    2340             : static GEN
    2341          56 : _ZXQ_powu(GEN x, ulong u, GEN T)
    2342          56 : { return typ(x) == t_INT? powiu(x, u): ZXQ_powu(x, u, T); }
    2343             : 
    2344             : /* Compute Res(A, B/dB) in Z[X]/T, assuming A,B in Z[X,Y], dB in Z or NULL (= 1)
    2345             :  * If B=NULL, take B = A' and assume deg A > 1 */
    2346             : static GEN
    2347        3773 : ZXQX_resultant_all(GEN A, GEN B, GEN T, GEN dB, ulong bound)
    2348             : {
    2349        3773 :   pari_sp av = avma;
    2350             :   forprime_t S;
    2351             :   GEN  H, worker;
    2352        3773 :   if (B)
    2353             :   {
    2354          63 :     long a = degpol(A), b = degpol(B);
    2355          63 :     if (a < 0 || b < 0) return gen_0;
    2356          63 :     if (!a) return _ZXQ_powu(gel(A,2), b, T);
    2357          63 :     if (!b) return _ZXQ_powu(gel(B,2), a, T);
    2358             :   } else
    2359        3710 :     if (!bound) B = RgX_deriv(A);
    2360        3773 :   if (!bound) bound = ZXQX_resultant_bound(nfinit(T, DEFAULTPREC), A, B);
    2361        3773 :   worker = snm_closure(is_entry("_ZXQX_resultant_worker"),
    2362             :                        mkvec4(A, B? B: gen_0, T, dB? dB: gen_0));
    2363        3773 :   init_modular_big(&S);
    2364        3773 :   H = gen_crt("ZXQX_resultant_all", worker, &S, dB, bound, 0, NULL,
    2365             :               nxV_chinese_center, FpX_center);
    2366        3773 :   if (DEBUGLEVEL)
    2367           0 :     err_printf("ZXQX_resultant_all: a priori bound: %lu, a posteriori: %lu\n",
    2368             :                bound, expi(gsupnorm(H, DEFAULTPREC)));
    2369        3773 :   return gc_upto(av, H);
    2370             : }
    2371             : 
    2372             : GEN
    2373         119 : nfX_resultant(GEN nf, GEN x, GEN y)
    2374             : {
    2375         119 :   pari_sp av = avma;
    2376         119 :   GEN cx, cy, D, T = nf_get_pol(nf);
    2377         119 :   long dx = degpol(x), dy = degpol(y);
    2378         119 :   if (dx < 0 || dy < 0) return gen_0;
    2379         119 :   x = Q_primitive_part(x, &cx); if (cx) cx = gpowgs(cx, dy);
    2380         119 :   y = Q_primitive_part(y, &cy); if (cy) cy = gpowgs(cy, dx);
    2381         119 :   if (!dx)      D = _ZXQ_powu(gel(x,2), dy, T);
    2382         119 :   else if (!dy) D = _ZXQ_powu(gel(y,2), dx, T);
    2383             :   else
    2384             :   {
    2385          63 :     ulong bound = ZXQX_resultant_bound(nf, x, y);
    2386          63 :     D = ZXQX_resultant_all(x, y, T, NULL, bound);
    2387             :   }
    2388         119 :   cx = mul_content(cx, cy); if (cx) D = gmul(D, cx);
    2389         119 :   return gc_upto(av, D);
    2390             : }
    2391             : 
    2392             : static GEN
    2393         252 : to_ZX(GEN a, long v) { return typ(a)==t_INT? scalarpol(a,v): a; }
    2394             : 
    2395             : static GEN
    2396        3710 : ZXQX_disc_all(GEN x, GEN T, ulong bound)
    2397             : {
    2398        3710 :   pari_sp av = avma;
    2399        3710 :   long s, d = degpol(x), v = varn(T);
    2400             :   GEN l, R;
    2401             : 
    2402        3710 :   if (d <= 1) return d == 1? pol_1(v): pol_0(v);
    2403        3710 :   s = (d & 2) ? -1: 1;
    2404        3710 :   l = leading_coeff(x);
    2405        3710 :   R = ZXQX_resultant_all(x, NULL, T, NULL, bound);
    2406        3710 :   if (!gequal1(l)) R = QXQ_div(R, to_ZX(l,v), T);
    2407        3710 :   if (s == -1) R = RgX_neg(R);
    2408        3710 :   return gc_upto(av, R);
    2409             : }
    2410             : 
    2411             : GEN
    2412           7 : QX_disc(GEN x)
    2413             : {
    2414           7 :   pari_sp av = avma;
    2415           7 :   GEN c, d = ZX_disc( Q_primitive_part(x, &c) );
    2416           7 :   if (c) d = gmul(d, gpowgs(c, 2*degpol(x) - 2));
    2417           7 :   return gc_upto(av, d);
    2418             : }
    2419             : 
    2420             : GEN
    2421        3941 : nfX_disc(GEN nf, GEN x)
    2422             : {
    2423        3941 :   pari_sp av = avma;
    2424        3941 :   GEN c, D, T = nf_get_pol(nf);
    2425             :   ulong bound;
    2426        3941 :   long d = degpol(x), v = varn(T);
    2427        3941 :   if (d <= 1) return d == 1? pol_1(v): pol_0(v);
    2428        3710 :   x = Q_primitive_part(x, &c);
    2429        3710 :   bound = ZXQX_resultant_bound(nf, x, RgX_deriv(x));
    2430        3710 :   D = ZXQX_disc_all(x, T, bound);
    2431        3710 :   if (c) D = gmul(D, gpowgs(c, 2*d - 2));
    2432        3710 :   return gc_upto(av, D);
    2433             : }
    2434             : 
    2435             : GEN
    2436      837295 : QXQ_mul(GEN x, GEN y, GEN T)
    2437             : {
    2438      837295 :   GEN dx, nx = Q_primitive_part(x, &dx);
    2439      837293 :   GEN dy, ny = Q_primitive_part(y, &dy);
    2440      837288 :   GEN z = ZXQ_mul(nx, ny, T);
    2441      837292 :   if (dx || dy)
    2442             :   {
    2443      834492 :     GEN d = dx ? dy ? gmul(dx, dy): dx : dy;
    2444      834492 :     if (!gequal1(d)) z = ZX_Q_mul(z, d);
    2445             :   }
    2446      837295 :   return z;
    2447             : }
    2448             : 
    2449             : GEN
    2450      399481 : QXQ_sqr(GEN x, GEN T)
    2451             : {
    2452      399481 :   GEN dx, nx = Q_primitive_part(x, &dx);
    2453      399481 :   GEN z = ZXQ_sqr(nx, T);
    2454      399481 :   if (dx)
    2455      397745 :     z = ZX_Q_mul(z, gsqr(dx));
    2456      399481 :   return z;
    2457             : }
    2458             : 
    2459             : static GEN
    2460      212647 : QXQ_inv_slice(GEN A, GEN B, GEN P, GEN *mod)
    2461             : {
    2462      212647 :   pari_sp av = avma;
    2463      212647 :   long i, n = lg(P)-1, v = varn(A), redo = 0;
    2464             :   GEN H, T;
    2465      212647 :   if (n == 1)
    2466             :   {
    2467      165610 :     ulong p = uel(P,1);
    2468      165610 :     GEN a = ZX_to_Flx(A, p), b = ZX_to_Flx(B, p);
    2469      165610 :     GEN U = Flxq_invsafe(a, b, p);
    2470      165610 :     if (!U)
    2471             :     {
    2472          24 :       set_avma(av);
    2473          24 :       *mod = gen_1; return pol_0(v);
    2474             :     }
    2475      165586 :     H = gc_GEN(av, Flx_to_ZX(U));
    2476      165586 :     *mod = utoipos(p); return H;
    2477             :   }
    2478       47037 :   T = ZV_producttree(P);
    2479       47037 :   A = ZX_nv_mod_tree(A, P, T);
    2480       47036 :   B = ZX_nv_mod_tree(B, P, T);
    2481       47037 :   H = cgetg(n+1, t_VEC);
    2482      237831 :   for(i=1; i <= n; i++)
    2483             :   {
    2484      190795 :     ulong p = P[i];
    2485      190795 :     GEN a = gel(A,i), b = gel(B,i);
    2486      190795 :     GEN U = Flxq_invsafe(a, b, p);
    2487      190793 :     if (!U)
    2488             :     {
    2489         601 :       gel(H,i) = pol_0(v);
    2490         601 :       P[i] = 1; redo = 1;
    2491             :     }
    2492             :     else
    2493      190192 :       gel(H,i) = U;
    2494             :   }
    2495       47036 :   if (redo) T = ZV_producttree(P);
    2496       47036 :   H = nxV_chinese_center_tree(H, P, T, ZV_chinesetree(P, T));
    2497       47037 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2498             : }
    2499             : 
    2500             : GEN
    2501      212647 : QXQ_inv_worker(GEN P, GEN A, GEN B)
    2502             : {
    2503      212647 :   GEN V = cgetg(3, t_VEC);
    2504      212647 :   gel(V,1) = QXQ_inv_slice(A, B, P, &gel(V,2));
    2505      212647 :   return V;
    2506             : }
    2507             : 
    2508             : /* lift(1 / Mod(A,B)). B a ZX, A a scalar or a QX */
    2509             : GEN
    2510      145976 : QXQ_inv(GEN A, GEN B)
    2511             : {
    2512             :   GEN D, Ap, Bp;
    2513             :   ulong pp;
    2514      145976 :   pari_sp av2, av = avma;
    2515             :   forprime_t S;
    2516      145976 :   GEN worker, U, H = NULL, mod = gen_1;
    2517             :   pari_timer ti;
    2518             :   long k, dA, dB;
    2519      145976 :   if (is_scalar_t(typ(A))) return scalarpol(ginv(A), varn(B));
    2520             :   /* A a QX, B a ZX */
    2521      145976 :   A = Q_primitive_part(A, &D);
    2522      145976 :   dA = degpol(A); dB= degpol(B);
    2523             :   /* A, B in Z[X] */
    2524      145976 :   init_modular_small(&S);
    2525             :   do {
    2526      145976 :     pp = u_forprime_next(&S);
    2527      145976 :     Ap = ZX_to_Flx(A, pp);
    2528      145976 :     Bp = ZX_to_Flx(B, pp);
    2529      145976 :   } while (degpol(Ap) != dA || degpol(Bp) != dB);
    2530      145976 :   if (degpol(Flx_gcd(Ap, Bp, pp)) != 0 && degpol(ZX_gcd(A,B))!=0)
    2531          14 :     pari_err_INV("QXQ_inv",mkpolmod(A,B));
    2532      145962 :   worker = snm_closure(is_entry("_QXQ_inv_worker"), mkvec2(A, B));
    2533      145962 :   av2 = avma;
    2534      145962 :   for (k = 1; ;k *= 2)
    2535       42486 :   {
    2536             :     GEN res, b, N, den;
    2537      188448 :     gen_inccrt_i("QXQ_inv", worker, NULL, (k+1)>>1, 0, &S, &H, &mod,
    2538             :                  nxV_chinese_center, FpX_center);
    2539      188448 :     (void)gc_all(av2, 2, &H, &mod);
    2540      188448 :     b = sqrti(shifti(mod,-1));
    2541      188448 :     if (DEBUGLEVEL>5) timer_start(&ti);
    2542      188448 :     U = FpX_ratlift(H, mod, b, b, NULL);
    2543      188448 :     if (DEBUGLEVEL>5) timer_printf(&ti,"QXQ_inv: ratlift");
    2544      194161 :     if (!U) continue;
    2545      151675 :     N = Q_remove_denom(U, &den); if (!den) den = gen_1;
    2546      151675 :     res = Flx_rem(Flx_Fl_sub(Flx_mul(Ap, ZX_to_Flx(N,pp), pp),
    2547             :                   umodiu(den, pp), pp), Bp, pp);
    2548      151675 :     if (degpol(res) >= 0) continue;
    2549      145962 :     res = ZX_Z_sub(ZX_mul(A, N), den);
    2550      145962 :     res = ZX_is_monic(B) ? ZX_rem(res, B): RgX_pseudorem(res, B);
    2551      145962 :     if (DEBUGLEVEL>5) timer_printf(&ti,"QXQ_inv: final check");
    2552      145962 :     if (degpol(res)<0)
    2553             :     {
    2554      145962 :       if (D) U = RgX_Rg_div(U, D);
    2555      145962 :       return gc_GEN(av, U);
    2556             :     }
    2557             :   }
    2558             : }
    2559             : 
    2560             : static GEN
    2561      120511 : QXQ_div_slice(GEN A, GEN B, GEN C, GEN P, GEN *mod)
    2562             : {
    2563      120511 :   pari_sp av = avma;
    2564      120511 :   long i, n = lg(P)-1, v = varn(A), redo = 0;
    2565             :   GEN H, T;
    2566      120511 :   if (n == 1)
    2567             :   {
    2568       44149 :     ulong p = uel(P,1);
    2569       44149 :     GEN a = ZX_to_Flx(A, p), b = ZX_to_Flx(B, p), c = ZX_to_Flx(C, p);
    2570       44149 :     GEN bi = Flxq_invsafe(b, c, p), U;
    2571       44149 :     if (!bi)
    2572             :     {
    2573           0 :       set_avma(av);
    2574           0 :       *mod = gen_1; return pol_0(v);
    2575             :     }
    2576       44149 :     U = Flxq_mul(a, bi, c, p);
    2577       44149 :     H = gc_GEN(av, Flx_to_ZX(U));
    2578       44149 :     *mod = utoipos(p); return H;
    2579             :   }
    2580       76362 :   T = ZV_producttree(P);
    2581       76362 :   A = ZX_nv_mod_tree(A, P, T);
    2582       76362 :   B = ZX_nv_mod_tree(B, P, T);
    2583       76362 :   C = ZX_nv_mod_tree(C, P, T);
    2584       76362 :   H = cgetg(n+1, t_VEC);
    2585      337311 :   for(i=1; i <= n; i++)
    2586             :   {
    2587      260950 :     ulong p = P[i];
    2588      260950 :     GEN a = gel(A,i), b = gel(B,i), c = gel(C, i);
    2589      260950 :     GEN bi = Flxq_invsafe(b, c, p);
    2590      260953 :     if (!bi)
    2591             :     {
    2592           4 :       gel(H,i) = pol_0(v);
    2593           4 :       P[i] = 1; redo = 1;
    2594             :     }
    2595             :     else
    2596      260949 :       gel(H,i) = Flxq_mul(a, bi, c, p);
    2597             :   }
    2598       76361 :   if (redo) T = ZV_producttree(P);
    2599       76361 :   H = nxV_chinese_center_tree(H, P, T, ZV_chinesetree(P, T));
    2600       76362 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2601             : }
    2602             : 
    2603             : GEN
    2604      120511 : QXQ_div_worker(GEN P, GEN A, GEN B, GEN C)
    2605             : {
    2606      120511 :   GEN V = cgetg(3, t_VEC);
    2607      120511 :   gel(V,1) = QXQ_div_slice(A, B, C, P, &gel(V,2));
    2608      120511 :   return V;
    2609             : }
    2610             : 
    2611             : /* lift(Mod(A/B, C)). C a ZX, A, B a scalar or a QX */
    2612             : GEN
    2613       32759 : QXQ_div(GEN A, GEN B, GEN C)
    2614             : {
    2615             :   GEN DA, DB, Ap, Bp, Cp;
    2616             :   ulong pp;
    2617       32759 :   pari_sp av2, av = avma;
    2618             :   forprime_t S;
    2619       32759 :   GEN worker, U, H = NULL, mod = gen_1;
    2620             :   pari_timer ti;
    2621             :   long k, dA, dB, dC;
    2622       32759 :   if (is_scalar_t(typ(A))) return scalarpol(ginv(A), varn(B));
    2623             :   /* A a QX, B a ZX */
    2624       32759 :   A = Q_primitive_part(A, &DA);
    2625       32759 :   B = Q_primitive_part(B, &DB);
    2626       32759 :   dA = degpol(A); dB = degpol(B); dC = degpol(C);
    2627             :   /* A, B in Z[X] */
    2628       32759 :   init_modular_small(&S);
    2629             :   do {
    2630       32759 :     pp = u_forprime_next(&S);
    2631       32759 :     Ap = ZX_to_Flx(A, pp);
    2632       32759 :     Bp = ZX_to_Flx(B, pp);
    2633       32759 :     Cp = ZX_to_Flx(C, pp);
    2634       32759 :   } while (degpol(Ap) != dA || degpol(Bp) != dB || degpol(Cp) != dC);
    2635       32759 :   if (degpol(Flx_gcd(Bp, Cp, pp)) != 0 && degpol(ZX_gcd(B,C))!=0)
    2636           0 :     pari_err_INV("QXQ_div",mkpolmod(B,C));
    2637       32758 :   worker = snm_closure(is_entry("_QXQ_div_worker"), mkvec3(A, B, C));
    2638       32759 :   av2 = avma;
    2639       32759 :   for (k = 1; ;k *= 2)
    2640       46576 :   {
    2641             :     GEN res, b, N, den;
    2642       79335 :     gen_inccrt_i("QXQ_div", worker, NULL, (k+1)>>1, 0, &S, &H, &mod,
    2643             :                  nxV_chinese_center, FpX_center);
    2644       79335 :     (void)gc_all(av2, 2, &H, &mod);
    2645       79335 :     b = sqrti(shifti(mod,-1));
    2646       79335 :     if (DEBUGLEVEL>5) timer_start(&ti);
    2647       79335 :     U = FpX_ratlift(H, mod, b, b, NULL);
    2648       79335 :     if (DEBUGLEVEL>5) timer_printf(&ti,"QXQ_div: ratlift");
    2649       89945 :     if (!U) continue;
    2650       43369 :     N = Q_remove_denom(U, &den); if (!den) den = gen_1;
    2651       43369 :     res = Flx_rem(Flx_sub(Flx_mul(Bp, ZX_to_Flx(N,pp), pp),
    2652             :                           Flx_Fl_mul(Ap, umodiu(den, pp), pp), pp), Cp, pp);
    2653       43369 :     if (degpol(res) >= 0) continue;
    2654       32759 :     res = ZX_sub(ZX_mul(B, N), ZX_Z_mul(A,den));
    2655       32759 :     res = ZX_is_monic(C) ? ZX_rem(res, C): RgX_pseudorem(res, C);
    2656       32759 :     if (DEBUGLEVEL>5) timer_printf(&ti,"QXQ_div: final check");
    2657       32759 :     if (degpol(res)<0)
    2658             :     {
    2659       32759 :       if (DA && DB) U = RgX_Rg_mul(U, gdiv(DA,DB));
    2660       27831 :       else if (DA) U = RgX_Rg_mul(U, DA);
    2661       15743 :       else if (DB) U = RgX_Rg_div(U, DB);
    2662       32759 :       return gc_GEN(av, U);
    2663             :     }
    2664             :   }
    2665             : }
    2666             : 
    2667             : /************************************************************************
    2668             :  *                                                                      *
    2669             :  *                           ZXQ_minpoly                                *
    2670             :  *                                                                      *
    2671             :  ************************************************************************/
    2672             : 
    2673             : static GEN
    2674        3523 : ZXQ_minpoly_slice(GEN A, GEN B, long d, GEN P, GEN *mod)
    2675             : {
    2676        3523 :   pari_sp av = avma;
    2677        3523 :   long i, n = lg(P)-1, v = evalvarn(varn(B));
    2678             :   GEN H, T;
    2679        3523 :   if (n == 1)
    2680             :   {
    2681         716 :     ulong p = uel(P,1);
    2682         716 :     GEN a = ZX_to_Flx(A, p), b = ZX_to_Flx(B, p);
    2683         716 :     GEN Hp = Flxq_minpoly(a, b, p);
    2684         716 :     if (degpol(Hp) != d) { p = 1; Hp = pol0_Flx(v); }
    2685         716 :     H = gc_upto(av, Flx_to_ZX(Hp));
    2686         716 :     *mod = utoipos(p); return H;
    2687             :   }
    2688        2807 :   T = ZV_producttree(P);
    2689        2807 :   A = ZX_nv_mod_tree(A, P, T);
    2690        2807 :   B = ZX_nv_mod_tree(B, P, T);
    2691        2807 :   H = cgetg(n+1, t_VEC);
    2692       16838 :   for(i=1; i <= n; i++)
    2693             :   {
    2694       14031 :     ulong p = P[i];
    2695       14031 :     GEN a = gel(A,i), b = gel(B,i);
    2696       14031 :     GEN m = Flxq_minpoly(a, b, p);
    2697       14031 :     if (degpol(m) != d) { P[i] = 1; m = pol0_Flx(v); }
    2698       14031 :     gel(H, i) = m;
    2699             :   }
    2700        2807 :   H = nxV_chinese_center_tree(H, P, T, ZV_chinesetree(P, T));
    2701        2807 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2702             : }
    2703             : 
    2704             : GEN
    2705        3523 : ZXQ_minpoly_worker(GEN P, GEN A, GEN B, long d)
    2706             : {
    2707        3523 :   GEN V = cgetg(3, t_VEC);
    2708        3523 :   gel(V,1) = ZXQ_minpoly_slice(A, B, d, P, &gel(V,2));
    2709        3523 :   return V;
    2710             : }
    2711             : 
    2712             : GEN
    2713        1701 : ZXQ_minpoly(GEN A, GEN B, long d, ulong bound)
    2714             : {
    2715        1701 :   pari_sp av = avma;
    2716             :   GEN worker, H, dB;
    2717             :   forprime_t S;
    2718        1701 :   B = Q_remove_denom(B, &dB);
    2719        1701 :   worker = strtoclosure("_ZXQ_minpoly_worker", 3, A, B, stoi(d));
    2720        1701 :   init_modular_big(&S);
    2721        1701 :   H = gen_crt("ZXQ_minpoly", worker, &S, dB, bound, 0, NULL,
    2722             :                nxV_chinese_center, FpX_center_i);
    2723        1701 :   return gc_GEN(av, H);
    2724             : }
    2725             : 
    2726             : /************************************************************************
    2727             :  *                                                                      *
    2728             :  *                   ZX_ZXY_resultant                                   *
    2729             :  *                                                                      *
    2730             :  ************************************************************************/
    2731             : 
    2732             : static GEN
    2733      364807 : ZX_ZXY_resultant_prime(GEN a, GEN b, ulong dp, ulong p,
    2734             :                        long degA, long degB, long dres, long sX)
    2735             : {
    2736      364807 :   long dropa = degA - degpol(a), dropb = degB - degpol(b);
    2737      364805 :   ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    2738      364803 :   GEN Hp = Flx_FlxY_resultant_polint(a, b, p, pi, dres, sX);
    2739      364811 :   if (dropa && dropb)
    2740           0 :     Hp = zero_Flx(sX);
    2741             :   else {
    2742      364811 :     if (dropa)
    2743             :     { /* multiply by ((-1)^deg B lc(B))^(deg A - deg a) */
    2744           0 :       GEN c = gel(b,degB+2); /* lc(B) */
    2745           0 :       if (odd(degB)) c = Flx_neg(c, p);
    2746           0 :       if (!Flx_equal1(c)) {
    2747           0 :         c = Flx_powu_pre(c, dropa, p, pi);
    2748           0 :         if (!Flx_equal1(c)) Hp = Flx_mul_pre(Hp, c, p, pi);
    2749             :       }
    2750             :     }
    2751      364811 :     else if (dropb)
    2752             :     { /* multiply by lc(A)^(deg B - deg b) */
    2753           0 :       ulong c = uel(a, degA+2); /* lc(A) */
    2754           0 :       c = Fl_powu(c, dropb, p);
    2755           0 :       if (c != 1) Hp = Flx_Fl_mul_pre(Hp, c, p, pi);
    2756             :     }
    2757             :   }
    2758      364811 :   if (dp != 1) Hp = Flx_Fl_mul_pre(Hp, Fl_powu_pre(Fl_inv(dp,p), degA, p, pi), p, pi);
    2759      364811 :   return Hp;
    2760             : }
    2761             : 
    2762             : static GEN
    2763      124940 : ZX_ZXY_resultant_slice(GEN A, GEN B, GEN dB, long degA, long degB, long dres,
    2764             :                        GEN P, GEN *mod, long sX, long vY)
    2765             : {
    2766      124940 :   pari_sp av = avma;
    2767      124940 :   long i, n = lg(P)-1;
    2768             :   GEN H, T, D;
    2769      124940 :   if (n == 1)
    2770             :   {
    2771       40164 :     ulong p = uel(P,1);
    2772       40164 :     ulong dp = dB ? umodiu(dB, p): 1;
    2773       40164 :     GEN a = ZX_to_Flx(A, p), b = ZXX_to_FlxX(B, p, vY);
    2774       40165 :     GEN Hp = ZX_ZXY_resultant_prime(a, b, dp, p, degA, degB, dres, sX);
    2775       40164 :     H = gc_upto(av, Flx_to_ZX(Hp));
    2776       40164 :     *mod = utoipos(p); return H;
    2777             :   }
    2778       84776 :   T = ZV_producttree(P);
    2779       84776 :   A = ZX_nv_mod_tree(A, P, T);
    2780       84776 :   B = ZXX_nv_mod_tree(B, P, T, vY);
    2781       84776 :   D = dB ? Z_ZV_mod_tree(dB, P, T): NULL;
    2782       84776 :   H = cgetg(n+1, t_VEC);
    2783      364102 :   for(i=1; i <= n; i++)
    2784             :   {
    2785      279325 :     ulong p = P[i];
    2786      279325 :     GEN a = gel(A,i), b = gel(B,i);
    2787      279325 :     ulong dp = D ? uel(D, i): 1;
    2788      279325 :     gel(H,i) = ZX_ZXY_resultant_prime(a, b, dp, p, degA, degB, dres, sX);
    2789             :   }
    2790       84777 :   H = nxV_chinese_center_tree(H, P, T, ZV_chinesetree(P, T));
    2791       84776 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2792             : }
    2793             : 
    2794             : GEN
    2795      124940 : ZX_ZXY_resultant_worker(GEN P, GEN A, GEN B, GEN dB, GEN v)
    2796             : {
    2797      124940 :   GEN V = cgetg(3, t_VEC);
    2798      124940 :   if (isintzero(dB)) dB = NULL;
    2799      124940 :   gel(V,1) = ZX_ZXY_resultant_slice(A, B, dB, v[1], v[2], v[3], P, &gel(V,2), v[4], v[5]);
    2800      124941 :   return V;
    2801             : }
    2802             : 
    2803             : GEN
    2804       79187 : ZX_ZXY_resultant(GEN A, GEN B)
    2805             : {
    2806       79187 :   pari_sp av = avma;
    2807             :   forprime_t S;
    2808             :   ulong bound;
    2809       79187 :   long v = fetch_var_higher();
    2810       79187 :   long degA = degpol(A), degB, dres = degA * degpol(B);
    2811       79188 :   long vX = varn(B), vY = varn(A); /* assume vY has lower priority */
    2812       79188 :   long sX = evalvarn(vX);
    2813             :   GEN worker, H, dB;
    2814       79188 :   B = Q_remove_denom(B, &dB);
    2815       79187 :   if (!dB) B = leafcopy(B);
    2816       79188 :   A = leafcopy(A); setvarn(A,v);
    2817       79188 :   B = swap_vars(B, vY, v); degB = degpol(B);
    2818       79187 :   bound = ZX_ZXY_ResBound(A, B, dB);
    2819       79189 :   if (DEBUGLEVEL>4) err_printf("bound for resultant coeffs: 2^%ld\n",bound);
    2820      158378 :   worker = snm_closure(is_entry("_ZX_ZXY_resultant_worker"),
    2821       79189 :                        mkvec4(A, B, dB? dB: gen_0,
    2822             :                               mkvecsmall5(degA, degB, dres, sX, vY)));
    2823       79189 :   init_modular_big(&S);
    2824       79188 :   H = gen_crt("ZX_ZXY_resultant_all", worker, &S, dB, bound, 0, NULL,
    2825             :                nxV_chinese_center, FpX_center_i);
    2826       79189 :   setvarn(H, vX); (void)delete_var();
    2827       79189 :   return gc_GEN(av, H);
    2828             : }
    2829             : 
    2830             : static long
    2831       40515 : ZX_ZXY_rnfequation_lambda(GEN A, GEN B0, long lambda)
    2832             : {
    2833       40515 :   pari_sp av = avma;
    2834       40515 :   long degA = degpol(A), degB, dres = degA*degpol(B0);
    2835       40515 :   long v = fetch_var_higher();
    2836       40515 :   long vX = varn(B0), vY = varn(A); /* assume vY has lower priority */
    2837       40515 :   long sX = evalvarn(vX);
    2838             :   GEN dB, B, a, b, Hp;
    2839             :   forprime_t S;
    2840             : 
    2841       40515 :   B0 = Q_remove_denom(B0, &dB);
    2842       40515 :   if (!dB) B0 = leafcopy(B0);
    2843       40515 :   A = leafcopy(A);
    2844       40515 :   B = B0;
    2845       40515 :   setvarn(A,v);
    2846       45320 : INIT:
    2847       45320 :   if (lambda) B = RgX_translate(B0, monomial(stoi(lambda), 1, vY));
    2848       45320 :   B = swap_vars(B, vY, v);
    2849             :   /* B0(lambda v + x, v) */
    2850       45320 :   if (DEBUGLEVEL>4) err_printf("Trying lambda = %ld\n", lambda);
    2851             : 
    2852       45320 :   degB = degpol(B);
    2853       45320 :   init_modular_big(&S);
    2854             :   while (1)
    2855           0 :   {
    2856       45320 :     ulong p = u_forprime_next(&S);
    2857       45320 :     ulong dp = dB ? umodiu(dB, p): 1;
    2858       45320 :     if (!dp) continue;
    2859       45320 :     a = ZX_to_Flx(A, p);
    2860       45320 :     b = ZXX_to_FlxX(B, p, v);
    2861       45319 :     Hp = ZX_ZXY_resultant_prime(a, b, dp, p, degA, degB, dres, sX);
    2862       45320 :     if (degpol(Hp) != dres) continue;
    2863       45320 :     if (dp != 1) Hp = Flx_Fl_mul(Hp, Fl_powu(Fl_inv(dp,p), degA, p), p);
    2864       45320 :     if (!Flx_is_squarefree(Hp, p)) { lambda = next_lambda(lambda); goto INIT; }
    2865       40514 :     if (DEBUGLEVEL>4) err_printf("Final lambda = %ld\n", lambda);
    2866       40514 :     (void)delete_var(); return gc_long(av,lambda);
    2867             :   }
    2868             : }
    2869             : 
    2870             : GEN
    2871       60554 : ZX_ZXY_rnfequation(GEN A, GEN B, long *lambda)
    2872             : {
    2873       60554 :   if (lambda)
    2874             :   {
    2875       40515 :     *lambda = ZX_ZXY_rnfequation_lambda(A, B, *lambda);
    2876       40514 :     if (*lambda) B = RgX_translate(B, monomial(stoi(*lambda), 1, varn(A)));
    2877             :   }
    2878       60553 :   return ZX_ZXY_resultant(A,B);
    2879             : }
    2880             : 
    2881             : static GEN
    2882       10346 : ZX_composedsum_slice(GEN A, GEN B, GEN P, GEN *mod)
    2883             : {
    2884       10346 :   pari_sp av = avma;
    2885       10346 :   long i, n = lg(P)-1;
    2886             :   GEN H, T;
    2887       10346 :   if (n == 1)
    2888             :   {
    2889        9844 :     ulong p = uel(P,1);
    2890        9844 :     GEN a = ZX_to_Flx(A, p), b = ZX_to_Flx(B, p);
    2891        9847 :     GEN Hp = Flx_composedsum(a, b, p);
    2892        9846 :     H = gc_upto(av, Flx_to_ZX(Hp));
    2893        9848 :     *mod = utoipos(p); return H;
    2894             :   }
    2895         502 :   T = ZV_producttree(P);
    2896         502 :   A = ZX_nv_mod_tree(A, P, T);
    2897         502 :   B = ZX_nv_mod_tree(B, P, T);
    2898         502 :   H = cgetg(n+1, t_VEC);
    2899        4526 :   for(i=1; i <= n; i++)
    2900             :   {
    2901        4024 :     ulong p = P[i];
    2902        4024 :     GEN a = gel(A,i), b = gel(B,i);
    2903        4024 :     gel(H,i) = Flx_composedsum(a, b, p);
    2904             :   }
    2905         502 :   H = nxV_chinese_center_tree(H, P, T, ZV_chinesetree(P, T));
    2906         502 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2907             : }
    2908             : 
    2909             : GEN
    2910       10347 : ZX_composedsum_worker(GEN P, GEN A, GEN B)
    2911             : {
    2912       10347 :   GEN V = cgetg(3, t_VEC);
    2913       10346 :   gel(V,1) = ZX_composedsum_slice(A, B, P, &gel(V,2));
    2914       10349 :   return V;
    2915             : }
    2916             : 
    2917             : static GEN
    2918       10085 : ZX_composedsum_i(GEN A, GEN B, GEN lead)
    2919             : {
    2920       10085 :   pari_sp av = avma;
    2921             :   forprime_t S;
    2922             :   ulong bound;
    2923             :   GEN H, worker, mod;
    2924       10085 :   if (degpol(A) < degpol(B)) swap(A, B);
    2925       10084 :   if (!lead) lead  = mulii(leading_coeff(A),leading_coeff(B));
    2926       10084 :   bound = ZX_ZXY_ResBound_1(A, B);
    2927       10085 :   worker = snm_closure(is_entry("_ZX_composedsum_worker"), mkvec2(A,B));
    2928       10086 :   init_modular_big(&S);
    2929       10082 :   H = gen_crt("ZX_composedsum", worker, &S, lead, bound, 0, &mod,
    2930             :               nxV_chinese_center, FpX_center);
    2931       10085 :   return gc_upto(av, H);
    2932             : }
    2933             : 
    2934             : static long
    2935        9697 : ZX_compositum_lambda(GEN A, GEN B, GEN lead, long lambda)
    2936             : {
    2937        9697 :   pari_sp av = avma;
    2938             :   forprime_t S;
    2939             :   ulong p;
    2940        9697 :   init_modular_big(&S);
    2941        9699 :   p = u_forprime_next(&S);
    2942             :   while (1)
    2943         112 :   {
    2944             :     GEN Hp, a;
    2945        9811 :     if (DEBUGLEVEL>4) err_printf("Trying lambda = %ld\n", lambda);
    2946        9811 :     if (lead && dvdiu(lead,p)) { p = u_forprime_next(&S); continue; }
    2947        9803 :     a = ZX_to_Flx(ZX_rescale(A, stoi(-lambda)), p);
    2948        9803 :     Hp = Flx_composedsum(a, ZX_to_Flx(B, p), p);
    2949        9801 :     if (!Flx_is_squarefree(Hp, p)) { lambda = next_lambda(lambda); continue; }
    2950        9693 :     if (DEBUGLEVEL>4) err_printf("Final lambda = %ld\n", lambda);
    2951        9693 :     return gc_long(av, lambda);
    2952             :   }
    2953             : }
    2954             : 
    2955             : GEN
    2956        9701 : ZX_compositum(GEN A, GEN B, long *lambda)
    2957             : {
    2958        9701 :   GEN lead  = mulii(leading_coeff(A),leading_coeff(B));
    2959        9697 :   if (lambda)
    2960             :   {
    2961        9697 :     *lambda = ZX_compositum_lambda(A, B, lead, *lambda);
    2962        9693 :     A = ZX_rescale(A, stoi(-*lambda));
    2963             :   }
    2964        9700 :   return ZX_composedsum_i(A, B, lead);
    2965             : }
    2966             : 
    2967             : GEN
    2968         385 : ZX_composedsum(GEN A, GEN B)
    2969         385 : { return ZX_composedsum_i(A, B, NULL); }
    2970             : 
    2971             : static GEN
    2972         359 : ZXQX_composedsum_slice(GEN A, GEN B, GEN C, GEN P, GEN *mod)
    2973             : {
    2974         359 :   pari_sp av = avma;
    2975         359 :   long i, n = lg(P)-1, dC = degpol(C), v = varn(C);
    2976             :   GEN H, T;
    2977         359 :   if (n == 1)
    2978             :   {
    2979         181 :     ulong p = uel(P,1);
    2980         181 :     GEN a = ZXX_to_FlxX(A, p, v), b = ZXX_to_FlxX(B, p, v);
    2981         181 :     GEN c = ZX_to_Flx(C, p);
    2982         181 :     GEN Hp = FlxX_to_Flm(FlxqX_composedsum(a, b, c, p), dC);
    2983         181 :     H = gc_upto(av, Flm_to_ZM(Hp));
    2984         181 :     *mod = utoipos(p); return H;
    2985             :   }
    2986         178 :   T = ZV_producttree(P);
    2987         178 :   A = ZXX_nv_mod_tree(A, P, T, v);
    2988         178 :   B = ZXX_nv_mod_tree(B, P, T, v);
    2989         178 :   C = ZX_nv_mod_tree(C, P, T);
    2990         178 :   H = cgetg(n+1, t_VEC);
    2991         660 :   for(i=1; i <= n; i++)
    2992             :   {
    2993         482 :     ulong p = P[i];
    2994         482 :     GEN a = gel(A,i), b = gel(B,i), c = gel(C,i);
    2995         482 :     gel(H,i) = FlxX_to_Flm(FlxqX_composedsum(a, b, c, p), dC);
    2996             :   }
    2997         178 :   H = nmV_chinese_center_tree_seq(H, P, T, ZV_chinesetree(P, T));
    2998         178 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2999             : }
    3000             : 
    3001             : GEN
    3002         359 : ZXQX_composedsum_worker(GEN P, GEN A, GEN B, GEN C)
    3003             : {
    3004         359 :   GEN V = cgetg(3, t_VEC);
    3005         359 :   gel(V,1) = ZXQX_composedsum_slice(A, B, C, P, &gel(V,2));
    3006         359 :   return V;
    3007             : }
    3008             : 
    3009             : static GEN
    3010         315 : ZXQX_composedsum(GEN A, GEN B, GEN T, ulong bound)
    3011             : {
    3012         315 :   pari_sp av = avma;
    3013             :   forprime_t S;
    3014             :   GEN H, worker, mod;
    3015         315 :   GEN lead = mulii(Q_content(leading_coeff(A)), Q_content(leading_coeff(B)));
    3016         315 :   worker = snm_closure(is_entry("_ZXQX_composedsum_worker")
    3017             :                       , mkvec3(A,B,T));
    3018         315 :   init_modular_big(&S);
    3019         315 :   H = gen_crt("ZXQX_composedsum", worker, &S, lead, bound, 0, &mod,
    3020             :               nmV_chinese_center, FpM_center);
    3021         315 :   if (DEBUGLEVEL > 4)
    3022           0 :     err_printf("nfcompositum: a priori bound: %lu, a posteriori: %lu\n",
    3023             :                bound, expi(gsupnorm(H, DEFAULTPREC)));
    3024         315 :   return gc_GEN(av, RgM_to_RgXX(H, varn(A), varn(T)));
    3025             : }
    3026             : 
    3027             : static long
    3028         315 : ZXQX_composedsum_bound(GEN nf, GEN A, GEN B)
    3029         315 : { return ZXQX_resultant_bound_i(nf, A, B, &RgX_RgXY_ResBound_1); }
    3030             : 
    3031             : GEN
    3032         315 : nf_direct_compositum(GEN nf, GEN A, GEN B)
    3033             : {
    3034         315 :   ulong bnd = ZXQX_composedsum_bound(nf, A, B);
    3035         315 :   return ZXQX_composedsum(A, B, nf_get_pol(nf), bnd);
    3036             : }
    3037             : 
    3038             : /************************************************************************
    3039             :  *                                                                      *
    3040             :  *                   IRREDUCIBLE POLYNOMIAL / Fp                        *
    3041             :  *                                                                      *
    3042             :  ************************************************************************/
    3043             : 
    3044             : /* irreducible (unitary) polynomial of degree n over Fp */
    3045             : GEN
    3046           0 : ffinit_rand(GEN p,long n)
    3047             : {
    3048           0 :   for(;;) {
    3049           0 :     pari_sp av = avma;
    3050           0 :     GEN pol = ZX_add(pol_xn(n, 0), random_FpX(n-1,0, p));
    3051           0 :     if (FpX_is_irred(pol, p)) return pol;
    3052           0 :     set_avma(av);
    3053             :   }
    3054             : }
    3055             : 
    3056             : /* return an extension of degree 2^l of F_2, assume l > 0
    3057             :  * Not stack clean. */
    3058             : static GEN
    3059         598 : ffinit_Artin_Schreier_2(long l)
    3060             : {
    3061             :   GEN Q, T, S;
    3062             :   long i, v;
    3063             : 
    3064         598 :   if (l == 1) return mkvecsmall4(0,1,1,1); /*x^2 + x + 1*/
    3065         549 :   v = fetch_var_higher();
    3066         549 :   S = mkvecsmall5(0, 0, 0, 1, 1); /* y(y^2 + y) */
    3067         549 :   Q = mkpoln(3, pol1_Flx(0), pol1_Flx(0), S); /* x^2 + x + y(y^2+y) */
    3068         549 :   setvarn(Q, v);
    3069             : 
    3070             :   /* x^4+x+1, irred over F_2, minimal polynomial of a root of Q */
    3071         549 :   T = mkvecsmalln(6,evalvarn(v),1UL,1UL,0UL,0UL,1UL);
    3072             :   /* Q = x^2 + x + a(y) irred. over K = F2[y] / (T(y))
    3073             :    * ==> x^2 + x + a(y) b irred. over K for any root b of Q
    3074             :    * ==> x^2 + x + (b^2+b)b */
    3075        3036 :   for (i=2; i<l; i++) T = Flx_FlxY_resultant(T, Q, 2); /* minpoly(b) / F2*/
    3076         551 :   (void)delete_var(); T[1] = 0; return T;
    3077             : }
    3078             : 
    3079             : /* return an extension of degree p^l of F_p, assume l > 0
    3080             :  * Not stack clean. */
    3081             : GEN
    3082         955 : ffinit_Artin_Schreier(ulong p, long l)
    3083             : {
    3084             :   long i, v;
    3085             :   GEN Q, R, S, T, xp;
    3086         955 :   if (p==2) return ffinit_Artin_Schreier_2(l);
    3087         357 :   xp = polxn_Flx(p,0); /* x^p */
    3088         357 :   T = Flx_sub(xp, mkvecsmall3(0,1,1),p); /* x^p - x - 1 */
    3089         357 :   if (l == 1) return T;
    3090             : 
    3091           7 :   v = evalvarn(fetch_var_higher());
    3092           7 :   xp[1] = v;
    3093           7 :   R = Flx_sub(polxn_Flx(2*p-1,0), polxn_Flx(p,0),p);
    3094           7 :   S = Flx_sub(xp, polx_Flx(0), p);
    3095           7 :   Q = FlxX_Flx_sub(Flx_to_FlxX(S, v), R, p); /* x^p - x - (y^(2p-1)-y^p) */
    3096          14 :   for (i = 2; i <= l; ++i) T = Flx_FlxY_resultant(T, Q, p);
    3097           7 :   (void)delete_var(); T[1] = 0; return T;
    3098             : }
    3099             : 
    3100             : static long
    3101      149709 : flinit_check(ulong p, long n, long l)
    3102             : {
    3103             :   ulong q;
    3104      149709 :   if (!uisprime(n)) return 0;
    3105      102496 :   q = p % n; if (!q) return 0;
    3106       99885 :   return ugcd((n-1)/Fl_order(q, n-1, n), l) == 1;
    3107             : }
    3108             : 
    3109             : static GEN
    3110       31944 : flinit(ulong p, long l)
    3111             : {
    3112       31944 :   ulong n = 1+l;
    3113       96782 :   while (!flinit_check(p,n,l)) n += l;
    3114       31944 :   if (DEBUGLEVEL>=4) err_printf("FFInit: using polsubcyclo(%ld, %ld)\n",n,l);
    3115       31944 :   return ZX_to_Flx(polsubcyclo(n,l,0), p);
    3116             : }
    3117             : 
    3118             : static GEN
    3119       28989 : ffinit_fact_Flx(ulong p, long n)
    3120             : {
    3121       28989 :   GEN P, F = factoru_pow(n), Fp = gel(F,1), Fe = gel(F,2), Fm = gel(F,3);
    3122       28989 :   long i, l = lg(Fm);
    3123       28989 :   P = cgetg(l, t_VEC);
    3124       61890 :   for (i = 1; i < l; i++)
    3125       32899 :     gel(P,i) = p==uel(Fp,i) ? ffinit_Artin_Schreier(p, Fe[i])
    3126       32899 :                             : flinit(p, uel(Fm,i));
    3127       28991 :   return FlxV_composedsum(P, p);
    3128             : }
    3129             : 
    3130             : static GEN
    3131       52934 : init_Flxq_i(ulong p, long n, long sv)
    3132             : {
    3133             :   GEN P;
    3134       52934 :   if (!odd(p) && p != 2) pari_err_PRIME("ffinit", utoi(p));
    3135       52927 :   if (n == 1) return polx_Flx(sv);
    3136       52927 :   if (flinit_check(p, n+1, n))
    3137             :   {
    3138       23938 :     P = const_vecsmall(n+2,1);
    3139       23938 :     P[1] = sv; return P;
    3140             :   }
    3141       28989 :   P = ffinit_fact_Flx(p,n);
    3142       28991 :   P[1] = sv; return P;
    3143             : }
    3144             : 
    3145             : GEN
    3146           0 : init_Flxq(ulong p, long n, long v)
    3147             : {
    3148           0 :   pari_sp av = avma;
    3149           0 :   return gc_upto(av, init_Flxq_i(p, n, v));
    3150             : }
    3151             : 
    3152             : /* check if polsubcyclo(n,l,0) is irreducible modulo p */
    3153             : static long
    3154        8207 : fpinit_check(GEN p, long n, long l)
    3155             : {
    3156             :   ulong q;
    3157        8207 :   if (!uisprime(n)) return 0;
    3158        4842 :   q = umodiu(p,n); if (!q) return 0;
    3159        4842 :   return ugcd((n-1)/Fl_order(q, n-1, n), l) == 1;
    3160             : }
    3161             : 
    3162             : /* let k=2 if p%4==1, and k=4 else and assume k*p does not divide l.
    3163             :  * Return an irreducible polynomial of degree l over F_p.
    3164             :  * Variant of Adleman and Lenstra "Finding irreducible polynomials over
    3165             :  * finite fields", ACM, 1986 (5) 350--355.
    3166             :  * Not stack clean */
    3167             : static GEN
    3168        1828 : fpinit(GEN p, long l)
    3169             : {
    3170        1828 :   ulong n = 1+l;
    3171        6168 :   while (!fpinit_check(p,n,l)) n += l;
    3172        1828 :   if (DEBUGLEVEL>=4) err_printf("FFInit: using polsubcyclo(%ld, %ld)\n",n,l);
    3173        1828 :   return FpX_red(polsubcyclo(n,l,0),p);
    3174             : }
    3175             : 
    3176             : static GEN
    3177        1637 : ffinit_fact(GEN p, long n)
    3178             : {
    3179        1637 :   GEN P, F = factoru_pow(n), Fp = gel(F,1), Fe = gel(F,2), Fm = gel(F,3);
    3180        1637 :   long i, l = lg(Fm);
    3181        1637 :   P = cgetg(l, t_VEC);
    3182        3465 :   for (i = 1; i < l; ++i)
    3183        3656 :     gel(P,i) = absequaliu(p, Fp[i]) ?
    3184           0 :                  Flx_to_ZX(ffinit_Artin_Schreier(Fp[i], Fe[i]))
    3185        1828 :                : fpinit(p, Fm[i]);
    3186        1637 :   return FpXV_composedsum(P, p);
    3187             : }
    3188             : 
    3189             : static GEN
    3190       55239 : init_Fq_i(GEN p, long n, long v)
    3191             : {
    3192             :   GEN P;
    3193       55239 :   if (n <= 0) pari_err_DOMAIN("ffinit", "degree", "<=", gen_0, stoi(n));
    3194       55239 :   if (typ(p) != t_INT) pari_err_TYPE("ffinit",p);
    3195       55239 :   if (cmpiu(p, 2) < 0) pari_err_PRIME("ffinit",p);
    3196       55232 :   if (v < 0) v = 0;
    3197       55232 :   if (n == 1) return pol_x(v);
    3198       54980 :   if (lgefint(p) == 3)
    3199       52934 :     return Flx_to_ZX(init_Flxq_i(p[2], n, evalvarn(v)));
    3200        2046 :   if (!mpodd(p)) pari_err_PRIME("ffinit", p);
    3201        2039 :   if (fpinit_check(p, n+1, n)) return polcyclo(n+1, v);
    3202        1637 :   P = ffinit_fact(p,n);
    3203        1637 :   setvarn(P, v); return P;
    3204             : }
    3205             : GEN
    3206       54672 : init_Fq(GEN p, long n, long v)
    3207             : {
    3208       54672 :   pari_sp av = avma;
    3209       54672 :   return gc_upto(av, init_Fq_i(p, n, v));
    3210             : }
    3211             : GEN
    3212         567 : ffinit(GEN p, long n, long v)
    3213             : {
    3214         567 :   pari_sp av = avma;
    3215         567 :   return gc_upto(av, FpX_to_mod(init_Fq_i(p, n, v), p));
    3216             : }
    3217             : 
    3218             : GEN
    3219        3178 : ffnbirred(GEN p, long n)
    3220             : {
    3221        3178 :   pari_sp av = avma;
    3222        3178 :   GEN s = powiu(p,n), F = factoru(n), D = divisorsu_moebius(gel(F, 1));
    3223        3178 :   long j, l = lg(D);
    3224        6797 :   for (j = 2; j < l; j++) /* skip d = 1 */
    3225             :   {
    3226        3619 :     long md = D[j]; /* mu(d) * d, d squarefree */
    3227        3619 :     GEN pd = powiu(p, n / labs(md)); /* p^{n/d} */
    3228        3619 :     s = md > 0? addii(s, pd): subii(s,pd);
    3229             :   }
    3230        3178 :   return gc_INT(av, diviuexact(s, n));
    3231             : }
    3232             : 
    3233             : GEN
    3234         616 : ffsumnbirred(GEN p, long n)
    3235             : {
    3236         616 :   pari_sp av = avma, av2;
    3237         616 :   GEN q, t = p, v = vecfactoru_i(1, n);
    3238             :   long i;
    3239         616 :   q = cgetg(n+1,t_VEC); gel(q,1) = p;
    3240        1764 :   for (i=2; i<=n; i++) gel(q,i) = mulii(gel(q,i-1), p);
    3241         616 :   av2 = avma;
    3242        1764 :   for (i=2; i<=n; i++)
    3243             :   {
    3244        1148 :     GEN s = gel(q,i), F = gel(v,i), D = divisorsu_moebius(gel(F,1));
    3245        1148 :     long j, l = lg(D);
    3246        2534 :     for (j = 2; j < l; j++) /* skip 1 */
    3247             :     {
    3248        1386 :       long md = D[j];
    3249        1386 :       GEN pd = gel(q, i / labs(md)); /* p^{i/d} */
    3250        1386 :       s = md > 0? addii(s, pd): subii(s, pd);
    3251             :     }
    3252        1148 :     t = gc_INT(av2, addii(t, diviuexact(s, i)));
    3253             :   }
    3254         616 :   return gc_INT(av, t);
    3255             : }
    3256             : 
    3257             : GEN
    3258         140 : ffnbirred0(GEN p, long n, long flag)
    3259             : {
    3260         140 :   if (typ(p) != t_INT) pari_err_TYPE("ffnbirred", p);
    3261         140 :   if (n <= 0) pari_err_DOMAIN("ffnbirred", "degree", "<=", gen_0, stoi(n));
    3262         140 :   switch(flag)
    3263             :   {
    3264          70 :     case 0: return ffnbirred(p, n);
    3265          70 :     case 1: return ffsumnbirred(p, n);
    3266             :   }
    3267           0 :   pari_err_FLAG("ffnbirred");
    3268             :   return NULL; /* LCOV_EXCL_LINE */
    3269             : }
    3270             : 
    3271             : static void
    3272        2261 : checkmap(GEN m, const char *s)
    3273             : {
    3274        2261 :   if (typ(m)!=t_VEC || lg(m)!=3 || typ(gel(m,1))!=t_FFELT)
    3275           0 :     pari_err_TYPE(s,m);
    3276        2261 : }
    3277             : 
    3278             : GEN
    3279         189 : ffembed(GEN a, GEN b)
    3280             : {
    3281         189 :   pari_sp av = avma;
    3282         189 :   GEN p, Ta, Tb, g, r = NULL;
    3283         189 :   if (typ(a)!=t_FFELT) pari_err_TYPE("ffembed",a);
    3284         189 :   if (typ(b)!=t_FFELT) pari_err_TYPE("ffembed",b);
    3285         189 :   p = FF_p_i(a); g = FF_gen(a);
    3286         189 :   if (!equalii(p, FF_p_i(b))) pari_err_MODULUS("ffembed",a,b);
    3287         189 :   Ta = FF_mod(a);
    3288         189 :   Tb = FF_mod(b);
    3289         189 :   if (degpol(Tb)%degpol(Ta)!=0)
    3290           7 :     pari_err_DOMAIN("ffembed",GENtostr_raw(a),"is not a subfield of",b,a);
    3291         182 :   r = gel(FFX_roots(Ta, b), 1);
    3292         182 :   return gc_GEN(av, mkvec2(g,r));
    3293             : }
    3294             : 
    3295             : GEN
    3296          91 : ffextend(GEN a, GEN P, long v)
    3297             : {
    3298          91 :   pari_sp av = avma;
    3299             :   long n;
    3300             :   GEN p, T, R, g, m;
    3301          91 :   if (typ(a)!=t_FFELT) pari_err_TYPE("ffextend",a);
    3302          91 :   T = a; p = FF_p_i(a);
    3303          91 :   if (typ(P)!=t_POL || !RgX_is_FpXQX(P,&T,&p)) pari_err_TYPE("ffextend", P);
    3304          49 :   if (!FF_samefield(a, T)) pari_err_MODULUS("ffextend",a,T);
    3305          49 :   if (v < 0) v = varn(P);
    3306          49 :   n = FF_f(T) * degpol(P); R = ffinit(p, n, v); g = ffgen(R, v);
    3307          49 :   m = ffembed(a, g);
    3308          49 :   R = FFX_roots(ffmap(m, P),g);
    3309          49 :   return gc_GEN(av, mkvec2(gel(R,1), m));
    3310             : }
    3311             : 
    3312             : GEN
    3313          42 : fffrobenius(GEN a, long n)
    3314             : {
    3315          42 :   if (typ(a)!=t_FFELT) pari_err_TYPE("fffrobenius",a);
    3316          42 :   retmkvec2(FF_gen(a), FF_Frobenius(a, n));
    3317             : }
    3318             : 
    3319             : GEN
    3320         133 : ffinvmap(GEN m)
    3321             : {
    3322         133 :   pari_sp av = avma;
    3323             :   long i, l;
    3324         133 :   GEN T, F, a, g, r, f = NULL;
    3325         133 :   checkmap(m, "ffinvmap");
    3326         133 :   a = gel(m,1); r = gel(m,2);
    3327         133 :   if (typ(r) != t_FFELT)
    3328           7 :    pari_err_TYPE("ffinvmap", m);
    3329         126 :   g = FF_gen(a);
    3330         126 :   T = FF_mod(r);
    3331         126 :   F = gel(FFX_factor(T, a), 1);
    3332         126 :   l = lg(F);
    3333         490 :   for(i=1; i<l; i++)
    3334             :   {
    3335         490 :     GEN s = FFX_rem(FF_to_FpXQ_i(r), gel(F, i), a);
    3336         490 :     if (degpol(s)==0 && gequal(constant_coeff(s),g)) { f = gel(F, i); break; }
    3337             :   }
    3338         126 :   if (f==NULL) pari_err_TYPE("ffinvmap", m);
    3339         126 :   if (degpol(f)==1) f = FF_neg_i(gel(f,2));
    3340         126 :   return gc_GEN(av, mkvec2(FF_gen(r),f));
    3341             : }
    3342             : 
    3343             : static GEN
    3344        1260 : ffpartmapimage(const char *s, GEN r)
    3345             : {
    3346        1260 :    GEN a = NULL, p = NULL;
    3347        1260 :    if (typ(r)==t_POL && degpol(r) >= 1
    3348        1260 :       && RgX_is_FpXQX(r,&a,&p) && a && typ(a)==t_FFELT) return a;
    3349           0 :    pari_err_TYPE(s, r);
    3350             :    return NULL; /* LCOV_EXCL_LINE */
    3351             : }
    3352             : 
    3353             : static GEN
    3354        2709 : ffeltmap_i(GEN m, GEN x)
    3355             : {
    3356        2709 :    GEN r = gel(m,2);
    3357        2709 :    if (!FF_samefield(x, gel(m,1)))
    3358          84 :      pari_err_DOMAIN("ffmap","m","domain does not contain", x, r);
    3359        2625 :    if (typ(r)==t_FFELT)
    3360        1659 :      return FF_map(r, x);
    3361             :    else
    3362         966 :      return FFX_preimage(x, r, ffpartmapimage("ffmap", r));
    3363             : }
    3364             : 
    3365             : static GEN
    3366        4459 : ffmap_i(GEN m, GEN x)
    3367             : {
    3368             :   GEN y;
    3369        4459 :   long i, lx, tx = typ(x);
    3370        4459 :   switch(tx)
    3371             :   {
    3372        2541 :     case t_FFELT:
    3373        2541 :       return ffeltmap_i(m, x);
    3374        1267 :     case t_POL: case t_RFRAC: case t_SER:
    3375             :     case t_VEC: case t_COL: case t_MAT:
    3376        1267 :       y = cgetg_copy(x, &lx);
    3377        1988 :       for (i = 1; i < lontyp[tx]; i++) y[i] = x[i];
    3378        4564 :       for (; i < lx; i++)
    3379             :       {
    3380        3339 :         GEN yi = ffmap_i(m, gel(x,i));
    3381        3297 :         if (!yi) return NULL;
    3382        3297 :         gel(y,i) = yi;
    3383             :       }
    3384        1225 :       return y;
    3385             :   }
    3386         651 :   return gcopy(x);
    3387             : }
    3388             : 
    3389             : GEN
    3390        1036 : ffmap(GEN m, GEN x)
    3391             : {
    3392        1036 :   pari_sp ltop = avma;
    3393             :   GEN y;
    3394        1036 :   checkmap(m, "ffmap");
    3395        1036 :   y = ffmap_i(m, x);
    3396        1036 :   if (y) return y;
    3397          42 :   retgc_const(ltop, cgetg(1, t_VEC));
    3398             : }
    3399             : 
    3400             : static GEN
    3401         252 : ffeltmaprel_i(GEN m, GEN x)
    3402             : {
    3403         252 :    GEN g = gel(m,1), r = gel(m,2);
    3404         252 :    if (!FF_samefield(x, g))
    3405           0 :      pari_err_DOMAIN("ffmap","m","domain does not contain", x, r);
    3406         252 :    if (typ(r)==t_FFELT)
    3407          84 :      retmkpolmod(FF_map(r, x), pol_x(FF_var(g)));
    3408             :    else
    3409         168 :      retmkpolmod(FFX_preimagerel(x, r, ffpartmapimage("ffmap", r)), gcopy(r));
    3410             : }
    3411             : 
    3412             : static GEN
    3413         252 : ffmaprel_i(GEN m, GEN x)
    3414             : {
    3415         252 :   switch(typ(x))
    3416             :   {
    3417         252 :     case t_FFELT:
    3418         252 :       return ffeltmaprel_i(m, x);
    3419           0 :     case t_POL: pari_APPLY_pol_normalized(ffmaprel_i(m, gel(x,i)));
    3420           0 :     case t_SER: pari_APPLY_ser_normalized(ffmaprel_i(m, gel(x,i)));
    3421           0 :     case t_RFRAC: case t_VEC: case t_COL: case t_MAT:
    3422           0 :       pari_APPLY_same(ffmaprel_i(m, gel(x,i)));
    3423             :   }
    3424           0 :   return gcopy(x);
    3425             : }
    3426             : GEN
    3427         252 : ffmaprel(GEN m, GEN x) { checkmap(m, "ffmaprel"); return ffmaprel_i(m, x); }
    3428             : 
    3429             : static void
    3430          84 : err_compo(GEN m, GEN n)
    3431          84 : { pari_err_DOMAIN("ffcompomap","m","domain does not contain codomain of",n,m); }
    3432             : 
    3433             : GEN
    3434         420 : ffcompomap(GEN m, GEN n)
    3435             : {
    3436         420 :   pari_sp av = avma;
    3437         420 :   GEN g = gel(n,1), r, m2, n2;
    3438         420 :   checkmap(m, "ffcompomap");
    3439         420 :   checkmap(n, "ffcompomap");
    3440         420 :   m2 = gel(m,2); n2 = gel(n,2);
    3441         420 :   switch((typ(m2)==t_POL)|((typ(n2)==t_POL)<<1))
    3442             :   {
    3443          84 :     case 0:
    3444          84 :       if (!FF_samefield(gel(m,1),n2)) err_compo(m,n);
    3445          42 :       r = FF_map(gel(m,2), n2);
    3446          42 :       break;
    3447          84 :     case 2:
    3448          84 :       r = ffmap_i(m, n2);
    3449          42 :       if (lg(r) == 1) err_compo(m,n);
    3450          42 :       break;
    3451         168 :     case 1:
    3452         168 :       r = ffeltmap_i(m, n2);
    3453         126 :       if (!r)
    3454             :       {
    3455             :         GEN a, A, R, M;
    3456             :         long dm, dn;
    3457          42 :         a = ffpartmapimage("ffcompomap",m2);
    3458          42 :         A = FF_to_FpXQ_i(FF_neg(n2));
    3459          42 :         setvarn(A, 1);
    3460          42 :         R = deg1pol(gen_1, A, 0);
    3461          42 :         setvarn(R, 0);
    3462          42 :         M = gcopy(m2);
    3463          42 :         setvarn(M, 1);
    3464          42 :         r = polresultant0(R, M, 1, 0);
    3465          42 :         dm = FF_f(gel(m,1)); dn = FF_f(gel(n,1));
    3466          42 :         if (dm % dn || !FFX_ispower(r, dm/dn, a, &r)) err_compo(m,n);
    3467          42 :         setvarn(r, varn(FF_mod(g)));
    3468             :       }
    3469         126 :       break;
    3470          84 :     case 3:
    3471             :     {
    3472             :       GEN M, R, T, p, a;
    3473          84 :       a = ffpartmapimage("ffcompomap",n2);
    3474          84 :       if (!FF_samefield(a, gel(m,1))) err_compo(m,n);
    3475          42 :       p = FF_p_i(gel(n,1));
    3476          42 :       T = FF_mod(gel(n,1));
    3477          42 :       setvarn(T, 1);
    3478          42 :       R = RgX_to_FpXQX(n2,T,p);
    3479          42 :       setvarn(R, 0);
    3480          42 :       M = gcopy(m2);
    3481          42 :       setvarn(M, 1);
    3482          42 :       r = polresultant0(R, M, 1, 0);
    3483          42 :       setvarn(r, varn(n2));
    3484             :     }
    3485             :   }
    3486         252 :   return gc_GEN(av, mkvec2(g,r));
    3487             : }

Generated by: LCOV version 1.16