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 29950-285c5b69ed) Lines: 1775 1977 89.8 %
Date: 2025-02-05 09:09:51 Functions: 189 203 93.1 %
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        6580 : char_update_int(struct charact *S, GEN n)
      43             : {
      44        6580 :   if (S->isprime)
      45             :   {
      46           7 :     if (dvdii(n, S->q)) return;
      47           7 :     pari_err_MODULUS("characteristic", S->q, n);
      48             :   }
      49        6573 :   S->q = gcdii(S->q, n);
      50             : }
      51             : static void
      52      178724 : charact(struct charact *S, GEN x)
      53             : {
      54      178724 :   const long tx = typ(x);
      55             :   long i, l;
      56      178724 :   switch(tx)
      57             :   {
      58        5131 :     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       26642 :     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       26642 :       l = lg(x);
      64      177765 :       for (i=lontyp[tx]; i < l; i++) charact(S,gel(x,i));
      65       26628 :       break;
      66           7 :     case t_LIST:
      67           7 :       x = list_data(x);
      68           7 :       if (x) charact(S, x);
      69           7 :       break;
      70             :   }
      71      178696 : }
      72             : static void
      73        4634 : charact_res(struct charact *S, GEN x)
      74             : {
      75        4634 :   const long tx = typ(x);
      76             :   long i, l;
      77        4634 :   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, gel(x,2)); break;
      82        1617 :     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        1617 :       l = lg(x);
      86        5922 :       for (i=lontyp[tx]; i < l; i++) charact_res(S,gel(x,i));
      87        1617 :       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        4634 : }
      94             : GEN
      95       27587 : characteristic(GEN x)
      96             : {
      97             :   struct charact S;
      98       27587 :   S.q = gen_0; S.isprime = 0;
      99       27587 :   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    71059607 : Rg_is_Fp(GEN x, GEN *pp)
     111             : {
     112             :   GEN mod;
     113    71059607 :   switch(typ(x))
     114             :   {
     115     2483670 :   case t_INTMOD:
     116     2483670 :     mod = gel(x,1);
     117     2483670 :     if (!*pp) *pp = mod;
     118     2342767 :     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     2483670 :     return 1;
     124    57170241 :   case t_INT:
     125    57170241 :     return 1;
     126    11405696 :   default: return 0;
     127             :   }
     128             : }
     129             : 
     130             : int
     131    28178075 : RgX_is_FpX(GEN x, GEN *pp)
     132             : {
     133    28178075 :   long i, lx = lg(x);
     134    87805846 :   for (i=2; i<lx; i++)
     135    71033468 :     if (!Rg_is_Fp(gel(x, i), pp))
     136    11405688 :       return 0;
     137    16772378 :   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       60613 : Rg_is_FpXQ(GEN x, GEN *pT, GEN *pp)
     160             : {
     161             :   GEN pol, mod, p;
     162       60613 :   switch(typ(x))
     163             :   {
     164       26131 :   case t_INTMOD:
     165       26131 :     return Rg_is_Fp(x, pp);
     166        8372 :   case t_INT:
     167        8372 :     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        3360 : RgX_is_FpXQX(GEN x, GEN *pT, GEN *pp)
     202             : {
     203        3360 :   long i, lx = lg(x);
     204       63217 :   for (i = 2; i < lx; i++)
     205       59955 :     if (!Rg_is_FpXQ(gel(x,i), pT, pp)) return 0;
     206        3262 :   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    51890242 : Rg_to_Fp(GEN x, GEN p)
     219             : {
     220    51890242 :   if (lgefint(p) == 3) return utoi(Rg_to_Fl(x, uel(p,2)));
     221     4554721 :   switch(typ(x))
     222             :   {
     223      288231 :     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 gerepileuptoint(av, remii(mulii(z, Fp_inv(gel(x,2), p)), p));
     229             :     }
     230          70 :     case t_PADIC: return padic_to_Fp(x, p);
     231     4247635 :     case t_INTMOD: {
     232     4247635 :       GEN q = gel(x,1), a = gel(x,2);
     233     4247635 :       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     3335267 : RgX_to_FpX(GEN x, GEN p)
     282             : {
     283             :   long i, l;
     284     3335267 :   GEN z = cgetg_copy(x, &l); z[1] = x[1];
     285    14763908 :   for (i = 2; i < l; i++) gel(z,i) = Rg_to_Fp(gel(x,i), p);
     286     3335267 :   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     1685157 : RgC_to_FpC(GEN x, GEN p)
     295    28092759 : { pari_APPLY_type(t_COL, Rg_to_Fp(gel(x,i), p)) }
     296             : 
     297             : GEN
     298      210170 : RgM_to_FpM(GEN x, GEN p)
     299     1895285 : { 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 = gerepileupto(av, z);
     356             :   }
     357      851487 :   return gerepileupto(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        1055 : FqX_Fq_sub(GEN y, GEN x, GEN T, GEN p)
     377             : {
     378        1055 :   long i, lz = lg(y);
     379             :   GEN z;
     380        1055 :   if (!T) return FpX_Fp_sub(y, x, p);
     381        1055 :   if (lz == 2) return scalarpol(x, varn(y));
     382        1055 :   z = cgetg(lz,t_POL); z[1] = y[1];
     383        1055 :   gel(z,2) = Fq_sub(gel(y,2), x, T, p);
     384        1055 :   if (lz == 3) z = FpXX_renormalize(z,lz);
     385             :   else
     386       10275 :     for(i=3;i<lz;i++) gel(z,i) = gcopy(gel(y,i));
     387        1055 :   return z;
     388             : }
     389             : 
     390             : GEN
     391      149023 : FqX_Fq_mul_to_monic(GEN P, GEN U, GEN T, GEN p)
     392             : {
     393             :   long i, lP;
     394      149023 :   GEN res = cgetg_copy(P, &lP); res[1] = P[1];
     395      918785 :   for(i=2; i<lP-1; i++) gel(res,i) = Fq_mul(U,gel(P,i), T,p);
     396      149023 :   gel(res,lP-1) = gen_1; return res;
     397             : }
     398             : 
     399             : GEN
     400       38123 : FpXQX_normalize(GEN z, GEN T, GEN p)
     401             : {
     402             :   GEN lc;
     403       38123 :   if (lg(z) == 2) return z;
     404       38109 :   lc = leading_coeff(z);
     405       38109 :   if (typ(lc) == t_POL)
     406             :   {
     407        2138 :     if (lg(lc) > 3) /* nonconstant */
     408        1873 :       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       36236 :   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      398873 : FqX_eval(GEN x, GEN y, GEN T, GEN p)
     421             : {
     422             :   pari_sp av;
     423             :   GEN p1, r;
     424      398873 :   long j, i=lg(x)-1;
     425      398873 :   if (i<=2)
     426       45971 :     return (i==2)? Fq_red(gel(x,2), T, p): gen_0;
     427      352902 :   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     1174025 :   for (i--; i>=2; i=j-1)
     431             :   {
     432      821810 :     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 gerepileupto(av, Fq_mul(p1,y, T, p));
     437             :       }
     438      821124 :     r = (i==j)? y: Fq_pow(y, utoipos(i-j+1), T, p);
     439      821124 :     p1 = Fq_add(Fq_mul(p1,r,T,p), gel(x,j), T, p);
     440             :   }
     441      352411 :   return gerepileupto(av, p1);
     442             : }
     443             : 
     444             : GEN
     445       99679 : FqXY_evalx(GEN Q, GEN x, GEN T, GEN p)
     446             : {
     447       99679 :   long i, lb = lg(Q);
     448             :   GEN z;
     449       99679 :   if (!T) return FpXY_evalx(Q, x, p);
     450       89319 :   z = cgetg(lb, t_POL); z[1] = Q[1];
     451      474735 :   for (i=2; i<lb; i++)
     452             :   {
     453      385416 :     GEN q = gel(Q,i);
     454      385416 :     gel(z,i) = typ(q) == t_INT? modii(q,p): FqX_eval(q, x, T, p);
     455             :   }
     456       89319 :   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 gerepileupto(av, FqX_eval(FqXY_evalx(Q, x, T, p), y, T, p));
     466             : }
     467             : 
     468             : /* a X^d */
     469             : GEN
     470    12256154 : monomial(GEN a, long d, long v)
     471             : {
     472             :   long i, n;
     473             :   GEN P;
     474    12256154 :   if (d < 0) {
     475          14 :     if (isrationalzero(a)) return pol_0(v);
     476          14 :     retmkrfrac(a, pol_xn(-d, v));
     477             :   }
     478    12256140 :   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    12162149 :     n = d+2; P = cgetg(n+1, t_POL);
     487    12162148 :     P[1] = evalsigne(1) | evalvarn(v);
     488             :   }
     489    31302485 :   for (i = 2; i < n; i++) gel(P,i) = gen_0;
     490    12162148 :   gel(P,i) = a; return P;
     491             : }
     492             : GEN
     493     1860552 : monomialcopy(GEN a, long d, long v)
     494             : {
     495             :   long i, n;
     496             :   GEN P;
     497     1860552 :   if (d < 0) {
     498          14 :     if (isrationalzero(a)) return pol_0(v);
     499          14 :     retmkrfrac(gcopy(a), pol_xn(-d, v));
     500             :   }
     501     1860538 :   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     1860524 :     n = d+2; P = cgetg(n+1, t_POL);
     510     1860524 :     P[1] = evalsigne(1) | evalvarn(v);
     511             :   }
     512     3503983 :   for (i = 2; i < n; i++) gel(P,i) = gen_0;
     513     1860531 :   gel(P,i) = gcopy(a); return P;
     514             : }
     515             : GEN
     516      326028 : pol_x_powers(long N, long v)
     517             : {
     518      326028 :   GEN L = cgetg(N+1,t_VEC);
     519             :   long i;
     520      789270 :   for (i=1; i<=N; i++) gel(L,i) = pol_xn(i-1, v);
     521      326033 :   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    11610790 : Fq_add(GEN x, GEN y, GEN T/*unused*/, GEN p)
     544             : {
     545             :   (void)T;
     546    11610790 :   switch((typ(x)==t_POL)|((typ(y)==t_POL)<<1))
     547             :   {
     548     1143687 :     case 0: return Fp_add(x,y,p);
     549      764642 :     case 1: return FpX_Fp_add(x,y,p);
     550       92147 :     case 2: return FpX_Fp_add(y,x,p);
     551     9610314 :     case 3: return FpX_add(x,y,p);
     552             :   }
     553             :   return NULL;/*LCOV_EXCL_LINE*/
     554             : }
     555             : 
     556             : GEN
     557     8564992 : Fq_sub(GEN x, GEN y, GEN T/*unused*/, GEN p)
     558             : {
     559             :   (void)T;
     560     8564992 :   switch((typ(x)==t_POL)|((typ(y)==t_POL)<<1))
     561             :   {
     562      256094 :     case 0: return Fp_sub(x,y,p);
     563       24480 :     case 1: return FpX_Fp_sub(x,y,p);
     564       23908 :     case 2: return Fp_FpX_sub(x,y,p);
     565     8260510 :     case 3: return FpX_sub(x,y,p);
     566             :   }
     567             :   return NULL;/*LCOV_EXCL_LINE*/
     568             : }
     569             : 
     570             : GEN
     571     1080430 : Fq_neg(GEN x, GEN T/*unused*/, GEN p)
     572             : {
     573             :   (void)T;
     574     1080430 :   return (typ(x)==t_POL)? FpX_neg(x,p): Fp_neg(x,p);
     575             : }
     576             : 
     577             : GEN
     578       83635 : Fq_halve(GEN x, GEN T/*unused*/, GEN p)
     579             : {
     580             :   (void)T;
     581       83635 :   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     8623634 : Fq_mul(GEN x, GEN y, GEN T, GEN p)
     587             : {
     588     8623634 :   switch((typ(x)==t_POL)|((typ(y)==t_POL)<<1))
     589             :   {
     590     1037917 :     case 0: return Fp_mul(x,y,p);
     591      129010 :     case 1: return FpX_Fp_mul(x,y,p);
     592      401759 :     case 2: return FpX_Fp_mul(y,x,p);
     593     7054949 :     case 3: if (T) return FpXQ_mul(x,y,T,p);
     594     4476374 :             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      492852 : Fq_mulu(GEN x, ulong y, /*unused*/GEN T, GEN p)
     602             : {
     603             :   (void) T;
     604      492852 :   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       43902 : Fq_Fp_mul(GEN x, GEN y, GEN T/*unused*/, GEN p)
     610             : {
     611             :   (void)T;
     612        6823 :   return (typ(x) == t_POL)? FpX_Fp_mul(x,y,p)
     613       50725 :                           : Fp_mul(x,y,p);
     614             : }
     615             : /* If T==NULL do not reduce*/
     616             : GEN
     617      613639 : Fq_sqr(GEN x, GEN T, GEN p)
     618             : {
     619      613639 :   if (typ(x) == t_POL)
     620             :   {
     621       72872 :     if (T) return FpXQ_sqr(x,T,p);
     622           0 :     else return FpX_sqr(x,p);
     623             :   }
     624             :   else
     625      540767 :     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       89265 : Fq_inv(GEN x, GEN pol, GEN p)
     644             : {
     645       89265 :   if (typ(x) == t_INT) return Fp_inv(x,p);
     646       81499 :   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      795381 : Fq_pow(GEN x, GEN n, GEN pol, GEN p)
     664             : {
     665      795381 :   if (typ(x) == t_INT) return Fp_pow(x,n,p);
     666      136912 :   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     1895207 : Fq_sqrt(GEN x, GEN T, GEN p)
     678             : {
     679     1895207 :   if (typ(x) == t_INT)
     680             :   {
     681     1825046 :     if (!T || odd(get_FpX_degree(T))) return Fp_sqrt(x,p);
     682        9603 :     x = scalarpol_shallow(x, get_FpX_var(T));
     683             :   }
     684       79764 :   return FpXQ_sqrt(x,T,p);
     685             : }
     686             : GEN
     687      170751 : Fq_sqrtn(GEN x, GEN n, GEN T, GEN p, GEN *zeta)
     688             : {
     689      170751 :   if (typ(x) == t_INT)
     690             :   {
     691             :     long d;
     692      170380 :     if (!T) return Fp_sqrtn(x,n,p,zeta);
     693         119 :     d = get_FpX_degree(T);
     694         119 :     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          70 :     x = scalarpol(x, get_FpX_var(T)); /* left on stack */
     702             :   }
     703         441 :   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 gerepileupto(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 = gerepilecopy(av, Q); R = (GEN*)Q+2;
     818             :     }
     819             :   }
     820         560 :   return gerepilecopy(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 gerepileupto(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 = gerepilecopy(av, Q); R = (GEN*)Q+2;
     861             :     }
     862             :   }
     863       33880 :   return gerepilecopy(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       31719 :     ulong pp = p[2];
     875       31719 :     GEN Tl = ZX_to_Flx(T, pp);
     876       31720 :     GEN Vl = ZXC_to_FlxC(V, pp, get_Flx_var(Tl));
     877       31719 :     Tl = FlxqV_roots_to_pol(Vl, Tl, pp, v);
     878       31719 :     return gerepileupto(ltop, FlxX_to_ZXX(Tl));
     879             :   }
     880        8733 :   W = cgetg(lg(V),t_VEC);
     881       78275 :   for(k=1; k < lg(V); k++)
     882       69542 :     gel(W,k) = deg1pol_shallow(gen_1,Fq_neg(gel(V,k),T,p),v);
     883        8733 :   return gerepileupto(ltop, FpXQXV_prod(W, T, p));
     884             : }
     885             : 
     886             : GEN
     887      109509 : FqV_red(GEN x, GEN T, GEN p)
     888      778193 : { pari_APPLY_type(t_VEC, Fq_red(gel(x,i), T, p)) }
     889             : 
     890             : GEN
     891       23945 : FqC_red(GEN x, GEN T, GEN p)
     892      163003 : { 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        5313 : FpXC_center(GEN x, GEN p, GEN pov2)
     937       40818 : { pari_APPLY_type(t_COL, FpX_center(gel(x,i), p, pov2)) }
     938             : 
     939             : GEN
     940        1737 : FpXM_center(GEN x, GEN p, GEN pov2)
     941        7050 : { pari_APPLY_same(FpXC_center(gel(x,i), p, pov2)) }
     942             : 
     943             : /*******************************************************************/
     944             : /*                                                                 */
     945             : /*                          GENERIC CRT                            */
     946             : /*                                                                 */
     947             : /*******************************************************************/
     948             : static GEN
     949     8293320 : primelist(forprime_t *S, long n, GEN dB)
     950             : {
     951     8293320 :   GEN P = cgetg(n+1, t_VECSMALL);
     952     8293302 :   long i = 1;
     953             :   ulong p;
     954    20033225 :   while (i <= n && (p = u_forprime_next(S)))
     955    11739924 :     if (!dB || umodiu(dB, p)) P[i++] = p;
     956     8293291 :   return P;
     957             : }
     958             : 
     959             : void
     960     7711697 : gen_inccrt_i(const char *str, GEN worker, GEN dB, long n, long mmin,
     961             :              forprime_t *S, GEN *pH, GEN *pmod, GEN crt(GEN, GEN, GEN*),
     962             :              GEN center(GEN, GEN, GEN))
     963             : {
     964     7711697 :   long m = mmin? minss(mmin, n): usqrt(n);
     965             :   GEN  H, P, mod;
     966             :   pari_timer ti;
     967     7711692 :   if (DEBUGLEVEL > 4)
     968             :   {
     969           0 :     timer_start(&ti);
     970           0 :     err_printf("%s: nb primes: %ld\n",str, n);
     971             :   }
     972     7711677 :   if (m == 1)
     973             :   {
     974     7401225 :     GEN P = primelist(S, n, dB);
     975     7401203 :     GEN done = closure_callgen1(worker, P);
     976     7401178 :     H = gel(done,1);
     977     7401178 :     mod = gel(done,2);
     978     7401178 :     if (!*pH && center) H = center(H, mod, shifti(mod,-1));
     979     7401141 :     if (DEBUGLEVEL>4) timer_printf(&ti,"%s: modular", str);
     980             :   }
     981             :   else
     982             :   {
     983      310452 :     long i, s = (n+m-1)/m, r = m - (m*s-n), di = 0;
     984             :     struct pari_mt pt;
     985      310452 :     long pending = 0;
     986      310452 :     H = cgetg(m+1, t_VEC); P = cgetg(m+1, t_VEC);
     987      310452 :     mt_queue_start_lim(&pt, worker, m);
     988     1268101 :     for (i=1; i<=m || pending; i++)
     989             :     {
     990             :       GEN done;
     991      957649 :       GEN pr = i <= m ? mkvec(primelist(S, i<=r ? s: s-1, dB)): NULL;
     992      957650 :       mt_queue_submit(&pt, i, pr);
     993      957648 :       done = mt_queue_get(&pt, NULL, &pending);
     994      957649 :       if (done)
     995             :       {
     996      892094 :         di++;
     997      892094 :         gel(H, di) = gel(done,1);
     998      892094 :         gel(P, di) = gel(done,2);
     999      892094 :         if (DEBUGLEVEL>5) err_printf("%ld%% ",100*di/m);
    1000             :       }
    1001             :     }
    1002      310452 :     mt_queue_end(&pt);
    1003      310452 :     if (DEBUGLEVEL>5) err_printf("\n");
    1004      310452 :     if (DEBUGLEVEL>4) timer_printf(&ti,"%s: modular", str);
    1005      310452 :     H = crt(H, P, &mod);
    1006      310452 :     if (DEBUGLEVEL>4) timer_printf(&ti,"%s: chinese", str);
    1007             :   }
    1008     7711593 :   if (*pH) H = crt(mkvec2(*pH, H), mkvec2(*pmod, mod), &mod);
    1009     7711594 :   *pH = H; *pmod = mod;
    1010     7711594 : }
    1011             : void
    1012     2057292 : gen_inccrt(const char *str, GEN worker, GEN dB, long n, long mmin,
    1013             :            forprime_t *S, GEN *pH, GEN *pmod, GEN crt(GEN, GEN, GEN*),
    1014             :            GEN center(GEN, GEN, GEN))
    1015             : {
    1016     2057292 :   pari_sp av = avma;
    1017     2057292 :   gen_inccrt_i(str, worker, dB, n, mmin, S, pH, pmod, crt, center);
    1018     2057224 :   gerepileall(av, 2, pH, pmod);
    1019     2057356 : }
    1020             : 
    1021             : GEN
    1022     1273100 : gen_crt(const char *str, GEN worker, forprime_t *S, GEN dB, ulong bound, long mmin, GEN *pmod,
    1023             :         GEN crt(GEN, GEN, GEN*), GEN center(GEN, GEN, GEN))
    1024             : {
    1025     1273100 :   GEN mod = gen_1, H = NULL;
    1026             :   ulong e;
    1027             : 
    1028     1273100 :   bound++;
    1029     2546246 :   while (bound > (e = expi(mod)))
    1030             :   {
    1031     1273053 :     long n = (bound - e) / expu(S->p) + 1;
    1032     1273084 :     gen_inccrt(str, worker, dB, n, mmin, S, &H, &mod, crt, center);
    1033             :   }
    1034     1273128 :   if (pmod) *pmod = mod;
    1035     1273128 :   return H;
    1036             : }
    1037             : 
    1038             : /*******************************************************************/
    1039             : /*                                                                 */
    1040             : /*                          MODULAR GCD                            */
    1041             : /*                                                                 */
    1042             : /*******************************************************************/
    1043             : /* return z = a mod q, b mod p (p,q) = 1; qinv = 1/q mod p; a in ]-q,q] */
    1044             : static GEN
    1045     5157274 : Fl_chinese_coprime(GEN a, ulong b, GEN q, ulong p, ulong qinv, GEN pq, GEN pq2)
    1046             : {
    1047     5157274 :   ulong d, amod = umodiu(a, p);
    1048     5157323 :   pari_sp av = avma;
    1049             :   GEN ax;
    1050             : 
    1051     5157323 :   if (b == amod) return NULL;
    1052     2126590 :   d = Fl_mul(Fl_sub(b, amod, p), qinv, p); /* != 0 */
    1053     2127077 :   if (d >= 1 + (p>>1))
    1054     1037897 :     ax = subii(a, mului(p-d, q));
    1055             :   else
    1056             :   {
    1057     1089180 :     ax = addii(a, mului(d, q)); /* in ]0, pq[ assuming a in ]-q,q[ */
    1058     1088764 :     if (cmpii(ax,pq2) > 0) ax = subii(ax,pq);
    1059             :   }
    1060     2126304 :   return gerepileuptoint(av, ax);
    1061             : }
    1062             : GEN
    1063         378 : Z_init_CRT(ulong Hp, ulong p) { return stoi(Fl_center(Hp, p, p>>1)); }
    1064             : GEN
    1065       31689 : ZX_init_CRT(GEN Hp, ulong p, long v)
    1066             : {
    1067       31689 :   long i, l = lg(Hp), lim = (long)(p>>1);
    1068       31689 :   GEN H = cgetg(l, t_POL);
    1069       31689 :   H[1] = evalsigne(1) | evalvarn(v);
    1070      796077 :   for (i=2; i<l; i++)
    1071      764388 :     gel(H,i) = stoi(Fl_center(Hp[i], p, lim));
    1072       31689 :   return ZX_renormalize(H,l);
    1073             : }
    1074             : 
    1075             : GEN
    1076        5789 : ZM_init_CRT(GEN Hp, ulong p)
    1077             : {
    1078        5789 :   long i,j, m, l = lg(Hp), lim = (long)(p>>1);
    1079        5789 :   GEN c, cp, H = cgetg(l, t_MAT);
    1080        5789 :   if (l==1) return H;
    1081        5789 :   m = lgcols(Hp);
    1082       19012 :   for (j=1; j<l; j++)
    1083             :   {
    1084       13223 :     cp = gel(Hp,j);
    1085       13223 :     c = cgetg(m, t_COL);
    1086       13223 :     gel(H,j) = c;
    1087      166691 :     for (i=1; i<m; i++) gel(c,i) = stoi(Fl_center(cp[i],p, lim));
    1088             :   }
    1089        5789 :   return H;
    1090             : }
    1091             : 
    1092             : int
    1093        7616 : Z_incremental_CRT(GEN *H, ulong Hp, GEN *ptq, ulong p)
    1094             : {
    1095        7616 :   GEN h, q = *ptq, qp = muliu(q,p);
    1096        7616 :   ulong qinv = Fl_inv(umodiu(q,p), p);
    1097        7616 :   int stable = 1;
    1098        7616 :   h = Fl_chinese_coprime(*H,Hp,q,p,qinv,qp,shifti(qp,-1));
    1099        7616 :   if (h) { *H = h; stable = 0; }
    1100        7616 :   *ptq = qp; return stable;
    1101             : }
    1102             : 
    1103             : static int
    1104      147473 : ZX_incremental_CRT_raw(GEN *ptH, GEN Hp, GEN q, GEN qp, ulong p)
    1105             : {
    1106      147473 :   GEN H = *ptH, h, qp2 = shifti(qp,-1);
    1107      147472 :   ulong qinv = Fl_inv(umodiu(q,p), p);
    1108      147477 :   long i, l = lg(H), lp = lg(Hp);
    1109      147477 :   int stable = 1;
    1110             : 
    1111      147477 :   if (l < lp)
    1112             :   { /* degree increases */
    1113           0 :     GEN x = cgetg(lp, t_POL);
    1114           0 :     for (i=1; i<l; i++)  x[i] = H[i];
    1115           0 :     for (   ; i<lp; i++) gel(x,i) = gen_0;
    1116           0 :     *ptH = H = x;
    1117           0 :     stable = 0;
    1118      147477 :   } else if (l > lp)
    1119             :   { /* degree decreases */
    1120           0 :     GEN x = cgetg(l, t_VECSMALL);
    1121           0 :     for (i=1; i<lp; i++)  x[i] = Hp[i];
    1122           0 :     for (   ; i<l; i++) x[i] = 0;
    1123           0 :     Hp = x; lp = l;
    1124             :   }
    1125     4933927 :   for (i=2; i<lp; i++)
    1126             :   {
    1127     4786532 :     h = Fl_chinese_coprime(gel(H,i),Hp[i],q,p,qinv,qp,qp2);
    1128     4786450 :     if (h) { gel(H,i) = h; stable = 0; }
    1129             :   }
    1130      147395 :   (void)ZX_renormalize(H,lp);
    1131      147477 :   return stable;
    1132             : }
    1133             : 
    1134             : int
    1135           0 : ZX_incremental_CRT(GEN *ptH, GEN Hp, GEN *ptq, ulong p)
    1136             : {
    1137           0 :   GEN q = *ptq, qp = muliu(q,p);
    1138           0 :   int stable = ZX_incremental_CRT_raw(ptH, Hp, q, qp, p);
    1139           0 :   *ptq = qp; return stable;
    1140             : }
    1141             : 
    1142             : int
    1143        7611 : ZM_incremental_CRT(GEN *pH, GEN Hp, GEN *ptq, ulong p)
    1144             : {
    1145        7611 :   GEN h, H = *pH, q = *ptq, qp = muliu(q, p), qp2 = shifti(qp,-1);
    1146        7611 :   ulong qinv = Fl_inv(umodiu(q,p), p);
    1147        7611 :   long i,j, l = lg(H), m = lgcols(H);
    1148        7611 :   int stable = 1;
    1149       26374 :   for (j=1; j<l; j++)
    1150      204136 :     for (i=1; i<m; i++)
    1151             :     {
    1152      185373 :       h = Fl_chinese_coprime(gcoeff(H,i,j), coeff(Hp,i,j),q,p,qinv,qp,qp2);
    1153      185373 :       if (h) { gcoeff(H,i,j) = h; stable = 0; }
    1154             :     }
    1155        7611 :   *ptq = qp; return stable;
    1156             : }
    1157             : 
    1158             : GEN
    1159         623 : ZXM_init_CRT(GEN Hp, long deg, ulong p)
    1160             : {
    1161             :   long i, j, k;
    1162             :   GEN H;
    1163         623 :   long m, l = lg(Hp), lim = (long)(p>>1), n;
    1164         623 :   H = cgetg(l, t_MAT);
    1165         623 :   if (l==1) return H;
    1166         623 :   m = lgcols(Hp);
    1167         623 :   n = deg + 3;
    1168        2114 :   for (j=1; j<l; j++)
    1169             :   {
    1170        1491 :     GEN cp = gel(Hp,j);
    1171        1491 :     GEN c = cgetg(m, t_COL);
    1172        1491 :     gel(H,j) = c;
    1173       23905 :     for (i=1; i<m; i++)
    1174             :     {
    1175       22414 :       GEN dp = gel(cp, i);
    1176       22414 :       long l = lg(dp);
    1177       22414 :       GEN d = cgetg(n, t_POL);
    1178       22414 :       gel(c, i) = d;
    1179       22414 :       d[1] = dp[1] | evalsigne(1);
    1180       45647 :       for (k=2; k<l; k++)
    1181       23233 :         gel(d,k) = stoi(Fl_center(dp[k], p, lim));
    1182       44457 :       for (   ; k<n; k++)
    1183       22043 :         gel(d,k) = gen_0;
    1184             :     }
    1185             :   }
    1186         623 :   return H;
    1187             : }
    1188             : 
    1189             : int
    1190         653 : ZXM_incremental_CRT(GEN *pH, GEN Hp, GEN *ptq, ulong p)
    1191             : {
    1192         653 :   GEN v, H = *pH, q = *ptq, qp = muliu(q, p), qp2 = shifti(qp,-1);
    1193         653 :   ulong qinv = Fl_inv(umodiu(q,p), p);
    1194         653 :   long i,j,k, l = lg(H), m = lgcols(H), n = lg(gmael(H,1,1));
    1195         653 :   int stable = 1;
    1196        2225 :   for (j=1; j<l; j++)
    1197       90418 :     for (i=1; i<m; i++)
    1198             :     {
    1199       88846 :       GEN h = gmael(H,j,i), hp = gmael(Hp,j,i);
    1200       88846 :       long lh = lg(hp);
    1201      246641 :       for (k=2; k<lh; k++)
    1202             :       {
    1203      157795 :         v = Fl_chinese_coprime(gel(h,k),uel(hp,k),q,p,qinv,qp,qp2);
    1204      157795 :         if (v) { gel(h,k) = v; stable = 0; }
    1205             :       }
    1206      108763 :       for (; k<n; k++)
    1207             :       {
    1208       19917 :         v = Fl_chinese_coprime(gel(h,k),0,q,p,qinv,qp,qp2);
    1209       19917 :         if (v) { gel(h,k) = v; stable = 0; }
    1210             :       }
    1211             :     }
    1212         653 :   *ptq = qp; return stable;
    1213             : }
    1214             : 
    1215             : /* record the degrees of Euclidean remainders (make them as large as
    1216             :  * possible : smaller values correspond to a degenerate sequence) */
    1217             : static void
    1218       23209 : Flx_resultant_set_dglist(GEN a, GEN b, GEN dglist, ulong p)
    1219             : {
    1220             :   long da,db,dc, ind;
    1221       23209 :   pari_sp av = avma;
    1222             : 
    1223       23209 :   if (lgpol(a)==0 || lgpol(b)==0) return;
    1224       21942 :   da = degpol(a);
    1225       21942 :   db = degpol(b);
    1226       21942 :   if (db > da)
    1227           0 :   { swapspec(a,b, da,db); }
    1228       21942 :   else if (!da) return;
    1229       21942 :   ind = 0;
    1230      144193 :   while (db)
    1231             :   {
    1232      122249 :     GEN c = Flx_rem(a,b, p);
    1233      122251 :     a = b; b = c; dc = degpol(c);
    1234      122251 :     if (dc < 0) break;
    1235             : 
    1236      122251 :     ind++;
    1237      122251 :     if (dc > dglist[ind]) dglist[ind] = dc;
    1238      122251 :     if (gc_needed(av,2))
    1239             :     {
    1240           0 :       if (DEBUGMEM>1) pari_warn(warnmem,"Flx_resultant_all");
    1241           0 :       gerepileall(av, 2, &a,&b);
    1242             :     }
    1243      122251 :     db = dc; /* = degpol(b) */
    1244             :   }
    1245       21944 :   if (ind+1 > lg(dglist)) setlg(dglist,ind+1);
    1246       21944 :   set_avma(av);
    1247             : }
    1248             : /* assuming the PRS finishes on a degree 1 polynomial C0 + C1X, with
    1249             :  * "generic" degree sequence as given by dglist, set *Ci and return
    1250             :  * resultant(a,b). Modular version of Collins's subresultant */
    1251             : static ulong
    1252     2084793 : Flx_resultant_all(GEN a, GEN b, long *C0, long *C1, GEN dglist, ulong p)
    1253             : {
    1254             :   long da,db,dc, ind;
    1255     2084793 :   ulong lb, res, g = 1UL, h = 1UL, ca = 1UL, cb = 1UL;
    1256     2084793 :   int s = 1;
    1257     2084793 :   pari_sp av = avma;
    1258             : 
    1259     2084793 :   *C0 = 1; *C1 = 0;
    1260     2084793 :   if (lgpol(a)==0 || lgpol(b)==0) return 0;
    1261     2075337 :   da = degpol(a);
    1262     2075384 :   db = degpol(b);
    1263     2075368 :   if (db > da)
    1264             :   {
    1265           0 :     swapspec(a,b, da,db);
    1266           0 :     if (both_odd(da,db)) s = -s;
    1267             :   }
    1268     2075368 :   else if (!da) return 1; /* = a[2] ^ db, since 0 <= db <= da = 0 */
    1269     2075368 :   ind = 0;
    1270    19801782 :   while (db)
    1271             :   { /* sub-resultant algo., applied to ca * a and cb * b, ca,cb scalars,
    1272             :      * da = deg a, db = deg b */
    1273    17730864 :     GEN c = Flx_rem(a,b, p);
    1274    17607871 :     long delta = da - db;
    1275             : 
    1276    17607871 :     if (both_odd(da,db)) s = -s;
    1277    17604809 :     lb = Fl_mul(b[db+2], cb, p);
    1278    17623791 :     a = b; b = c; dc = degpol(c);
    1279    17622826 :     ind++;
    1280    17622826 :     if (dc != dglist[ind]) return gc_ulong(av,0); /* degenerates */
    1281    17617935 :     if (g == h)
    1282             :     { /* frequent */
    1283    17558091 :       ulong cc = Fl_mul(ca, Fl_powu(Fl_div(lb,g,p), delta+1, p), p);
    1284    17668520 :       ca = cb;
    1285    17668520 :       cb = cc;
    1286             :     }
    1287             :     else
    1288             :     {
    1289       59844 :       ulong cc = Fl_mul(ca, Fl_powu(lb, delta+1, p), p);
    1290       59844 :       ulong ghdelta = Fl_mul(g, Fl_powu(h, delta, p), p);
    1291       59844 :       ca = cb;
    1292       59844 :       cb = Fl_div(cc, ghdelta, p);
    1293             :     }
    1294    17727428 :     da = db; /* = degpol(a) */
    1295    17727428 :     db = dc; /* = degpol(b) */
    1296             : 
    1297    17727428 :     g = lb;
    1298    17727428 :     if (delta == 1)
    1299    17627905 :       h = g; /* frequent */
    1300             :     else
    1301       99523 :       h = Fl_mul(h, Fl_powu(Fl_div(g,h,p), delta, p), p);
    1302             : 
    1303    17727439 :     if (gc_needed(av,2))
    1304             :     {
    1305           0 :       if (DEBUGMEM>1) pari_warn(warnmem,"Flx_resultant_all");
    1306           0 :       gerepileall(av, 2, &a,&b);
    1307             :     }
    1308             :   }
    1309     2070918 :   if (da > 1) return 0; /* Failure */
    1310             :   /* last nonconstant polynomial has degree 1 */
    1311     2070918 :   *C0 = Fl_mul(ca, a[2], p);
    1312     2070880 :   *C1 = Fl_mul(ca, a[3], p);
    1313     2070888 :   res = Fl_mul(cb, b[2], p);
    1314     2070889 :   if (s == -1) res = p - res;
    1315     2070889 :   return gc_ulong(av,res);
    1316             : }
    1317             : 
    1318             : /* Q a vector of polynomials representing B in Fp[X][Y], evaluate at X = x,
    1319             :  * Return 0 in case of degree drop. */
    1320             : static GEN
    1321     2108370 : FlxY_evalx_drop(GEN Q, ulong x, ulong p)
    1322             : {
    1323             :   GEN z;
    1324     2108370 :   long i, lb = lg(Q);
    1325     2108370 :   ulong leadz = Flx_eval(leading_coeff(Q), x, p);
    1326     2108028 :   long vs=mael(Q,2,1);
    1327     2108028 :   if (!leadz) return zero_Flx(vs);
    1328             : 
    1329     2097368 :   z = cgetg(lb, t_VECSMALL); z[1] = vs;
    1330    20061749 :   for (i=2; i<lb-1; i++) z[i] = Flx_eval(gel(Q,i), x, p);
    1331     2095592 :   z[i] = leadz; return z;
    1332             : }
    1333             : 
    1334             : GEN
    1335        2072 : FpXY_FpXQ_evaly(GEN Q, GEN y, GEN T, GEN p, long vx)
    1336             : {
    1337        2072 :   pari_sp av = avma;
    1338        2072 :   long i, lb = lg(Q);
    1339             :   GEN z;
    1340        2072 :   if (lb == 2) return pol_0(vx);
    1341        2072 :   z = gel(Q, lb-1);
    1342        2072 :   if (lb == 3 || !signe(y)) return typ(z)==t_INT? scalar_ZX(z, vx): ZX_copy(z);
    1343             : 
    1344        2072 :   if (typ(z) == t_INT) z = scalar_ZX_shallow(z, vx);
    1345       48636 :   for (i=lb-2; i>=2; i--)
    1346             :   {
    1347       46564 :     GEN c = gel(Q,i);
    1348       46564 :     z = FqX_Fq_mul(z, y, T, p);
    1349       46564 :     z = typ(c) == t_INT? FqX_Fq_add(z,c,T,p): FqX_add(z,c,T,p);
    1350             :   }
    1351        2072 :   return gerepileupto(av, z);
    1352             : }
    1353             : 
    1354             : static GEN
    1355      291662 : ZX_norml1(GEN x)
    1356             : {
    1357      291662 :   long i, l = lg(x);
    1358             :   GEN s;
    1359             : 
    1360      291662 :   if (l == 2) return gen_0;
    1361      199108 :   s = gel(x, l-1); /* != 0 */
    1362      696998 :   for (i = l-2; i > 1; i--) {
    1363      497901 :     GEN xi = gel(x,i);
    1364      497901 :     if (!signe(xi)) continue;
    1365      259202 :     s = addii_sign(s,1, xi,1);
    1366             :   }
    1367      199097 :   return s;
    1368             : }
    1369             : /* x >= 0, y != 0, return x + |y| */
    1370             : static GEN
    1371       25554 : addii_abs(GEN x, GEN y)
    1372             : {
    1373       25554 :   if (!signe(x)) return absi_shallow(y);
    1374       16044 :   return addii_sign(x,1, y,1);
    1375             : }
    1376             : 
    1377             : /* x a ZX, return sum_{i >= k} |x[i]| binomial(i, k) */
    1378             : static GEN
    1379       31647 : ZX_norml1_1(GEN x, long k)
    1380             : {
    1381       31647 :   long i, d = degpol(x);
    1382             :   GEN s, C; /* = binomial(i, k) */
    1383             : 
    1384       31647 :   if (!d || k > d) return gen_0;
    1385       31647 :   s = absi_shallow(gel(x, k+2)); /* may be 0 */
    1386       31646 :   C = gen_1;
    1387       68046 :   for (i = k+1; i <= d; i++) {
    1388       36397 :     GEN xi = gel(x,i+2);
    1389       36397 :     if (k) C = diviuexact(muliu(C, i), i-k);
    1390       36405 :     if (signe(xi)) s = addii_abs(s, mulii(C, xi));
    1391             :   }
    1392       31649 :   return s;
    1393             : }
    1394             : /* x has non-negative real coefficients */
    1395             : static GEN
    1396        3283 : RgX_norml1_1(GEN x, long k)
    1397             : {
    1398        3283 :   long i, d = degpol(x);
    1399             :   GEN s, C; /* = binomial(i, k) */
    1400             : 
    1401        3283 :   if (!d || k > d) return gen_0;
    1402        3283 :   s = gel(x, k+2); /* may be 0 */
    1403        3283 :   C = gen_1;
    1404        9198 :   for (i = k+1; i <= d; i++) {
    1405        5915 :     GEN xi = gel(x,i+2);
    1406        5915 :     if (k) C = diviuexact(muliu(C, i), i-k);
    1407        5915 :     if (!gequal0(xi)) s = gadd(s, gmul(C, xi));
    1408             :   }
    1409        3283 :   return s;
    1410             : }
    1411             : 
    1412             : /* N_2(A)^2 */
    1413             : static GEN
    1414        8179 : sqrN2(GEN A, long prec)
    1415             : {
    1416        8179 :   pari_sp av = avma;
    1417        8179 :   long i, l = lg(A);
    1418        8179 :   GEN a = gen_0;
    1419       39961 :   for (i = 2; i < l; i++)
    1420             :   {
    1421       31782 :     a = gadd(a, gabs(gnorm(gel(A,i)), prec));
    1422       31782 :     if (gc_needed(av,1))
    1423             :     {
    1424           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"RgX_RgXY_ResBound i = %ld",i);
    1425           0 :       a = gerepileupto(av, a);
    1426             :     }
    1427             :   }
    1428        8179 :   return a;
    1429             : }
    1430             : /* Interpolate at roots of 1 and use Hadamard bound for univariate resultant:
    1431             :  *   bound = N_2(A)^degpol B N_2(B)^degpol(A),  where
    1432             :  *     N_2(A) = sqrt(sum (N_1(Ai))^2)
    1433             :  * Return e such that Res(A, B) < 2^e */
    1434             : static GEN
    1435        7325 : RgX_RgXY_ResBound(GEN A, GEN B, long prec)
    1436             : {
    1437        7325 :   pari_sp av = avma;
    1438        7325 :   GEN b = gen_0, bnd;
    1439        7325 :   long i, lB = lg(B);
    1440       28821 :   for (i=2; i<lB; i++)
    1441             :   {
    1442       21496 :     GEN t = gel(B,i);
    1443       21496 :     if (typ(t) == t_POL) t = gnorml1(t, prec);
    1444       21496 :     b = gadd(b, gabs(gsqr(t), prec));
    1445       21496 :     if (gc_needed(av,1))
    1446             :     {
    1447           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"RgX_RgXY_ResBound i = %ld",i);
    1448           0 :       b = gerepileupto(av, b);
    1449             :     }
    1450             :   }
    1451        7325 :   bnd = gsqrt(gmul(gpowgs(sqrN2(A,prec), degpol(B)),
    1452             :                    gpowgs(b, degpol(A))), prec);
    1453        7325 :   return gerepileupto(av, bnd);
    1454             : }
    1455             : /* A,B in C[X] return RgX_RgXY_ResBound(A, B(x+y)) */
    1456             : static GEN
    1457         854 : RgX_RgXY_ResBound_1(GEN A, GEN B, long prec)
    1458             : {
    1459         854 :   pari_sp av = avma, av2;
    1460         854 :   GEN b = gen_0, bnd;
    1461         854 :   long i, lB = lg(B);
    1462         854 :   B = shallowcopy(B);
    1463        4137 :   for (i=2; i<lB; i++) gel(B,i) = gabs(gel(B,i), prec);
    1464         854 :   av2 = avma;
    1465        4137 :   for (i=2; i<lB; i++)
    1466             :   {
    1467        3283 :     b = gadd(b, gsqr(RgX_norml1_1(B, i-2)));
    1468        3283 :     if (gc_needed(av2,1))
    1469             :     {
    1470           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"RgX_RgXY_ResBound i = %ld",i);
    1471           0 :       b = gerepileupto(av2, b);
    1472             :     }
    1473             :   }
    1474         854 :   bnd = gsqrt(gmul(gpowgs(sqrN2(A,prec), degpol(B)),
    1475             :                    gpowgs(b, degpol(A))), prec);
    1476         854 :   return gerepileupto(av, bnd);
    1477             : }
    1478             : 
    1479             : /* log2 N_2(A)^2 */
    1480             : static double
    1481      176582 : log2N2(GEN A)
    1482             : {
    1483      176582 :   pari_sp av = avma;
    1484      176582 :   long i, l = lg(A);
    1485      176582 :   GEN a = gen_0;
    1486     1334252 :   for (i=2; i < l; i++)
    1487             :   {
    1488     1157664 :     a = addii(a, sqri(gel(A,i)));
    1489     1157669 :     if (gc_needed(av,1))
    1490             :     {
    1491           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"ZX_ZXY_ResBound i = %ld",i);
    1492           0 :       a = gerepileupto(av, a);
    1493             :     }
    1494             :   }
    1495      176588 :   return gc_double(av, dbllog2(a));
    1496             : }
    1497             : /* Interpolate at roots of 1 and use Hadamard bound for univariate resultant:
    1498             :  *   bound = N_2(A)^degpol B N_2(B)^degpol(A),  where
    1499             :  *     N_2(A) = sqrt(sum (N_1(Ai))^2)
    1500             :  * Return e such that Res(A, B) < 2^e */
    1501             : ulong
    1502      166501 : ZX_ZXY_ResBound(GEN A, GEN B, GEN dB)
    1503             : {
    1504      166501 :   pari_sp av = avma;
    1505      166501 :   GEN b = gen_0;
    1506      166501 :   long i, lB = lg(B);
    1507             :   double logb;
    1508     1260180 :   for (i=2; i<lB; i++)
    1509             :   {
    1510     1093692 :     GEN t = gel(B,i);
    1511     1093692 :     if (typ(t) == t_POL) t = ZX_norml1(t);
    1512     1093690 :     b = addii(b, sqri(t));
    1513     1093679 :     if (gc_needed(av,1))
    1514             :     {
    1515           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"ZX_ZXY_ResBound i = %ld",i);
    1516           0 :       b = gerepileupto(av, b);
    1517             :     }
    1518             :   }
    1519      166488 :   logb = dbllog2(b); if (dB) logb -= 2 * dbllog2(dB);
    1520      166496 :   i = (long)((degpol(B) * log2N2(A) + degpol(A) * logb) / 2);
    1521      166500 :   return gc_ulong(av, (i <= 0)? 1: 1 + (ulong)i);
    1522             : }
    1523             : /* A,B ZX. Return ZX_ZXY_ResBound(A(x), B(x+y)) */
    1524             : static ulong
    1525       10083 : ZX_ZXY_ResBound_1(GEN A, GEN B)
    1526             : {
    1527       10083 :   pari_sp av = avma;
    1528       10083 :   GEN b = gen_0;
    1529       10083 :   long i, lB = lg(B);
    1530       41733 :   for (i=2; i<lB; i++)
    1531             :   {
    1532       31646 :     b = addii(b, sqri(ZX_norml1_1(B, i-2)));
    1533       31650 :     if (gc_needed(av,1))
    1534             :     {
    1535           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"ZX_ZXY_ResBound i = %ld",i);
    1536           0 :       b = gerepileupto(av, b);
    1537             :     }
    1538             :   }
    1539       10087 :   i = (long)((degpol(B) * log2N2(A) + degpol(A) * dbllog2(b)) / 2);
    1540       10085 :   return gc_ulong(av, (i <= 0)? 1: 1 + (ulong)i);
    1541             : }
    1542             : /* special case B = A' */
    1543             : static ulong
    1544     1134045 : ZX_discbound(GEN A)
    1545             : {
    1546     1134045 :   pari_sp av = avma;
    1547     1134045 :   GEN a = gen_0, b = gen_0;
    1548     1134045 :   long i , lA = lg(A), dA = degpol(A);
    1549             :   double loga, logb;
    1550     6766473 :   for (i = 2; i < lA; i++)
    1551             :   {
    1552     5632634 :     GEN c = sqri(gel(A,i));
    1553     5632343 :     a = addii(a, c);
    1554     5632482 :     if (i > 2) b = addii(b, mulii(c, sqru(i-2)));
    1555     5632420 :     if (gc_needed(av,1))
    1556             :     {
    1557           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"ZX_discbound i = %ld",i);
    1558           0 :       gerepileall(av, 2, &a, &b);
    1559             :     }
    1560             :   }
    1561     1133839 :   loga = dbllog2(a);
    1562     1133964 :   logb = dbllog2(b); set_avma(av);
    1563     1133996 :   i = (long)(((dA-1) * loga + dA * logb) / 2);
    1564     1133996 :   return (i <= 0)? 1: 1 + (ulong)i;
    1565             : }
    1566             : 
    1567             : /* return Res(a(Y), b(n,Y)) over Fp. la = leading_coeff(a) [for efficiency] */
    1568             : static ulong
    1569     5536059 : Flx_FlxY_eval_resultant(GEN a, GEN b, ulong n, ulong p, ulong pi, ulong la)
    1570             : {
    1571     5536059 :   GEN ev = FlxY_evalx_pre(b, n, p, pi);
    1572     5536608 :   long drop = lg(b) - lg(ev);
    1573     5536608 :   ulong r = Flx_resultant_pre(a, ev, p, pi);
    1574     5535850 :   if (drop && la != 1) r = Fl_mul(r, Fl_powu_pre(la, drop, p, pi), p);
    1575     5535874 :   return r;
    1576             : }
    1577             : static GEN
    1578         284 : FpX_FpXY_eval_resultant(GEN a, GEN b, GEN n, GEN p, GEN la, long db, long vX)
    1579             : {
    1580         284 :   GEN ev = FpXY_evaly(b, n, p, vX);
    1581         284 :   long drop = db-degpol(ev);
    1582         284 :   GEN r = FpX_resultant(a, ev, p);
    1583         284 :   if (drop && !gequal1(la)) r = Fp_mul(r, Fp_powu(la, drop,p),p);
    1584         284 :   return r;
    1585             : }
    1586             : 
    1587             : /* assume dres := deg(Res_X(a,b), Y) <= deg(a,X) * deg(b,Y) < p */
    1588             : /* Return a Fly */
    1589             : static GEN
    1590      368316 : Flx_FlxY_resultant_polint(GEN a, GEN b, ulong p, ulong pi, long dres, long sx)
    1591             : {
    1592             :   long i;
    1593      368316 :   ulong n, la = Flx_lead(a);
    1594      368316 :   GEN  x = cgetg(dres+2, t_VECSMALL);
    1595      368316 :   GEN  y = cgetg(dres+2, t_VECSMALL);
    1596             :  /* Evaluate at dres+ 1 points: 0 (if dres even) and +/- n, so that P_n(X) =
    1597             :   * P_{-n}(-X), where P_i is Lagrange polynomial: P_i(j) = delta_{i,j} */
    1598     2955505 :   for (i=0,n = 1; i < dres; n++)
    1599             :   {
    1600     2587187 :     x[++i] = n;   y[i] = Flx_FlxY_eval_resultant(a,b, x[i], p,pi,la);
    1601     2587116 :     x[++i] = p-n; y[i] = Flx_FlxY_eval_resultant(a,b, x[i], p,pi,la);
    1602             :   }
    1603      368318 :   if (i == dres)
    1604             :   {
    1605      362812 :     x[++i] = 0;   y[i] = Flx_FlxY_eval_resultant(a,b, x[i], p,pi,la);
    1606             :   }
    1607      368318 :   return Flv_polint(x,y, p, sx);
    1608             : }
    1609             : 
    1610             : static GEN
    1611        7650 : FlxX_pseudorem(GEN x, GEN y, ulong p, ulong pi)
    1612             : {
    1613        7650 :   long vx = varn(x), dx, dy, dz, i, lx, dp;
    1614        7650 :   pari_sp av = avma, av2;
    1615             : 
    1616        7650 :   if (!signe(y)) pari_err_INV("FlxX_pseudorem",y);
    1617        7650 :   (void)new_chunk(2);
    1618        7649 :   dx=degpol(x); x = RgX_recip_i(x)+2;
    1619        7650 :   dy=degpol(y); y = RgX_recip_i(y)+2; dz=dx-dy; dp = dz+1;
    1620        7648 :   av2 = avma;
    1621             :   for (;;)
    1622             :   {
    1623       62733 :     gel(x,0) = Flx_neg(gel(x,0), p); dp--;
    1624      235076 :     for (i=1; i<=dy; i++)
    1625      172214 :       gel(x,i) = Flx_add( Flx_mul_pre(gel(y,0), gel(x,i), p, pi),
    1626      172302 :                           Flx_mul_pre(gel(x,0), gel(y,i), p, pi), p );
    1627     1141788 :     for (   ; i<=dx; i++)
    1628     1079886 :       gel(x,i) = Flx_mul_pre(gel(y,0), gel(x,i), p, pi);
    1629       66713 :     do { x++; dx--; } while (dx >= 0 && lg(gel(x,0))==2);
    1630       61902 :     if (dx < dy) break;
    1631       54251 :     if (gc_needed(av2,1))
    1632             :     {
    1633           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"FlxX_pseudorem dx = %ld >= %ld",dx,dy);
    1634           0 :       gerepilecoeffs(av2,x,dx+1);
    1635             :     }
    1636             :   }
    1637        7651 :   if (dx < 0) return zero_Flx(0);
    1638        7651 :   lx = dx+3; x -= 2;
    1639        7651 :   x[0]=evaltyp(t_POL) | _evallg(lx);
    1640        7651 :   x[1]=evalsigne(1) | evalvarn(vx);
    1641        7651 :   x = RgX_recip_i(x);
    1642        7649 :   if (dp)
    1643             :   { /* multiply by y[0]^dp   [beware dummy vars from FpX_FpXY_resultant] */
    1644        1998 :     GEN t = Flx_powu_pre(gel(y,0), dp, p, pi);
    1645        8000 :     for (i=2; i<lx; i++) gel(x,i) = Flx_mul_pre(gel(x,i), t, p, pi);
    1646             :   }
    1647        7649 :   return gerepilecopy(av, x);
    1648             : }
    1649             : 
    1650             : /* return a Flx */
    1651             : GEN
    1652        2556 : FlxX_resultant(GEN u, GEN v, ulong p, long sx)
    1653             : {
    1654        2556 :   pari_sp av = avma, av2;
    1655             :   long degq, dx, dy, du, dv, dr, signh;
    1656             :   ulong pi;
    1657             :   GEN z, g, h, r, p1;
    1658             : 
    1659        2556 :   dx = degpol(u); dy = degpol(v); signh = 1;
    1660        2558 :   if (dx < dy)
    1661             :   {
    1662           7 :     swap(u,v); lswap(dx,dy);
    1663           7 :     if (both_odd(dx, dy)) signh = -signh;
    1664             :   }
    1665        2558 :   if (dy < 0) return zero_Flx(sx);
    1666        2558 :   pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    1667        2558 :   if (dy==0) return gerepileupto(av, Flx_powu_pre(gel(v,2),dx,p,pi));
    1668             : 
    1669        2558 :   g = h = pol1_Flx(sx); av2 = avma;
    1670             :   for(;;)
    1671             :   {
    1672        7651 :     r = FlxX_pseudorem(u,v,p,pi); dr = lg(r);
    1673        7651 :     if (dr == 2) { set_avma(av); return zero_Flx(sx); }
    1674        7651 :     du = degpol(u); dv = degpol(v); degq = du-dv;
    1675        7651 :     u = v; p1 = g; g = leading_coeff(u);
    1676        7651 :     switch(degq)
    1677             :     {
    1678           0 :       case 0: break;
    1679        5638 :       case 1:
    1680        5638 :         p1 = Flx_mul_pre(h,p1, p, pi); h = g; break;
    1681        2013 :       default:
    1682        2013 :         p1 = Flx_mul_pre(Flx_powu_pre(h,degq,p,pi), p1, p, pi);
    1683        2013 :         h = Flx_div_pre(Flx_powu_pre(g,degq,p,pi),
    1684        2012 :                         Flx_powu_pre(h,degq-1,p,pi), p, pi);
    1685             :     }
    1686        7650 :     if (both_odd(du,dv)) signh = -signh;
    1687        7649 :     v = FlxY_Flx_div(r, p1, p);
    1688        7650 :     if (dr==3) break;
    1689        5091 :     if (gc_needed(av2,1))
    1690             :     {
    1691           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"FlxX_resultant, dr = %ld",dr);
    1692           0 :       gerepileall(av2,4, &u, &v, &g, &h);
    1693             :     }
    1694             :   }
    1695        2559 :   z = gel(v,2);
    1696        2559 :   if (dv > 1) z = Flx_div_pre(Flx_powu_pre(z,dv,p,pi),
    1697           0 :                               Flx_powu_pre(h,dv-1,p,pi), p, pi);
    1698        2559 :   if (signh < 0) z = Flx_neg(z,p);
    1699        2559 :   return gerepileupto(av, z);
    1700             : }
    1701             : 
    1702             : /* Warning:
    1703             :  * This function switches between valid and invalid variable ordering*/
    1704             : 
    1705             : static GEN
    1706        6178 : FlxY_to_FlyX(GEN b, long sv)
    1707             : {
    1708        6178 :   long i, n=-1;
    1709        6178 :   long sw = b[1]&VARNBITS;
    1710       21092 :   for(i=2;i<lg(b);i++) n = maxss(n,lgpol(gel(b,i)));
    1711        6175 :   return Flm_to_FlxX(Flm_transpose(FlxX_to_Flm(b,n)),sv,sw);
    1712             : }
    1713             : 
    1714             : /* Return a Fly*/
    1715             : GEN
    1716        6177 : Flx_FlxY_resultant(GEN a, GEN b, ulong p)
    1717             : {
    1718        6177 :   pari_sp ltop=avma;
    1719        6177 :   long dres = degpol(a)*degpol(b);
    1720        6177 :   long sx=a[1], sy=b[1]&VARNBITS;
    1721             :   GEN z;
    1722        6177 :   b = FlxY_to_FlyX(b,sx);
    1723        6175 :   if ((ulong)dres >= p)
    1724        2557 :     z = FlxX_resultant(Fly_to_FlxY(a, sy), b, p, sx);
    1725             :   else
    1726             :   {
    1727        3618 :     ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    1728        3618 :     z = Flx_FlxY_resultant_polint(a, b, p, pi, (ulong)dres, sy);
    1729             :   }
    1730        6178 :   return gerepileupto(ltop,z);
    1731             : }
    1732             : 
    1733             : /* Return a t_POL in variable vc whose coeffs are the coeffs of b in
    1734             :  * variable v; vc must have higher priority than all variables occuring in b. */
    1735             : GEN
    1736      145796 : swap_vars(GEN b, long v, long vc)
    1737             : {
    1738      145796 :   long i, n = RgX_degree(b, v);
    1739             :   GEN c, x;
    1740      145796 :   if (n < 0) return pol_0(vc);
    1741      145796 :   c = cgetg(n+3, t_POL); x = c + 2;
    1742      145796 :   c[1] = evalsigne(1) | evalvarn(vc);
    1743      966840 :   for (i = 0; i <= n; i++) gel(x,i) = polcoef_i(b, i, v);
    1744      145794 :   return c;
    1745             : }
    1746             : 
    1747             : /* assume varn(b) << varn(a) */
    1748             : /* return a FpY*/
    1749             : GEN
    1750          15 : FpX_FpXY_resultant(GEN a, GEN b, GEN p)
    1751             : {
    1752          15 :   long i,n,dres, db, vY = varn(b), vX = varn(a);
    1753             :   GEN la,x,y;
    1754             : 
    1755          15 :   if (lgefint(p) == 3)
    1756             :   {
    1757           0 :     ulong pp = uel(p,2);
    1758           0 :     b = ZXX_to_FlxX(b, pp, vX);
    1759           0 :     a = ZX_to_Flx(a, pp);
    1760           0 :     x = Flx_FlxY_resultant(a, b, pp);
    1761           0 :     return Flx_to_ZX(x);
    1762             :   }
    1763          15 :   db = RgXY_degreex(b);
    1764          15 :   dres = degpol(a)*degpol(b);
    1765          15 :   la = leading_coeff(a);
    1766          15 :   x = cgetg(dres+2, t_VEC);
    1767          15 :   y = cgetg(dres+2, t_VEC);
    1768             :  /* Evaluate at dres+ 1 points: 0 (if dres even) and +/- n, so that P_n(X) =
    1769             :   * P_{-n}(-X), where P_i is Lagrange polynomial: P_i(j) = delta_{i,j} */
    1770         157 :   for (i=0,n = 1; i < dres; n++)
    1771             :   {
    1772         142 :     gel(x,++i) = utoipos(n);
    1773         142 :     gel(y,i) = FpX_FpXY_eval_resultant(a,b,gel(x,i),p,la,db,vY);
    1774         142 :     gel(x,++i) = subiu(p,n);
    1775         142 :     gel(y,i) = FpX_FpXY_eval_resultant(a,b,gel(x,i),p,la,db,vY);
    1776             :   }
    1777          15 :   if (i == dres)
    1778             :   {
    1779           0 :     gel(x,++i) = gen_0;
    1780           0 :     gel(y,i) = FpX_FpXY_eval_resultant(a,b, gel(x,i), p,la,db,vY);
    1781             :   }
    1782          15 :   return FpV_polint(x,y, p, vY);
    1783             : }
    1784             : 
    1785             : GEN
    1786          79 : FpX_composedsum(GEN P, GEN Q, GEN p)
    1787             : {
    1788          79 :   pari_sp av = avma;
    1789          79 :   if (lgefint(p)==3)
    1790             :   {
    1791           0 :     ulong pp = p[2];
    1792           0 :     GEN z = Flx_composedsum(ZX_to_Flx(P, pp), ZX_to_Flx(Q, pp), pp);
    1793           0 :     return gerepileupto(av, Flx_to_ZX(z));
    1794             :   }
    1795             :   else
    1796             :   {
    1797          79 :     long n = 1+ degpol(P)*degpol(Q);
    1798          79 :     GEN Pl = FpX_invLaplace(FpX_Newton(P,n,p), p);
    1799          79 :     GEN Ql = FpX_invLaplace(FpX_Newton(Q,n,p), p);
    1800          79 :     GEN L = FpX_Laplace(FpXn_mul(Pl, Ql, n, p), p);
    1801          79 :     GEN lead = Fp_mul(Fp_powu(leading_coeff(P),degpol(Q), p),
    1802          79 :         Fp_powu(leading_coeff(Q),degpol(P), p), p);
    1803          79 :     GEN R = FpX_fromNewton(L, p);
    1804          79 :     return gerepileupto(av, FpX_Fp_mul(R, lead, p));
    1805             :   }
    1806             : }
    1807             : 
    1808             : GEN
    1809           0 : FpX_composedprod(GEN P, GEN Q, GEN p)
    1810             : {
    1811           0 :   pari_sp av = avma;
    1812           0 :   if (lgefint(p)==3)
    1813             :   {
    1814           0 :     ulong pp = p[2];
    1815           0 :     GEN z = Flx_composedprod(ZX_to_Flx(P, pp), ZX_to_Flx(Q, pp), pp);
    1816           0 :     return gerepileupto(av, Flx_to_ZX(z));
    1817             :   }
    1818             :   else
    1819             :   {
    1820           0 :     long n = 1+ degpol(P)*degpol(Q);
    1821           0 :     GEN L = FpX_convol(FpX_Newton(P,n,p), FpX_Newton(Q,n,p), p);
    1822           0 :     return gerepileupto(av,FpX_fromNewton(L, p));
    1823             :   }
    1824             : }
    1825             : 
    1826             : static GEN
    1827          79 : _FpX_composedsum(void *E, GEN a, GEN b)
    1828          79 : { return FpX_composedsum(a,b, (GEN)E); }
    1829             : 
    1830             : GEN
    1831        1581 : FpXV_composedsum(GEN V, GEN p)
    1832             : {
    1833        1581 :   if (lgefint(p)==3)
    1834             :   {
    1835           0 :     ulong pp = p[2];
    1836           0 :     return Flx_to_ZX(FlxV_composedsum(ZXV_to_FlxV(V, pp), pp));
    1837             :   }
    1838        1581 :   return gen_product(V, (void *)p, &_FpX_composedsum);
    1839             : }
    1840             : 
    1841             : /* 0, 1, -1, 2, -2, ... */
    1842             : #define next_lambda(a) (a>0 ? -a : 1-a)
    1843             : 
    1844             : /* Assume A in Z[Y], B in Q[Y][X], B squarefree in (Q[Y]/(A))[X] and
    1845             :  * Res_Y(A, B) in Z[X]. Find a small lambda (start from *lambda, use
    1846             :  * next_lambda successively) such that C(X) = Res_Y(A(Y), B(X + lambda Y))
    1847             :  * is squarefree, reset *lambda to the chosen value and return C. Set LERS to
    1848             :  * the Last nonconstant polynomial in the Euclidean Remainder Sequence */
    1849             : static GEN
    1850       21623 : ZX_ZXY_resultant_LERS(GEN A, GEN B0, long *plambda, GEN *LERS)
    1851             : {
    1852             :   ulong bound, dp;
    1853       21623 :   pari_sp av = avma, av2 = 0;
    1854       21623 :   long lambda = *plambda, degA = degpol(A), dres = degA*degpol(B0);
    1855             :   long stable, checksqfree, i,n, cnt, degB;
    1856       21623 :   long v, vX = varn(B0), vY = varn(A); /* vY < vX */
    1857             :   GEN x, y, dglist, B, q, a, b, ev, H, H0, H1, Hp, H0p, H1p, C0, C1;
    1858             :   forprime_t S;
    1859             : 
    1860       21623 :   if (degA == 1)
    1861             :   {
    1862        1197 :     GEN a1 = gel(A,3), a0 = gel(A,2);
    1863        1197 :     B = lambda? RgX_translate(B0, monomial(stoi(lambda), 1, vY)): B0;
    1864        1197 :     H = gsubst(B, vY, gdiv(gneg(a0),a1));
    1865        1197 :    if (!equali1(a1)) H = RgX_Rg_mul(H, powiu(a1, poldegree(B,vY)));
    1866        1197 :     *LERS = mkvec2(scalarpol_shallow(a0,vX), scalarpol_shallow(a1,vX));
    1867        1197 :     return gc_all(av, 2, &H, LERS);
    1868             :   }
    1869             : 
    1870       20426 :   dglist = Hp = H0p = H1p = C0 = C1 = NULL; /* gcc -Wall */
    1871       20426 :   C0 = cgetg(dres+2, t_VECSMALL);
    1872       20426 :   C1 = cgetg(dres+2, t_VECSMALL);
    1873       20426 :   dglist = cgetg(dres+1, t_VECSMALL);
    1874       20426 :   x = cgetg(dres+2, t_VECSMALL);
    1875       20426 :   y = cgetg(dres+2, t_VECSMALL);
    1876       20426 :   B0 = leafcopy(B0);
    1877       20426 :   A = leafcopy(A);
    1878       20426 :   B = B0;
    1879       20426 :   v = fetch_var_higher(); setvarn(A,v);
    1880             :   /* make sure p large enough */
    1881       21242 : INIT:
    1882             :   /* always except the first time */
    1883       21242 :   if (av2) { set_avma(av2); lambda = next_lambda(lambda); }
    1884       21242 :   if (lambda) B = RgX_translate(B0, monomial(stoi(lambda), 1, vY));
    1885       21242 :   B = swap_vars(B, vY, v);
    1886             :   /* B0(lambda v + x, v) */
    1887       21242 :   if (DEBUGLEVEL>4) err_printf("Trying lambda = %ld\n", lambda);
    1888       21242 :   av2 = avma;
    1889             : 
    1890       21242 :   if (degA <= 3)
    1891             :   { /* sub-resultant faster for small degrees */
    1892       10570 :     H = RgX_resultant_all(A,B,&q);
    1893       10570 :     if (typ(q) != t_POL || degpol(q)!=1) goto INIT;
    1894        9905 :     H0 = gel(q,2);
    1895        9905 :     if (typ(H0) == t_POL) setvarn(H0,vX); else H0 = scalarpol(H0,vX);
    1896        9905 :     H1 = gel(q,3);
    1897        9905 :     if (typ(H1) == t_POL) setvarn(H1,vX); else H1 = scalarpol(H1,vX);
    1898        9905 :     if (!ZX_is_squarefree(H)) goto INIT;
    1899        9863 :     goto END;
    1900             :   }
    1901             : 
    1902       10672 :   H = H0 = H1 = NULL;
    1903       10672 :   degB = degpol(B);
    1904       10672 :   bound = ZX_ZXY_ResBound(A, B, NULL);
    1905       10672 :   if (DEBUGLEVEL>4) err_printf("bound for resultant coeffs: 2^%ld\n",bound);
    1906       10672 :   dp = 1;
    1907       10672 :   init_modular_big(&S);
    1908       10672 :   for(cnt = 0, checksqfree = 1;;)
    1909       49159 :   {
    1910       59831 :     ulong p = u_forprime_next(&S);
    1911             :     GEN Hi;
    1912       59831 :     a = ZX_to_Flx(A, p);
    1913       59831 :     b = ZXX_to_FlxX(B, p, varn(A));
    1914       59830 :     if (degpol(a) < degA || degpol(b) < degB) continue; /* p | lc(A)lc(B) */
    1915       59830 :     if (checksqfree)
    1916             :     { /* find degree list for generic Euclidean Remainder Sequence */
    1917       10672 :       long goal = minss(degpol(a), degpol(b)); /* longest possible */
    1918       73077 :       for (n=1; n <= goal; n++) dglist[n] = 0;
    1919       10672 :       setlg(dglist, 1);
    1920       23601 :       for (n=0; n <= dres; n++)
    1921             :       {
    1922       23209 :         ev = FlxY_evalx_drop(b, n, p);
    1923       23209 :         Flx_resultant_set_dglist(a, ev, dglist, p);
    1924       23208 :         if (lg(dglist)-1 == goal) break;
    1925             :       }
    1926             :       /* last pol in ERS has degree > 1 ? */
    1927       10671 :       goal = lg(dglist)-1;
    1928       10671 :       if (degpol(B) == 1) { if (!goal) goto INIT; }
    1929             :       else
    1930             :       {
    1931       10615 :         if (goal <= 1) goto INIT;
    1932       10559 :         if (dglist[goal] != 0 || dglist[goal-1] != 1) goto INIT;
    1933             :       }
    1934       10615 :       if (DEBUGLEVEL>4)
    1935           0 :         err_printf("Degree list for ERS (trials: %ld) = %Ps\n",n+1,dglist);
    1936             :     }
    1937             : 
    1938     2144945 :     for (i=0,n = 0; i <= dres; n++)
    1939             :     {
    1940     2085168 :       ev = FlxY_evalx_drop(b, n, p);
    1941     2084762 :       x[++i] = n; y[i] = Flx_resultant_all(a, ev, C0+i, C1+i, dglist, p);
    1942     2085172 :       if (!C1[i]) i--; /* C1(i) = 0. No way to recover C0(i) */
    1943             :     }
    1944       59777 :     Hi = Flv_Flm_polint(x, mkvec3(y,C0,C1), p, 0);
    1945       59775 :     Hp = gel(Hi,1); H0p = gel(Hi,2); H1p = gel(Hi,3);
    1946       59775 :     if (!H && degpol(Hp) != dres) continue;
    1947       59775 :     if (dp != 1) Hp = Flx_Fl_mul(Hp, Fl_powu(Fl_inv(dp,p), degA, p), p);
    1948       59775 :     if (checksqfree) {
    1949       10616 :       if (!Flx_is_squarefree(Hp, p)) goto INIT;
    1950       10563 :       if (DEBUGLEVEL>4) err_printf("Final lambda = %ld\n", lambda);
    1951       10563 :       checksqfree = 0;
    1952             :     }
    1953             : 
    1954       59722 :     if (!H)
    1955             :     { /* initialize */
    1956       10563 :       q = utoipos(p); stable = 0;
    1957       10563 :       H = ZX_init_CRT(Hp, p,vX);
    1958       10563 :       H0= ZX_init_CRT(H0p, p,vX);
    1959       10563 :       H1= ZX_init_CRT(H1p, p,vX);
    1960             :     }
    1961             :     else
    1962             :     {
    1963       49159 :       GEN qp = muliu(q,p);
    1964       49157 :       stable  = ZX_incremental_CRT_raw(&H, Hp, q,qp, p)
    1965       49159 :               & ZX_incremental_CRT_raw(&H0,H0p, q,qp, p)
    1966       49159 :               & ZX_incremental_CRT_raw(&H1,H1p, q,qp, p);
    1967       49159 :       q = qp;
    1968             :     }
    1969             :     /* could make it probabilistic for H ? [e.g if stable twice, etc]
    1970             :      * Probabilistic anyway for H0, H1 */
    1971       59722 :     if (DEBUGLEVEL>5 && (stable ||  ++cnt==100))
    1972           0 :     { cnt=0; err_printf("%ld%%%s ",100*expi(q)/bound,stable?"s":""); }
    1973       59722 :     if (stable && (ulong)expi(q) >= bound) break; /* DONE */
    1974       49159 :     if (gc_needed(av,2))
    1975             :     {
    1976           0 :       if (DEBUGMEM>1) pari_warn(warnmem,"ZX_ZXY_rnfequation");
    1977           0 :       gerepileall(av2, 4, &H, &q, &H0, &H1);
    1978             :     }
    1979             :   }
    1980       20426 : END:
    1981       20426 :   if (DEBUGLEVEL>5) err_printf(" done\n");
    1982       20426 :   setvarn(H, vX); (void)delete_var();
    1983       20426 :   *LERS = mkvec2(H0,H1);
    1984       20426 :   *plambda = lambda; return gc_all(av, 2, &H, LERS);
    1985             : }
    1986             : 
    1987             : GEN
    1988       59435 : ZX_ZXY_resultant_all(GEN A, GEN B, long *plambda, GEN *LERS)
    1989             : {
    1990       59435 :   if (LERS)
    1991             :   {
    1992       21623 :     if (!plambda)
    1993           0 :       pari_err_BUG("ZX_ZXY_resultant_all [LERS != NULL needs lambda]");
    1994       21623 :     return ZX_ZXY_resultant_LERS(A, B, plambda, LERS);
    1995             :   }
    1996       37812 :   return ZX_ZXY_rnfequation(A, B, plambda);
    1997             : }
    1998             : 
    1999             : /* If lambda = NULL, return caract(Mod(A, T)), T,A in Z[X].
    2000             :  * Otherwise find a small lambda such that caract (Mod(A + lambda X, T)) is
    2001             :  * squarefree */
    2002             : GEN
    2003       22553 : ZXQ_charpoly_sqf(GEN A, GEN T, long *lambda, long v)
    2004             : {
    2005       22553 :   pari_sp av = avma;
    2006             :   GEN R, a;
    2007             :   long dA;
    2008             :   int delvar;
    2009             : 
    2010       22553 :   if (v < 0) v = 0;
    2011       22553 :   switch (typ(A))
    2012             :   {
    2013       22553 :     case t_POL: dA = degpol(A); if (dA > 0) break;
    2014           0 :       A = constant_coeff(A);
    2015           0 :     default:
    2016           0 :       if (lambda) { A = scalar_ZX_shallow(A,varn(T)); dA = 0; break;}
    2017           0 :       return gerepileupto(av, gpowgs(gsub(pol_x(v), A), degpol(T)));
    2018             :   }
    2019       22553 :   delvar = 0;
    2020       22553 :   if (varncmp(varn(T), 0) <= 0)
    2021             :   {
    2022        3646 :     long v0 = fetch_var(); delvar = 1;
    2023        3646 :     T = leafcopy(T); setvarn(T,v0);
    2024        3646 :     A = leafcopy(A); setvarn(A,v0);
    2025             :   }
    2026       22553 :   R = ZX_ZXY_rnfequation(T, deg1pol_shallow(gen_1, gneg_i(A), 0), lambda);
    2027       22553 :   if (delvar) (void)delete_var();
    2028       22553 :   setvarn(R, v); a = leading_coeff(T);
    2029       22553 :   if (!gequal1(a)) R = gdiv(R, powiu(a, dA));
    2030       22553 :   return gerepileupto(av, R);
    2031             : }
    2032             : 
    2033             : /* charpoly(Mod(A,T)), A may be in Q[X], but assume T and result are integral */
    2034             : GEN
    2035      994048 : ZXQ_charpoly(GEN A, GEN T, long v)
    2036             : {
    2037      994048 :   return (degpol(T) < 16) ? RgXQ_charpoly_i(A,T,v): ZXQ_charpoly_sqf(A,T, NULL, v);
    2038             : }
    2039             : 
    2040             : GEN
    2041        9780 : QXQ_charpoly(GEN A, GEN T, long v)
    2042             : {
    2043        9780 :   pari_sp av = avma;
    2044        9780 :   GEN den, B = Q_remove_denom(A, &den);
    2045        9780 :   GEN P = ZXQ_charpoly(B, T, v);
    2046        9780 :   return gerepilecopy(av, den ? RgX_rescale(P, ginv(den)): P);
    2047             : }
    2048             : 
    2049             : static ulong
    2050     3863410 : ZX_resultant_prime(GEN a, GEN b, GEN dB, long degA, long degB, ulong p)
    2051             : {
    2052     3863410 :   long dropa = degA - degpol(a), dropb = degB - degpol(b);
    2053             :   ulong H, dp;
    2054     3863260 :   if (dropa && dropb) return 0; /* p | lc(A), p | lc(B) */
    2055     3863260 :   H = Flx_resultant(a, b, p);
    2056     3862950 :   if (dropa)
    2057             :   { /* multiply by ((-1)^deg B lc(B))^(deg A - deg a) */
    2058           0 :     ulong c = b[degB+2]; /* lc(B) */
    2059           0 :     if (odd(degB)) c = p - c;
    2060           0 :     c = Fl_powu(c, dropa, p);
    2061           0 :     if (c != 1) H = Fl_mul(H, c, p);
    2062             :   }
    2063     3862950 :   else if (dropb)
    2064             :   { /* multiply by lc(A)^(deg B - deg b) */
    2065           0 :     ulong c = a[degA+2]; /* lc(A) */
    2066           0 :     c = Fl_powu(c, dropb, p);
    2067           0 :     if (c != 1) H = Fl_mul(H, c, p);
    2068             :   }
    2069     3862949 :   dp = dB ? umodiu(dB, p): 1;
    2070     3862948 :   if (dp != 1) H = Fl_mul(H, Fl_powu(Fl_inv(dp,p), degA, p), p);
    2071     3862949 :   return H;
    2072             : }
    2073             : 
    2074             : /* If B=NULL, assume B=A' */
    2075             : static GEN
    2076     1494373 : ZX_resultant_slice(GEN A, GEN B, GEN dB, GEN P, GEN *mod)
    2077             : {
    2078     1494373 :   pari_sp av = avma, av2;
    2079     1494373 :   long degA, degB, i, n = lg(P)-1;
    2080             :   GEN H, T;
    2081             : 
    2082     1494373 :   degA = degpol(A);
    2083     1494370 :   degB = B? degpol(B): degA - 1;
    2084     1494371 :   if (n == 1)
    2085             :   {
    2086      810470 :     ulong Hp, p = uel(P,1);
    2087      810470 :     GEN a = ZX_to_Flx(A, p), b = B? ZX_to_Flx(B, p): Flx_deriv(a, p);
    2088      810464 :     Hp = ZX_resultant_prime(a, b, dB, degA, degB, p);
    2089      810454 :     set_avma(av); *mod = utoipos(p); return utoi(Hp);
    2090             :   }
    2091      683901 :   T = ZV_producttree(P);
    2092      683902 :   A = ZX_nv_mod_tree(A, P, T);
    2093      683894 :   if (B) B = ZX_nv_mod_tree(B, P, T);
    2094      683894 :   H = cgetg(n+1, t_VECSMALL); av2 = avma;
    2095     3736462 :   for(i=1; i <= n; i++, set_avma(av2))
    2096             :   {
    2097     3052566 :     ulong p = P[i];
    2098     3052566 :     GEN a = gel(A,i), b = B? gel(B,i): Flx_deriv(a, p);
    2099     3052954 :     H[i] = ZX_resultant_prime(a, b, dB, degA, degB, p);
    2100             :   }
    2101      683896 :   H = ZV_chinese_tree(H, P, T, ZV_chinesetree(P,T));
    2102      683898 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2103             : }
    2104             : 
    2105             : GEN
    2106     1494387 : ZX_resultant_worker(GEN P, GEN A, GEN B, GEN dB)
    2107             : {
    2108     1494387 :   GEN V = cgetg(3, t_VEC);
    2109     1494374 :   if (typ(B) == t_INT) B = NULL;
    2110     1494374 :   if (!signe(dB)) dB = NULL;
    2111     1494374 :   gel(V,1) = ZX_resultant_slice(A, B, dB, P, &gel(V,2));
    2112     1494374 :   return V;
    2113             : }
    2114             : 
    2115             : /* Compute Res(A, B/dB) in Z, assuming A,B in Z[X], dB in Z or NULL (= 1)
    2116             :  * If B=NULL, take B = A' and assume deg A > 1 and 'bound' is set */
    2117             : GEN
    2118     1350939 : ZX_resultant_all(GEN A, GEN B, GEN dB, ulong bound)
    2119             : {
    2120     1350939 :   pari_sp av = avma;
    2121             :   forprime_t S;
    2122             :   GEN  H, worker;
    2123     1350939 :   if (!B && degpol(A)==2)
    2124             :   {
    2125      113924 :     GEN a = gel(A,4), b = gel(A,3), c = gel(A,2);
    2126      113924 :     H = mulii(a, subii(shifti(mulii(a, c), 2), sqri(b)));
    2127      113921 :     if (dB) H = diviiexact(H, sqri(dB));
    2128      113921 :     return gerepileuptoint(av, H);
    2129             :   }
    2130     1237015 :   if (B)
    2131             :   {
    2132      155097 :     long a = degpol(A), b = degpol(B);
    2133      155097 :     if (a < 0 || b < 0) return gen_0;
    2134      155067 :     if (!a) return powiu(gel(A,2), b);
    2135      155067 :     if (!b) return powiu(gel(B,2), a);
    2136      153322 :     if (minss(a, b) <= 1)
    2137             :     {
    2138       76662 :       H = RgX_resultant_all(A, B, NULL);
    2139       76662 :       if (dB) H = diviiexact(H, powiu(dB, a));
    2140       76662 :       return gerepileuptoint(av, H);
    2141             :     }
    2142       76660 :     if (!bound) bound = ZX_ZXY_ResBound(A, B, dB);
    2143             :   }
    2144     1158585 :   worker = snm_closure(is_entry("_ZX_resultant_worker"),
    2145             :                        mkvec3(A, B? B: gen_0, dB? dB: gen_0));
    2146     1158644 :   init_modular_big(&S);
    2147     1158608 :   H = gen_crt("ZX_resultant_all", worker, &S, dB, bound, 0, NULL,
    2148             :               ZV_chinese_center, Fp_center);
    2149     1158632 :   return gerepileuptoint(av, H);
    2150             : }
    2151             : 
    2152             : /* A0 and B0 in Q[X] */
    2153             : GEN
    2154          56 : QX_resultant(GEN A0, GEN B0)
    2155             : {
    2156             :   GEN s, a, b, A, B;
    2157          56 :   pari_sp av = avma;
    2158             : 
    2159          56 :   A = Q_primitive_part(A0, &a);
    2160          56 :   B = Q_primitive_part(B0, &b);
    2161          56 :   s = ZX_resultant(A, B);
    2162          56 :   if (!signe(s)) { set_avma(av); return gen_0; }
    2163          56 :   if (a) s = gmul(s, gpowgs(a,degpol(B)));
    2164          56 :   if (b) s = gmul(s, gpowgs(b,degpol(A)));
    2165          56 :   return gerepileupto(av, s);
    2166             : }
    2167             : 
    2168             : GEN
    2169       57239 : ZX_resultant(GEN A, GEN B) { return ZX_resultant_all(A,B,NULL,0); }
    2170             : 
    2171             : GEN
    2172           0 : QXQ_intnorm(GEN A, GEN B)
    2173             : {
    2174             :   GEN c, n, R, lB;
    2175           0 :   long dA = degpol(A), dB = degpol(B);
    2176           0 :   pari_sp av = avma;
    2177           0 :   if (dA < 0) return gen_0;
    2178           0 :   A = Q_primitive_part(A, &c);
    2179           0 :   if (!c || typ(c) == t_INT) {
    2180           0 :     n = c;
    2181           0 :     R = ZX_resultant(B, A);
    2182             :   } else {
    2183           0 :     n = gel(c,1);
    2184           0 :     R = ZX_resultant_all(B, A, gel(c,2), 0);
    2185             :   }
    2186           0 :   if (n && !equali1(n)) R = mulii(R, powiu(n, dB));
    2187           0 :   lB = leading_coeff(B);
    2188           0 :   if (!equali1(lB)) R = diviiexact(R, powiu(lB, dA));
    2189           0 :   return gerepileuptoint(av, R);
    2190             : }
    2191             : 
    2192             : GEN
    2193       19418 : QXQ_norm(GEN A, GEN B)
    2194             : {
    2195             :   GEN c, R, lB;
    2196       19418 :   long dA = degpol(A), dB = degpol(B);
    2197       19418 :   pari_sp av = avma;
    2198       19418 :   if (dA < 0) return gen_0;
    2199       19418 :   A = Q_primitive_part(A, &c);
    2200       19418 :   R = ZX_resultant(B, A);
    2201       19418 :   if (c) R = gmul(R, gpowgs(c, dB));
    2202       19418 :   lB = leading_coeff(B);
    2203       19418 :   if (!equali1(lB)) R = gdiv(R, gpowgs(lB, dA));
    2204       19418 :   return gerepileupto(av, R);
    2205             : }
    2206             : 
    2207             : /* assume x has integral coefficients */
    2208             : GEN
    2209     1199096 : ZX_disc_all(GEN x, ulong bound)
    2210             : {
    2211     1199096 :   pari_sp av = avma;
    2212     1199096 :   long s, d = degpol(x);
    2213             :   GEN l, R;
    2214             : 
    2215     1199093 :   if (d <= 1) return d == 1? gen_1: gen_0;
    2216     1195863 :   s = (d & 2) ? -1: 1;
    2217     1195863 :   l = leading_coeff(x);
    2218     1195860 :   if (!bound) bound = ZX_discbound(x);
    2219     1195810 :   R = ZX_resultant_all(x, NULL, NULL, bound);
    2220     1195871 :   if (is_pm1(l))
    2221     1016843 :   { if (signe(l) < 0) s = -s; }
    2222             :   else
    2223      179023 :     R = diviiexact(R,l);
    2224     1195866 :   if (s == -1) togglesign_safe(&R);
    2225     1195864 :   return gerepileuptoint(av,R);
    2226             : }
    2227             : 
    2228             : GEN
    2229     1137233 : ZX_disc(GEN x) { return ZX_disc_all(x,0); }
    2230             : 
    2231             : static GEN
    2232       10404 : ZXQX_resultant_prime(GEN a, GEN b, GEN dB, long degA, long degB, GEN T, ulong p)
    2233             : {
    2234       10404 :   long dropa = degA - degpol(a), dropb = degB - degpol(b);
    2235             :   GEN H, dp;
    2236       10403 :   if (dropa && dropb) return pol0_Flx(T[1]); /* p | lc(A), p | lc(B) */
    2237       10403 :   H = FlxqX_saferesultant(a, b, T, p);
    2238       10401 :   if (!H) return NULL;
    2239       10401 :   if (dropa)
    2240             :   { /* multiply by ((-1)^deg B lc(B))^(deg A - deg a) */
    2241           0 :     GEN c = gel(b,degB+2); /* lc(B) */
    2242           0 :     if (odd(degB)) c = Flx_neg(c, p);
    2243           0 :     c = Flxq_powu(c, dropa, T, p);
    2244           0 :     if (!Flx_equal1(c)) H = Flxq_mul(H, c, T, p);
    2245             :   }
    2246       10401 :   else if (dropb)
    2247             :   { /* multiply by lc(A)^(deg B - deg b) */
    2248           0 :     GEN c = gel(a,degA+2); /* lc(A) */
    2249           0 :     c = Flxq_powu(c, dropb, T, p);
    2250           0 :     if (!Flx_equal1(c)) H = Flxq_mul(H, c, T, p);
    2251             :   }
    2252       10401 :   dp = dB ? ZX_to_Flx(dB, p): pol1_Flx(T[1]);
    2253       10403 :   if (!Flx_equal1(dp))
    2254             :   {
    2255           0 :     GEN idp = Flxq_invsafe(dp, T, p);
    2256           0 :     if (!idp) return NULL;
    2257           0 :     H = Flxq_mul(H, Flxq_powu(idp, degA, T, p), T, p);
    2258             :   }
    2259       10403 :   return H;
    2260             : }
    2261             : 
    2262             : /* If B=NULL, assume B=A' */
    2263             : static GEN
    2264        4447 : ZXQX_resultant_slice(GEN A, GEN B, GEN U, GEN dB, GEN P, GEN *mod)
    2265             : {
    2266        4447 :   pari_sp av = avma;
    2267        4447 :   long degA, degB, i, n = lg(P)-1;
    2268             :   GEN H, T;
    2269        4447 :   long v = varn(U), redo = 0;
    2270             : 
    2271        4447 :   degA = degpol(A);
    2272        4447 :   degB = B? degpol(B): degA - 1;
    2273        4447 :   if (n == 1)
    2274             :   {
    2275        2760 :     ulong p = uel(P,1);
    2276        2760 :     GEN a = ZXX_to_FlxX(A, p, v), b = B? ZXX_to_FlxX(B, p, v): FlxX_deriv(a, p);
    2277        2760 :     GEN u = ZX_to_Flx(U, p);
    2278        2760 :     GEN Hp = ZXQX_resultant_prime(a, b, dB, degA, degB, u, p);
    2279        2760 :     if (!Hp) { set_avma(av); *mod = gen_1; return pol_0(v); }
    2280        2760 :     Hp = gerepileupto(av, Flx_to_ZX(Hp)); *mod = utoipos(p); return Hp;
    2281             :   }
    2282        1687 :   T = ZV_producttree(P);
    2283        1687 :   A = ZXX_nv_mod_tree(A, P, T, v);
    2284        1687 :   if (B) B = ZXX_nv_mod_tree(B, P, T, v);
    2285        1687 :   U = ZX_nv_mod_tree(U, P, T);
    2286        1687 :   H = cgetg(n+1, t_VEC);
    2287        9330 :   for(i=1; i <= n; i++)
    2288             :   {
    2289        7644 :     ulong p = P[i];
    2290        7644 :     GEN a = gel(A,i), b = B? gel(B,i): FlxX_deriv(a, p), u = gel(U, i);
    2291        7644 :     GEN h = ZXQX_resultant_prime(a, b, dB, degA, degB, u, p);
    2292        7643 :     if (!h)
    2293             :     {
    2294           0 :       gel(H,i) = pol_0(v);
    2295           0 :       P[i] = 1; redo = 1;
    2296             :     }
    2297             :     else
    2298        7643 :       gel(H,i) = h;
    2299             :   }
    2300        1686 :   if (redo) T = ZV_producttree(P);
    2301        1686 :   H = nxV_chinese_center_tree(H, P, T, ZV_chinesetree(P, T));
    2302        1687 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2303             : }
    2304             : 
    2305             : GEN
    2306        4447 : ZXQX_resultant_worker(GEN P, GEN A, GEN B, GEN T, GEN dB)
    2307             : {
    2308        4447 :   GEN V = cgetg(3, t_VEC);
    2309        4447 :   if (isintzero(B)) B = NULL;
    2310        4447 :   if (!signe(dB)) dB = NULL;
    2311        4447 :   gel(V,1) = ZXQX_resultant_slice(A, B, T, dB, P, &gel(V,2));
    2312        4447 :   return V;
    2313             : }
    2314             : 
    2315             : static ulong
    2316        3874 : ZXQX_resultant_bound_i(GEN nf, GEN A, GEN B, GEN (*f)(GEN,GEN,long))
    2317             : {
    2318        3874 :   pari_sp av = avma;
    2319        3874 :   GEN r, M = nf_L2_bound(nf, NULL, &r);
    2320        3874 :   long v = nf_get_varn(nf), i, l = lg(r);
    2321        3874 :   GEN a = cgetg(l, t_COL);
    2322       12053 :   for (i = 1; i < l; i++)
    2323        8179 :     gel(a, i) = f(gsubst(A, v, gel(r,i)), gsubst(B, v, gel(r,i)), DEFAULTPREC);
    2324        3874 :   return gc_ulong(av, (ulong) dbllog2(gmul(M,RgC_fpnorml2(a, DEFAULTPREC))));
    2325             : }
    2326             : static ulong
    2327        3559 : ZXQX_resultant_bound(GEN nf, GEN A, GEN B)
    2328        3559 : { return ZXQX_resultant_bound_i(nf, A, B, &RgX_RgXY_ResBound); }
    2329             : 
    2330             : static GEN
    2331          56 : _ZXQ_powu(GEN x, ulong u, GEN T)
    2332          56 : { return typ(x) == t_INT? powiu(x, u): ZXQ_powu(x, u, T); }
    2333             : 
    2334             : /* Compute Res(A, B/dB) in Z[X]/T, assuming A,B in Z[X,Y], dB in Z or NULL (= 1)
    2335             :  * If B=NULL, take B = A' and assume deg A > 1 */
    2336             : static GEN
    2337        3556 : ZXQX_resultant_all(GEN A, GEN B, GEN T, GEN dB, ulong bound)
    2338             : {
    2339        3556 :   pari_sp av = avma;
    2340             :   forprime_t S;
    2341             :   GEN  H, worker;
    2342        3556 :   if (B)
    2343             :   {
    2344          63 :     long a = degpol(A), b = degpol(B);
    2345          63 :     if (a < 0 || b < 0) return gen_0;
    2346          63 :     if (!a) return _ZXQ_powu(gel(A,2), b, T);
    2347          63 :     if (!b) return _ZXQ_powu(gel(B,2), a, T);
    2348             :   } else
    2349        3493 :     if (!bound) B = RgX_deriv(A);
    2350        3556 :   if (!bound) bound = ZXQX_resultant_bound(nfinit(T, DEFAULTPREC), A, B);
    2351        3556 :   worker = snm_closure(is_entry("_ZXQX_resultant_worker"),
    2352             :                        mkvec4(A, B? B: gen_0, T, dB? dB: gen_0));
    2353        3556 :   init_modular_big(&S);
    2354        3556 :   H = gen_crt("ZXQX_resultant_all", worker, &S, dB, bound, 0, NULL,
    2355             :               nxV_chinese_center, FpX_center);
    2356        3556 :   if (DEBUGLEVEL)
    2357           0 :     err_printf("ZXQX_resultant_all: a priori bound: %lu, a posteriori: %lu\n",
    2358             :                bound, expi(gsupnorm(H, DEFAULTPREC)));
    2359        3556 :   return gerepileupto(av, H);
    2360             : }
    2361             : 
    2362             : GEN
    2363         119 : nfX_resultant(GEN nf, GEN x, GEN y)
    2364             : {
    2365         119 :   pari_sp av = avma;
    2366         119 :   GEN cx, cy, D, T = nf_get_pol(nf);
    2367         119 :   long dx = degpol(x), dy = degpol(y);
    2368         119 :   if (dx < 0 || dy < 0) return gen_0;
    2369         119 :   x = Q_primitive_part(x, &cx); if (cx) cx = gpowgs(cx, dy);
    2370         119 :   y = Q_primitive_part(y, &cy); if (cy) cy = gpowgs(cy, dx);
    2371         119 :   if (!dx)      D = _ZXQ_powu(gel(x,2), dy, T);
    2372         119 :   else if (!dy) D = _ZXQ_powu(gel(y,2), dx, T);
    2373             :   else
    2374             :   {
    2375          63 :     ulong bound = ZXQX_resultant_bound(nf, x, y);
    2376          63 :     D = ZXQX_resultant_all(x, y, T, NULL, bound);
    2377             :   }
    2378         119 :   cx = mul_content(cx, cy); if (cx) D = gmul(D, cx);
    2379         119 :   return gerepileupto(av, D);
    2380             : }
    2381             : 
    2382             : static GEN
    2383         231 : to_ZX(GEN a, long v) { return typ(a)==t_INT? scalarpol(a,v): a; }
    2384             : 
    2385             : static GEN
    2386        3493 : ZXQX_disc_all(GEN x, GEN T, ulong bound)
    2387             : {
    2388        3493 :   pari_sp av = avma;
    2389        3493 :   long s, d = degpol(x), v = varn(T);
    2390             :   GEN l, R;
    2391             : 
    2392        3493 :   if (d <= 1) return d == 1? pol_1(v): pol_0(v);
    2393        3493 :   s = (d & 2) ? -1: 1;
    2394        3493 :   l = leading_coeff(x);
    2395        3493 :   R = ZXQX_resultant_all(x, NULL, T, NULL, bound);
    2396        3493 :   if (!gequal1(l)) R = QXQ_div(R, to_ZX(l,v), T);
    2397        3493 :   if (s == -1) R = RgX_neg(R);
    2398        3493 :   return gerepileupto(av, R);
    2399             : }
    2400             : 
    2401             : GEN
    2402           7 : QX_disc(GEN x)
    2403             : {
    2404           7 :   pari_sp av = avma;
    2405           7 :   GEN c, d = ZX_disc( Q_primitive_part(x, &c) );
    2406           7 :   if (c) d = gmul(d, gpowgs(c, 2*degpol(x) - 2));
    2407           7 :   return gerepileupto(av, d);
    2408             : }
    2409             : 
    2410             : GEN
    2411        3689 : nfX_disc(GEN nf, GEN x)
    2412             : {
    2413        3689 :   pari_sp av = avma;
    2414        3689 :   GEN c, D, T = nf_get_pol(nf);
    2415             :   ulong bound;
    2416        3689 :   long d = degpol(x), v = varn(T);
    2417        3689 :   if (d <= 1) return d == 1? pol_1(v): pol_0(v);
    2418        3493 :   x = Q_primitive_part(x, &c);
    2419        3493 :   bound = ZXQX_resultant_bound(nf, x, RgX_deriv(x));
    2420        3493 :   D = ZXQX_disc_all(x, T, bound);
    2421        3493 :   if (c) D = gmul(D, gpowgs(c, 2*d - 2));
    2422        3493 :   return gerepileupto(av, D);
    2423             : }
    2424             : 
    2425             : GEN
    2426      835589 : QXQ_mul(GEN x, GEN y, GEN T)
    2427             : {
    2428      835589 :   GEN dx, nx = Q_primitive_part(x, &dx);
    2429      835589 :   GEN dy, ny = Q_primitive_part(y, &dy);
    2430      835586 :   GEN z = ZXQ_mul(nx, ny, T);
    2431      835589 :   if (dx || dy)
    2432             :   {
    2433      832789 :     GEN d = dx ? dy ? gmul(dx, dy): dx : dy;
    2434      832789 :     if (!gequal1(d)) z = ZX_Q_mul(z, d);
    2435             :   }
    2436      835589 :   return z;
    2437             : }
    2438             : 
    2439             : GEN
    2440      399431 : QXQ_sqr(GEN x, GEN T)
    2441             : {
    2442      399431 :   GEN dx, nx = Q_primitive_part(x, &dx);
    2443      399431 :   GEN z = ZXQ_sqr(nx, T);
    2444      399431 :   if (dx)
    2445      397695 :     z = ZX_Q_mul(z, gsqr(dx));
    2446      399431 :   return z;
    2447             : }
    2448             : 
    2449             : static GEN
    2450      212266 : QXQ_inv_slice(GEN A, GEN B, GEN P, GEN *mod)
    2451             : {
    2452      212266 :   pari_sp av = avma;
    2453      212266 :   long i, n = lg(P)-1, v = varn(A), redo = 0;
    2454             :   GEN H, T;
    2455      212266 :   if (n == 1)
    2456             :   {
    2457      165276 :     ulong p = uel(P,1);
    2458      165276 :     GEN a = ZX_to_Flx(A, p), b = ZX_to_Flx(B, p);
    2459      165276 :     GEN U = Flxq_invsafe(a, b, p);
    2460      165276 :     if (!U)
    2461             :     {
    2462          24 :       set_avma(av);
    2463          24 :       *mod = gen_1; return pol_0(v);
    2464             :     }
    2465      165252 :     H = gerepilecopy(av, Flx_to_ZX(U));
    2466      165252 :     *mod = utoipos(p); return H;
    2467             :   }
    2468       46990 :   T = ZV_producttree(P);
    2469       46990 :   A = ZX_nv_mod_tree(A, P, T);
    2470       46989 :   B = ZX_nv_mod_tree(B, P, T);
    2471       46989 :   H = cgetg(n+1, t_VEC);
    2472      237688 :   for(i=1; i <= n; i++)
    2473             :   {
    2474      190698 :     ulong p = P[i];
    2475      190698 :     GEN a = gel(A,i), b = gel(B,i);
    2476      190698 :     GEN U = Flxq_invsafe(a, b, p);
    2477      190699 :     if (!U)
    2478             :     {
    2479         601 :       gel(H,i) = pol_0(v);
    2480         601 :       P[i] = 1; redo = 1;
    2481             :     }
    2482             :     else
    2483      190098 :       gel(H,i) = U;
    2484             :   }
    2485       46990 :   if (redo) T = ZV_producttree(P);
    2486       46990 :   H = nxV_chinese_center_tree(H, P, T, ZV_chinesetree(P, T));
    2487       46990 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2488             : }
    2489             : 
    2490             : GEN
    2491      212266 : QXQ_inv_worker(GEN P, GEN A, GEN B)
    2492             : {
    2493      212266 :   GEN V = cgetg(3, t_VEC);
    2494      212266 :   gel(V,1) = QXQ_inv_slice(A, B, P, &gel(V,2));
    2495      212266 :   return V;
    2496             : }
    2497             : 
    2498             : /* lift(1 / Mod(A,B)). B a ZX, A a scalar or a QX */
    2499             : GEN
    2500      145674 : QXQ_inv(GEN A, GEN B)
    2501             : {
    2502             :   GEN D, Ap, Bp;
    2503             :   ulong pp;
    2504      145674 :   pari_sp av2, av = avma;
    2505             :   forprime_t S;
    2506      145674 :   GEN worker, U, H = NULL, mod = gen_1;
    2507             :   pari_timer ti;
    2508             :   long k, dA, dB;
    2509      145674 :   if (is_scalar_t(typ(A))) return scalarpol(ginv(A), varn(B));
    2510             :   /* A a QX, B a ZX */
    2511      145674 :   A = Q_primitive_part(A, &D);
    2512      145674 :   dA = degpol(A); dB= degpol(B);
    2513             :   /* A, B in Z[X] */
    2514      145674 :   init_modular_small(&S);
    2515             :   do {
    2516      145674 :     pp = u_forprime_next(&S);
    2517      145674 :     Ap = ZX_to_Flx(A, pp);
    2518      145674 :     Bp = ZX_to_Flx(B, pp);
    2519      145674 :   } while (degpol(Ap) != dA || degpol(Bp) != dB);
    2520      145674 :   if (degpol(Flx_gcd(Ap, Bp, pp)) != 0 && degpol(ZX_gcd(A,B))!=0)
    2521          14 :     pari_err_INV("QXQ_inv",mkpolmod(A,B));
    2522      145660 :   worker = snm_closure(is_entry("_QXQ_inv_worker"), mkvec2(A, B));
    2523      145660 :   av2 = avma;
    2524      145660 :   for (k = 1; ;k *= 2)
    2525       42412 :   {
    2526             :     GEN res, b, N, den;
    2527      188072 :     gen_inccrt_i("QXQ_inv", worker, NULL, (k+1)>>1, 0, &S, &H, &mod,
    2528             :                  nxV_chinese_center, FpX_center);
    2529      188071 :     gerepileall(av2, 2, &H, &mod);
    2530      188072 :     b = sqrti(shifti(mod,-1));
    2531      188072 :     if (DEBUGLEVEL>5) timer_start(&ti);
    2532      188072 :     U = FpX_ratlift(H, mod, b, b, NULL);
    2533      188072 :     if (DEBUGLEVEL>5) timer_printf(&ti,"QXQ_inv: ratlift");
    2534      193767 :     if (!U) continue;
    2535      151355 :     N = Q_remove_denom(U, &den); if (!den) den = gen_1;
    2536      151355 :     res = Flx_rem(Flx_Fl_sub(Flx_mul(Ap, ZX_to_Flx(N,pp), pp),
    2537             :                   umodiu(den, pp), pp), Bp, pp);
    2538      151355 :     if (degpol(res) >= 0) continue;
    2539      145660 :     res = ZX_Z_sub(ZX_mul(A, N), den);
    2540      145660 :     res = ZX_is_monic(B) ? ZX_rem(res, B): RgX_pseudorem(res, B);
    2541      145660 :     if (DEBUGLEVEL>5) timer_printf(&ti,"QXQ_inv: final check");
    2542      145660 :     if (degpol(res)<0)
    2543             :     {
    2544      145660 :       if (D) U = RgX_Rg_div(U, D);
    2545      145660 :       return gerepilecopy(av, U);
    2546             :     }
    2547             :   }
    2548             : }
    2549             : 
    2550             : static GEN
    2551      120238 : QXQ_div_slice(GEN A, GEN B, GEN C, GEN P, GEN *mod)
    2552             : {
    2553      120238 :   pari_sp av = avma;
    2554      120238 :   long i, n = lg(P)-1, v = varn(A), redo = 0;
    2555             :   GEN H, T;
    2556      120238 :   if (n == 1)
    2557             :   {
    2558       43886 :     ulong p = uel(P,1);
    2559       43886 :     GEN a = ZX_to_Flx(A, p), b = ZX_to_Flx(B, p), c = ZX_to_Flx(C, p);
    2560       43886 :     GEN bi = Flxq_invsafe(b, c, p), U;
    2561       43886 :     if (!bi)
    2562             :     {
    2563           0 :       set_avma(av);
    2564           0 :       *mod = gen_1; return pol_0(v);
    2565             :     }
    2566       43886 :     U = Flxq_mul(a, bi, c, p);
    2567       43886 :     H = gerepilecopy(av, Flx_to_ZX(U));
    2568       43886 :     *mod = utoipos(p); return H;
    2569             :   }
    2570       76352 :   T = ZV_producttree(P);
    2571       76352 :   A = ZX_nv_mod_tree(A, P, T);
    2572       76351 :   B = ZX_nv_mod_tree(B, P, T);
    2573       76351 :   C = ZX_nv_mod_tree(C, P, T);
    2574       76352 :   H = cgetg(n+1, t_VEC);
    2575      337290 :   for(i=1; i <= n; i++)
    2576             :   {
    2577      260938 :     ulong p = P[i];
    2578      260938 :     GEN a = gel(A,i), b = gel(B,i), c = gel(C, i);
    2579      260938 :     GEN bi = Flxq_invsafe(b, c, p);
    2580      260942 :     if (!bi)
    2581             :     {
    2582           4 :       gel(H,i) = pol_0(v);
    2583           4 :       P[i] = 1; redo = 1;
    2584             :     }
    2585             :     else
    2586      260938 :       gel(H,i) = Flxq_mul(a, bi, c, p);
    2587             :   }
    2588       76352 :   if (redo) T = ZV_producttree(P);
    2589       76352 :   H = nxV_chinese_center_tree(H, P, T, ZV_chinesetree(P, T));
    2590       76352 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2591             : }
    2592             : 
    2593             : GEN
    2594      120238 : QXQ_div_worker(GEN P, GEN A, GEN B, GEN C)
    2595             : {
    2596      120238 :   GEN V = cgetg(3, t_VEC);
    2597      120238 :   gel(V,1) = QXQ_div_slice(A, B, C, P, &gel(V,2));
    2598      120238 :   return V;
    2599             : }
    2600             : 
    2601             : /* lift(Mod(A/B, C)). C a ZX, A, B a scalar or a QX */
    2602             : GEN
    2603       32521 : QXQ_div(GEN A, GEN B, GEN C)
    2604             : {
    2605             :   GEN DA, DB, Ap, Bp, Cp;
    2606             :   ulong pp;
    2607       32521 :   pari_sp av2, av = avma;
    2608             :   forprime_t S;
    2609       32521 :   GEN worker, U, H = NULL, mod = gen_1;
    2610             :   pari_timer ti;
    2611             :   long k, dA, dB, dC;
    2612       32521 :   if (is_scalar_t(typ(A))) return scalarpol(ginv(A), varn(B));
    2613             :   /* A a QX, B a ZX */
    2614       32521 :   A = Q_primitive_part(A, &DA);
    2615       32521 :   B = Q_primitive_part(B, &DB);
    2616       32521 :   dA = degpol(A); dB = degpol(B); dC = degpol(C);
    2617             :   /* A, B in Z[X] */
    2618       32521 :   init_modular_small(&S);
    2619             :   do {
    2620       32521 :     pp = u_forprime_next(&S);
    2621       32521 :     Ap = ZX_to_Flx(A, pp);
    2622       32521 :     Bp = ZX_to_Flx(B, pp);
    2623       32521 :     Cp = ZX_to_Flx(C, pp);
    2624       32521 :   } while (degpol(Ap) != dA || degpol(Bp) != dB || degpol(Cp) != dC);
    2625       32521 :   if (degpol(Flx_gcd(Bp, Cp, pp)) != 0 && degpol(ZX_gcd(B,C))!=0)
    2626           0 :     pari_err_INV("QXQ_div",mkpolmod(B,C));
    2627       32521 :   worker = snm_closure(is_entry("_QXQ_div_worker"), mkvec3(A, B, C));
    2628       32521 :   av2 = avma;
    2629       32521 :   for (k = 1; ;k *= 2)
    2630       46540 :   {
    2631             :     GEN res, b, N, den;
    2632       79061 :     gen_inccrt_i("QXQ_div", worker, NULL, (k+1)>>1, 0, &S, &H, &mod,
    2633             :                  nxV_chinese_center, FpX_center);
    2634       79061 :     gerepileall(av2, 2, &H, &mod);
    2635       79061 :     b = sqrti(shifti(mod,-1));
    2636       79061 :     if (DEBUGLEVEL>5) timer_start(&ti);
    2637       79061 :     U = FpX_ratlift(H, mod, b, b, NULL);
    2638       79061 :     if (DEBUGLEVEL>5) timer_printf(&ti,"QXQ_div: ratlift");
    2639       89676 :     if (!U) continue;
    2640       43136 :     N = Q_remove_denom(U, &den); if (!den) den = gen_1;
    2641       43136 :     res = Flx_rem(Flx_sub(Flx_mul(Bp, ZX_to_Flx(N,pp), pp),
    2642             :                           Flx_Fl_mul(Ap, umodiu(den, pp), pp), pp), Cp, pp);
    2643       43136 :     if (degpol(res) >= 0) continue;
    2644       32521 :     res = ZX_sub(ZX_mul(B, N), ZX_Z_mul(A,den));
    2645       32521 :     res = ZX_is_monic(C) ? ZX_rem(res, C): RgX_pseudorem(res, C);
    2646       32521 :     if (DEBUGLEVEL>5) timer_printf(&ti,"QXQ_div: final check");
    2647       32521 :     if (degpol(res)<0)
    2648             :     {
    2649       32521 :       if (DA && DB) U = RgX_Rg_mul(U, gdiv(DA,DB));
    2650       27635 :       else if (DA) U = RgX_Rg_mul(U, DA);
    2651       15596 :       else if (DB) U = RgX_Rg_div(U, DB);
    2652       32521 :       return gerepilecopy(av, U);
    2653             :     }
    2654             :   }
    2655             : }
    2656             : 
    2657             : /************************************************************************
    2658             :  *                                                                      *
    2659             :  *                           ZXQ_minpoly                                *
    2660             :  *                                                                      *
    2661             :  ************************************************************************/
    2662             : 
    2663             : static GEN
    2664        3523 : ZXQ_minpoly_slice(GEN A, GEN B, long d, GEN P, GEN *mod)
    2665             : {
    2666        3523 :   pari_sp av = avma;
    2667        3523 :   long i, n = lg(P)-1, v = evalvarn(varn(B));
    2668             :   GEN H, T;
    2669        3523 :   if (n == 1)
    2670             :   {
    2671         716 :     ulong p = uel(P,1);
    2672         716 :     GEN a = ZX_to_Flx(A, p), b = ZX_to_Flx(B, p);
    2673         716 :     GEN Hp = Flxq_minpoly(a, b, p);
    2674         716 :     if (degpol(Hp) != d) { p = 1; Hp = pol0_Flx(v); }
    2675         716 :     H = gerepileupto(av, Flx_to_ZX(Hp));
    2676         716 :     *mod = utoipos(p); return H;
    2677             :   }
    2678        2807 :   T = ZV_producttree(P);
    2679        2807 :   A = ZX_nv_mod_tree(A, P, T);
    2680        2807 :   B = ZX_nv_mod_tree(B, P, T);
    2681        2807 :   H = cgetg(n+1, t_VEC);
    2682       16838 :   for(i=1; i <= n; i++)
    2683             :   {
    2684       14031 :     ulong p = P[i];
    2685       14031 :     GEN a = gel(A,i), b = gel(B,i);
    2686       14031 :     GEN m = Flxq_minpoly(a, b, p);
    2687       14031 :     if (degpol(m) != d) { P[i] = 1; m = pol0_Flx(v); }
    2688       14031 :     gel(H, i) = m;
    2689             :   }
    2690        2807 :   H = nxV_chinese_center_tree(H, P, T, ZV_chinesetree(P, T));
    2691        2807 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2692             : }
    2693             : 
    2694             : GEN
    2695        3523 : ZXQ_minpoly_worker(GEN P, GEN A, GEN B, long d)
    2696             : {
    2697        3523 :   GEN V = cgetg(3, t_VEC);
    2698        3523 :   gel(V,1) = ZXQ_minpoly_slice(A, B, d, P, &gel(V,2));
    2699        3523 :   return V;
    2700             : }
    2701             : 
    2702             : GEN
    2703        1701 : ZXQ_minpoly(GEN A, GEN B, long d, ulong bound)
    2704             : {
    2705        1701 :   pari_sp av = avma;
    2706             :   GEN worker, H, dB;
    2707             :   forprime_t S;
    2708        1701 :   B = Q_remove_denom(B, &dB);
    2709        1701 :   worker = strtoclosure("_ZXQ_minpoly_worker", 3, A, B, stoi(d));
    2710        1701 :   init_modular_big(&S);
    2711        1701 :   H = gen_crt("ZXQ_minpoly", worker, &S, dB, bound, 0, NULL,
    2712             :                nxV_chinese_center, FpX_center_i);
    2713        1701 :   return gerepilecopy(av, H);
    2714             : }
    2715             : 
    2716             : /************************************************************************
    2717             :  *                                                                      *
    2718             :  *                   ZX_ZXY_resultant                                   *
    2719             :  *                                                                      *
    2720             :  ************************************************************************/
    2721             : 
    2722             : static GEN
    2723      364699 : ZX_ZXY_resultant_prime(GEN a, GEN b, ulong dp, ulong p,
    2724             :                        long degA, long degB, long dres, long sX)
    2725             : {
    2726      364699 :   long dropa = degA - degpol(a), dropb = degB - degpol(b);
    2727      364698 :   ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    2728      364697 :   GEN Hp = Flx_FlxY_resultant_polint(a, b, p, pi, dres, sX);
    2729      364703 :   if (dropa && dropb)
    2730           0 :     Hp = zero_Flx(sX);
    2731             :   else {
    2732      364703 :     if (dropa)
    2733             :     { /* multiply by ((-1)^deg B lc(B))^(deg A - deg a) */
    2734           0 :       GEN c = gel(b,degB+2); /* lc(B) */
    2735           0 :       if (odd(degB)) c = Flx_neg(c, p);
    2736           0 :       if (!Flx_equal1(c)) {
    2737           0 :         c = Flx_powu_pre(c, dropa, p, pi);
    2738           0 :         if (!Flx_equal1(c)) Hp = Flx_mul_pre(Hp, c, p, pi);
    2739             :       }
    2740             :     }
    2741      364703 :     else if (dropb)
    2742             :     { /* multiply by lc(A)^(deg B - deg b) */
    2743           0 :       ulong c = uel(a, degA+2); /* lc(A) */
    2744           0 :       c = Fl_powu(c, dropb, p);
    2745           0 :       if (c != 1) Hp = Flx_Fl_mul_pre(Hp, c, p, pi);
    2746             :     }
    2747             :   }
    2748      364703 :   if (dp != 1) Hp = Flx_Fl_mul_pre(Hp, Fl_powu_pre(Fl_inv(dp,p), degA, p, pi), p, pi);
    2749      364697 :   return Hp;
    2750             : }
    2751             : 
    2752             : static GEN
    2753      124910 : ZX_ZXY_resultant_slice(GEN A, GEN B, GEN dB, long degA, long degB, long dres,
    2754             :                        GEN P, GEN *mod, long sX, long vY)
    2755             : {
    2756      124910 :   pari_sp av = avma;
    2757      124910 :   long i, n = lg(P)-1;
    2758             :   GEN H, T, D;
    2759      124910 :   if (n == 1)
    2760             :   {
    2761       40200 :     ulong p = uel(P,1);
    2762       40200 :     ulong dp = dB ? umodiu(dB, p): 1;
    2763       40200 :     GEN a = ZX_to_Flx(A, p), b = ZXX_to_FlxX(B, p, vY);
    2764       40200 :     GEN Hp = ZX_ZXY_resultant_prime(a, b, dp, p, degA, degB, dres, sX);
    2765       40198 :     H = gerepileupto(av, Flx_to_ZX(Hp));
    2766       40199 :     *mod = utoipos(p); return H;
    2767             :   }
    2768       84710 :   T = ZV_producttree(P);
    2769       84709 :   A = ZX_nv_mod_tree(A, P, T);
    2770       84710 :   B = ZXX_nv_mod_tree(B, P, T, vY);
    2771       84710 :   D = dB ? Z_ZV_mod_tree(dB, P, T): NULL;
    2772       84709 :   H = cgetg(n+1, t_VEC);
    2773      363859 :   for(i=1; i <= n; i++)
    2774             :   {
    2775      279149 :     ulong p = P[i];
    2776      279149 :     GEN a = gel(A,i), b = gel(B,i);
    2777      279149 :     ulong dp = D ? uel(D, i): 1;
    2778      279149 :     gel(H,i) = ZX_ZXY_resultant_prime(a, b, dp, p, degA, degB, dres, sX);
    2779             :   }
    2780       84710 :   H = nxV_chinese_center_tree(H, P, T, ZV_chinesetree(P, T));
    2781       84710 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2782             : }
    2783             : 
    2784             : GEN
    2785      124910 : ZX_ZXY_resultant_worker(GEN P, GEN A, GEN B, GEN dB, GEN v)
    2786             : {
    2787      124910 :   GEN V = cgetg(3, t_VEC);
    2788      124910 :   if (isintzero(dB)) dB = NULL;
    2789      124910 :   gel(V,1) = ZX_ZXY_resultant_slice(A, B, dB, v[1], v[2], v[3], P, &gel(V,2), v[4], v[5]);
    2790      124908 :   return V;
    2791             : }
    2792             : 
    2793             : GEN
    2794       79169 : ZX_ZXY_resultant(GEN A, GEN B)
    2795             : {
    2796       79169 :   pari_sp av = avma;
    2797             :   forprime_t S;
    2798             :   ulong bound;
    2799       79169 :   long v = fetch_var_higher();
    2800       79169 :   long degA = degpol(A), degB, dres = degA * degpol(B);
    2801       79169 :   long vX = varn(B), vY = varn(A); /* assume vY has lower priority */
    2802       79169 :   long sX = evalvarn(vX);
    2803             :   GEN worker, H, dB;
    2804       79169 :   B = Q_remove_denom(B, &dB);
    2805       79169 :   if (!dB) B = leafcopy(B);
    2806       79169 :   A = leafcopy(A); setvarn(A,v);
    2807       79169 :   B = swap_vars(B, vY, v); degB = degpol(B);
    2808       79169 :   bound = ZX_ZXY_ResBound(A, B, dB);
    2809       79169 :   if (DEBUGLEVEL>4) err_printf("bound for resultant coeffs: 2^%ld\n",bound);
    2810      158338 :   worker = snm_closure(is_entry("_ZX_ZXY_resultant_worker"),
    2811       79169 :                        mkvec4(A, B, dB? dB: gen_0,
    2812             :                               mkvecsmall5(degA, degB, dres, sX, vY)));
    2813       79169 :   init_modular_big(&S);
    2814       79169 :   H = gen_crt("ZX_ZXY_resultant_all", worker, &S, dB, bound, 0, NULL,
    2815             :                nxV_chinese_center, FpX_center_i);
    2816       79169 :   setvarn(H, vX); (void)delete_var();
    2817       79169 :   return gerepilecopy(av, H);
    2818             : }
    2819             : 
    2820             : static long
    2821       40535 : ZX_ZXY_rnfequation_lambda(GEN A, GEN B0, long lambda)
    2822             : {
    2823       40535 :   pari_sp av = avma;
    2824       40535 :   long degA = degpol(A), degB, dres = degA*degpol(B0);
    2825       40535 :   long v = fetch_var_higher();
    2826       40535 :   long vX = varn(B0), vY = varn(A); /* assume vY has lower priority */
    2827       40535 :   long sX = evalvarn(vX);
    2828             :   GEN dB, B, a, b, Hp;
    2829             :   forprime_t S;
    2830             : 
    2831       40535 :   B0 = Q_remove_denom(B0, &dB);
    2832       40536 :   if (!dB) B0 = leafcopy(B0);
    2833       40536 :   A = leafcopy(A);
    2834       40537 :   B = B0;
    2835       40537 :   setvarn(A,v);
    2836       45350 : INIT:
    2837       45350 :   if (lambda) B = RgX_translate(B0, monomial(stoi(lambda), 1, vY));
    2838       45350 :   B = swap_vars(B, vY, v);
    2839             :   /* B0(lambda v + x, v) */
    2840       45349 :   if (DEBUGLEVEL>4) err_printf("Trying lambda = %ld\n", lambda);
    2841             : 
    2842       45349 :   degB = degpol(B);
    2843       45349 :   init_modular_big(&S);
    2844             :   while (1)
    2845           0 :   {
    2846       45349 :     ulong p = u_forprime_next(&S);
    2847       45349 :     ulong dp = dB ? umodiu(dB, p): 1;
    2848       45349 :     if (!dp) continue;
    2849       45349 :     a = ZX_to_Flx(A, p);
    2850       45350 :     b = ZXX_to_FlxX(B, p, v);
    2851       45350 :     Hp = ZX_ZXY_resultant_prime(a, b, dp, p, degA, degB, dres, sX);
    2852       45350 :     if (degpol(Hp) != dres) continue;
    2853       45350 :     if (dp != 1) Hp = Flx_Fl_mul(Hp, Fl_powu(Fl_inv(dp,p), degA, p), p);
    2854       45350 :     if (!Flx_is_squarefree(Hp, p)) { lambda = next_lambda(lambda); goto INIT; }
    2855       40537 :     if (DEBUGLEVEL>4) err_printf("Final lambda = %ld\n", lambda);
    2856       40537 :     (void)delete_var(); return gc_long(av,lambda);
    2857             :   }
    2858             : }
    2859             : 
    2860             : GEN
    2861       60533 : ZX_ZXY_rnfequation(GEN A, GEN B, long *lambda)
    2862             : {
    2863       60533 :   if (lambda)
    2864             :   {
    2865       40535 :     *lambda = ZX_ZXY_rnfequation_lambda(A, B, *lambda);
    2866       40537 :     if (*lambda) B = RgX_translate(B, monomial(stoi(*lambda), 1, varn(A)));
    2867             :   }
    2868       60535 :   return ZX_ZXY_resultant(A,B);
    2869             : }
    2870             : 
    2871             : static GEN
    2872       10347 : ZX_composedsum_slice(GEN A, GEN B, GEN P, GEN *mod)
    2873             : {
    2874       10347 :   pari_sp av = avma;
    2875       10347 :   long i, n = lg(P)-1;
    2876             :   GEN H, T;
    2877       10347 :   if (n == 1)
    2878             :   {
    2879        9845 :     ulong p = uel(P,1);
    2880        9845 :     GEN a = ZX_to_Flx(A, p), b = ZX_to_Flx(B, p);
    2881        9846 :     GEN Hp = Flx_composedsum(a, b, p);
    2882        9845 :     H = gerepileupto(av, Flx_to_ZX(Hp));
    2883        9849 :     *mod = utoipos(p); return H;
    2884             :   }
    2885         502 :   T = ZV_producttree(P);
    2886         502 :   A = ZX_nv_mod_tree(A, P, T);
    2887         502 :   B = ZX_nv_mod_tree(B, P, T);
    2888         502 :   H = cgetg(n+1, t_VEC);
    2889        4526 :   for(i=1; i <= n; i++)
    2890             :   {
    2891        4024 :     ulong p = P[i];
    2892        4024 :     GEN a = gel(A,i), b = gel(B,i);
    2893        4024 :     gel(H,i) = Flx_composedsum(a, b, p);
    2894             :   }
    2895         502 :   H = nxV_chinese_center_tree(H, P, T, ZV_chinesetree(P, T));
    2896         502 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2897             : }
    2898             : 
    2899             : GEN
    2900       10347 : ZX_composedsum_worker(GEN P, GEN A, GEN B)
    2901             : {
    2902       10347 :   GEN V = cgetg(3, t_VEC);
    2903       10347 :   gel(V,1) = ZX_composedsum_slice(A, B, P, &gel(V,2));
    2904       10351 :   return V;
    2905             : }
    2906             : 
    2907             : static GEN
    2908       10083 : ZX_composedsum_i(GEN A, GEN B, GEN lead)
    2909             : {
    2910       10083 :   pari_sp av = avma;
    2911             :   forprime_t S;
    2912             :   ulong bound;
    2913             :   GEN H, worker, mod;
    2914       10083 :   if (degpol(A) < degpol(B)) swap(A, B);
    2915       10083 :   if (!lead) lead  = mulii(leading_coeff(A),leading_coeff(B));
    2916       10083 :   bound = ZX_ZXY_ResBound_1(A, B);
    2917       10085 :   worker = snm_closure(is_entry("_ZX_composedsum_worker"), mkvec2(A,B));
    2918       10087 :   init_modular_big(&S);
    2919       10087 :   H = gen_crt("ZX_composedsum", worker, &S, lead, bound, 0, &mod,
    2920             :               nxV_chinese_center, FpX_center);
    2921       10087 :   return gerepileupto(av, H);
    2922             : }
    2923             : 
    2924             : static long
    2925        9699 : ZX_compositum_lambda(GEN A, GEN B, GEN lead, long lambda)
    2926             : {
    2927        9699 :   pari_sp av = avma;
    2928             :   forprime_t S;
    2929             :   ulong p;
    2930        9699 :   init_modular_big(&S);
    2931        9701 :   p = u_forprime_next(&S);
    2932             :   while (1)
    2933         112 :   {
    2934             :     GEN Hp, a;
    2935        9813 :     if (DEBUGLEVEL>4) err_printf("Trying lambda = %ld\n", lambda);
    2936        9813 :     if (lead && dvdiu(lead,p)) { p = u_forprime_next(&S); continue; }
    2937        9806 :     a = ZX_to_Flx(ZX_rescale(A, stoi(-lambda)), p);
    2938        9803 :     Hp = Flx_composedsum(a, ZX_to_Flx(B, p), p);
    2939        9801 :     if (!Flx_is_squarefree(Hp, p)) { lambda = next_lambda(lambda); continue; }
    2940        9692 :     if (DEBUGLEVEL>4) err_printf("Final lambda = %ld\n", lambda);
    2941        9692 :     return gc_long(av, lambda);
    2942             :   }
    2943             : }
    2944             : 
    2945             : GEN
    2946        9700 : ZX_compositum(GEN A, GEN B, long *lambda)
    2947             : {
    2948        9700 :   GEN lead  = mulii(leading_coeff(A),leading_coeff(B));
    2949        9699 :   if (lambda)
    2950             :   {
    2951        9699 :     *lambda = ZX_compositum_lambda(A, B, lead, *lambda);
    2952        9692 :     A = ZX_rescale(A, stoi(-*lambda));
    2953             :   }
    2954        9698 :   return ZX_composedsum_i(A, B, lead);
    2955             : }
    2956             : 
    2957             : GEN
    2958         385 : ZX_composedsum(GEN A, GEN B)
    2959         385 : { return ZX_composedsum_i(A, B, NULL); }
    2960             : 
    2961             : static GEN
    2962         359 : ZXQX_composedsum_slice(GEN A, GEN B, GEN C, GEN P, GEN *mod)
    2963             : {
    2964         359 :   pari_sp av = avma;
    2965         359 :   long i, n = lg(P)-1, dC = degpol(C), v = varn(C);
    2966             :   GEN H, T;
    2967         359 :   if (n == 1)
    2968             :   {
    2969         181 :     ulong p = uel(P,1);
    2970         181 :     GEN a = ZXX_to_FlxX(A, p, v), b = ZXX_to_FlxX(B, p, v);
    2971         181 :     GEN c = ZX_to_Flx(C, p);
    2972         181 :     GEN Hp = FlxX_to_Flm(FlxqX_composedsum(a, b, c, p), dC);
    2973         181 :     H = gerepileupto(av, Flm_to_ZM(Hp));
    2974         181 :     *mod = utoipos(p); return H;
    2975             :   }
    2976         178 :   T = ZV_producttree(P);
    2977         178 :   A = ZXX_nv_mod_tree(A, P, T, v);
    2978         178 :   B = ZXX_nv_mod_tree(B, P, T, v);
    2979         178 :   C = ZX_nv_mod_tree(C, P, T);
    2980         178 :   H = cgetg(n+1, t_VEC);
    2981         660 :   for(i=1; i <= n; i++)
    2982             :   {
    2983         482 :     ulong p = P[i];
    2984         482 :     GEN a = gel(A,i), b = gel(B,i), c = gel(C,i);
    2985         482 :     gel(H,i) = FlxX_to_Flm(FlxqX_composedsum(a, b, c, p), dC);
    2986             :   }
    2987         178 :   H = nmV_chinese_center_tree_seq(H, P, T, ZV_chinesetree(P, T));
    2988         178 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2989             : }
    2990             : 
    2991             : GEN
    2992         359 : ZXQX_composedsum_worker(GEN P, GEN A, GEN B, GEN C)
    2993             : {
    2994         359 :   GEN V = cgetg(3, t_VEC);
    2995         359 :   gel(V,1) = ZXQX_composedsum_slice(A, B, C, P, &gel(V,2));
    2996         359 :   return V;
    2997             : }
    2998             : 
    2999             : static GEN
    3000         315 : ZXQX_composedsum(GEN A, GEN B, GEN T, ulong bound)
    3001             : {
    3002         315 :   pari_sp av = avma;
    3003             :   forprime_t S;
    3004             :   GEN H, worker, mod;
    3005         315 :   GEN lead = mulii(Q_content(leading_coeff(A)), Q_content(leading_coeff(B)));
    3006         315 :   worker = snm_closure(is_entry("_ZXQX_composedsum_worker")
    3007             :                       , mkvec3(A,B,T));
    3008         315 :   init_modular_big(&S);
    3009         315 :   H = gen_crt("ZXQX_composedsum", worker, &S, lead, bound, 0, &mod,
    3010             :               nmV_chinese_center, FpM_center);
    3011         315 :   if (DEBUGLEVEL > 4)
    3012           0 :     err_printf("nfcompositum: a priori bound: %lu, a posteriori: %lu\n",
    3013             :                bound, expi(gsupnorm(H, DEFAULTPREC)));
    3014         315 :   return gerepilecopy(av, RgM_to_RgXX(H, varn(A), varn(T)));
    3015             : }
    3016             : 
    3017             : static long
    3018         315 : ZXQX_composedsum_bound(GEN nf, GEN A, GEN B)
    3019         315 : { return ZXQX_resultant_bound_i(nf, A, B, &RgX_RgXY_ResBound_1); }
    3020             : 
    3021             : GEN
    3022         315 : nf_direct_compositum(GEN nf, GEN A, GEN B)
    3023             : {
    3024         315 :   ulong bnd = ZXQX_composedsum_bound(nf, A, B);
    3025         315 :   return ZXQX_composedsum(A, B, nf_get_pol(nf), bnd);
    3026             : }
    3027             : 
    3028             : /************************************************************************
    3029             :  *                                                                      *
    3030             :  *                   IRREDUCIBLE POLYNOMIAL / Fp                        *
    3031             :  *                                                                      *
    3032             :  ************************************************************************/
    3033             : 
    3034             : /* irreducible (unitary) polynomial of degree n over Fp */
    3035             : GEN
    3036           0 : ffinit_rand(GEN p,long n)
    3037             : {
    3038           0 :   for(;;) {
    3039           0 :     pari_sp av = avma;
    3040           0 :     GEN pol = ZX_add(pol_xn(n, 0), random_FpX(n-1,0, p));
    3041           0 :     if (FpX_is_irred(pol, p)) return pol;
    3042           0 :     set_avma(av);
    3043             :   }
    3044             : }
    3045             : 
    3046             : /* return an extension of degree 2^l of F_2, assume l > 0
    3047             :  * Not stack clean. */
    3048             : static GEN
    3049         608 : ffinit_Artin_Schreier_2(long l)
    3050             : {
    3051             :   GEN Q, T, S;
    3052             :   long i, v;
    3053             : 
    3054         608 :   if (l == 1) return mkvecsmall4(0,1,1,1); /*x^2 + x + 1*/
    3055         559 :   v = fetch_var_higher();
    3056         559 :   S = mkvecsmall5(0, 0, 0, 1, 1); /* y(y^2 + y) */
    3057         559 :   Q = mkpoln(3, pol1_Flx(0), pol1_Flx(0), S); /* x^2 + x + y(y^2+y) */
    3058         560 :   setvarn(Q, v);
    3059             : 
    3060             :   /* x^4+x+1, irred over F_2, minimal polynomial of a root of Q */
    3061         560 :   T = mkvecsmalln(6,evalvarn(v),1UL,1UL,0UL,0UL,1UL);
    3062             :   /* Q = x^2 + x + a(y) irred. over K = F2[y] / (T(y))
    3063             :    * ==> x^2 + x + a(y) b irred. over K for any root b of Q
    3064             :    * ==> x^2 + x + (b^2+b)b */
    3065        3098 :   for (i=2; i<l; i++) T = Flx_FlxY_resultant(T, Q, 2); /* minpoly(b) / F2*/
    3066         561 :   (void)delete_var(); T[1] = 0; return T;
    3067             : }
    3068             : 
    3069             : /* return an extension of degree p^l of F_p, assume l > 0
    3070             :  * Not stack clean. */
    3071             : GEN
    3072         965 : ffinit_Artin_Schreier(ulong p, long l)
    3073             : {
    3074             :   long i, v;
    3075             :   GEN Q, R, S, T, xp;
    3076         965 :   if (p==2) return ffinit_Artin_Schreier_2(l);
    3077         357 :   xp = polxn_Flx(p,0); /* x^p */
    3078         357 :   T = Flx_sub(xp, mkvecsmall3(0,1,1),p); /* x^p - x - 1 */
    3079         357 :   if (l == 1) return T;
    3080             : 
    3081           7 :   v = evalvarn(fetch_var_higher());
    3082           7 :   xp[1] = v;
    3083           7 :   R = Flx_sub(polxn_Flx(2*p-1,0), polxn_Flx(p,0),p);
    3084           7 :   S = Flx_sub(xp, polx_Flx(0), p);
    3085           7 :   Q = FlxX_Flx_sub(Flx_to_FlxX(S, v), R, p); /* x^p - x - (y^(2p-1)-y^p) */
    3086          14 :   for (i = 2; i <= l; ++i) T = Flx_FlxY_resultant(T, Q, p);
    3087           7 :   (void)delete_var(); T[1] = 0; return T;
    3088             : }
    3089             : 
    3090             : static long
    3091      148788 : flinit_check(ulong p, long n, long l)
    3092             : {
    3093             :   ulong q;
    3094      148788 :   if (!uisprime(n)) return 0;
    3095      102027 :   q = p % n; if (!q) return 0;
    3096       99486 :   return ugcd((n-1)/Fl_order(q, n-1, n), l) == 1;
    3097             : }
    3098             : 
    3099             : static GEN
    3100       31776 : flinit(ulong p, long l)
    3101             : {
    3102       31776 :   ulong n = 1+l;
    3103       95935 :   while (!flinit_check(p,n,l)) n += l;
    3104       31776 :   if (DEBUGLEVEL>=4) err_printf("FFInit: using polsubcyclo(%ld, %ld)\n",n,l);
    3105       31776 :   return ZX_to_Flx(polsubcyclo(n,l,0), p);
    3106             : }
    3107             : 
    3108             : static GEN
    3109       28915 : ffinit_fact_Flx(ulong p, long n)
    3110             : {
    3111       28915 :   GEN P, F = factoru_pow(n), Fp = gel(F,1), Fe = gel(F,2), Fm = gel(F,3);
    3112       28915 :   long i, l = lg(Fm);
    3113       28915 :   P = cgetg(l, t_VEC);
    3114       61658 :   for (i = 1; i < l; i++)
    3115       32741 :     gel(P,i) = p==uel(Fp,i) ? ffinit_Artin_Schreier(p, Fe[i])
    3116       32741 :                             : flinit(p, uel(Fm,i));
    3117       28917 :   return FlxV_composedsum(P, p);
    3118             : }
    3119             : 
    3120             : static GEN
    3121       52860 : init_Flxq_i(ulong p, long n, long sv)
    3122             : {
    3123             :   GEN P;
    3124       52860 :   if (!odd(p) && p != 2) pari_err_PRIME("ffinit", utoi(p));
    3125       52853 :   if (n == 1) return polx_Flx(sv);
    3126       52853 :   if (flinit_check(p, n+1, n))
    3127             :   {
    3128       23938 :     P = const_vecsmall(n+2,1);
    3129       23938 :     P[1] = sv; return P;
    3130             :   }
    3131       28915 :   P = ffinit_fact_Flx(p,n);
    3132       28917 :   P[1] = sv; return P;
    3133             : }
    3134             : 
    3135             : GEN
    3136           0 : init_Flxq(ulong p, long n, long v)
    3137             : {
    3138           0 :   pari_sp av = avma;
    3139           0 :   return gerepileupto(av, init_Flxq_i(p, n, v));
    3140             : }
    3141             : 
    3142             : /* check if polsubcyclo(n,l,0) is irreducible modulo p */
    3143             : static long
    3144        7199 : fpinit_check(GEN p, long n, long l)
    3145             : {
    3146             :   ulong q;
    3147        7199 :   if (!uisprime(n)) return 0;
    3148        4450 :   q = umodiu(p,n); if (!q) return 0;
    3149        4450 :   return ugcd((n-1)/Fl_order(q, n-1, n), l) == 1;
    3150             : }
    3151             : 
    3152             : /* let k=2 if p%4==1, and k=4 else and assume k*p does not divide l.
    3153             :  * Return an irreducible polynomial of degree l over F_p.
    3154             :  * Variant of Adleman and Lenstra "Finding irreducible polynomials over
    3155             :  * finite fields", ACM, 1986 (5) 350--355.
    3156             :  * Not stack clean */
    3157             : static GEN
    3158        1660 : fpinit(GEN p, long l)
    3159             : {
    3160        1660 :   ulong n = 1+l;
    3161        5216 :   while (!fpinit_check(p,n,l)) n += l;
    3162        1660 :   if (DEBUGLEVEL>=4) err_printf("FFInit: using polsubcyclo(%ld, %ld)\n",n,l);
    3163        1660 :   return FpX_red(polsubcyclo(n,l,0),p);
    3164             : }
    3165             : 
    3166             : static GEN
    3167        1581 : ffinit_fact(GEN p, long n)
    3168             : {
    3169        1581 :   GEN P, F = factoru_pow(n), Fp = gel(F,1), Fe = gel(F,2), Fm = gel(F,3);
    3170        1581 :   long i, l = lg(Fm);
    3171        1581 :   P = cgetg(l, t_VEC);
    3172        3241 :   for (i = 1; i < l; ++i)
    3173        3320 :     gel(P,i) = absequaliu(p, Fp[i]) ?
    3174           0 :                  Flx_to_ZX(ffinit_Artin_Schreier(Fp[i], Fe[i]))
    3175        1660 :                : fpinit(p, Fm[i]);
    3176        1581 :   return FpXV_composedsum(P, p);
    3177             : }
    3178             : 
    3179             : static GEN
    3180       55109 : init_Fq_i(GEN p, long n, long v)
    3181             : {
    3182             :   GEN P;
    3183       55109 :   if (n <= 0) pari_err_DOMAIN("ffinit", "degree", "<=", gen_0, stoi(n));
    3184       55109 :   if (typ(p) != t_INT) pari_err_TYPE("ffinit",p);
    3185       55109 :   if (cmpiu(p, 2) < 0) pari_err_PRIME("ffinit",p);
    3186       55102 :   if (v < 0) v = 0;
    3187       55102 :   if (n == 1) return pol_x(v);
    3188       54850 :   if (lgefint(p) == 3)
    3189       52860 :     return Flx_to_ZX(init_Flxq_i(p[2], n, evalvarn(v)));
    3190        1990 :   if (!mpodd(p)) pari_err_PRIME("ffinit", p);
    3191        1983 :   if (fpinit_check(p, n+1, n)) return polcyclo(n+1, v);
    3192        1581 :   P = ffinit_fact(p,n);
    3193        1581 :   setvarn(P, v); return P;
    3194             : }
    3195             : GEN
    3196       54542 : init_Fq(GEN p, long n, long v)
    3197             : {
    3198       54542 :   pari_sp av = avma;
    3199       54542 :   return gerepileupto(av, init_Fq_i(p, n, v));
    3200             : }
    3201             : GEN
    3202         567 : ffinit(GEN p, long n, long v)
    3203             : {
    3204         567 :   pari_sp av = avma;
    3205         567 :   return gerepileupto(av, FpX_to_mod(init_Fq_i(p, n, v), p));
    3206             : }
    3207             : 
    3208             : GEN
    3209        3178 : ffnbirred(GEN p, long n)
    3210             : {
    3211        3178 :   pari_sp av = avma;
    3212        3178 :   GEN s = powiu(p,n), F = factoru(n), D = divisorsu_moebius(gel(F, 1));
    3213        3178 :   long j, l = lg(D);
    3214        6797 :   for (j = 2; j < l; j++) /* skip d = 1 */
    3215             :   {
    3216        3619 :     long md = D[j]; /* mu(d) * d, d squarefree */
    3217        3619 :     GEN pd = powiu(p, n / labs(md)); /* p^{n/d} */
    3218        3619 :     s = md > 0? addii(s, pd): subii(s,pd);
    3219             :   }
    3220        3178 :   return gerepileuptoint(av, diviuexact(s, n));
    3221             : }
    3222             : 
    3223             : GEN
    3224         616 : ffsumnbirred(GEN p, long n)
    3225             : {
    3226         616 :   pari_sp av = avma, av2;
    3227         616 :   GEN q, t = p, v = vecfactoru_i(1, n);
    3228             :   long i;
    3229         616 :   q = cgetg(n+1,t_VEC); gel(q,1) = p;
    3230        1764 :   for (i=2; i<=n; i++) gel(q,i) = mulii(gel(q,i-1), p);
    3231         616 :   av2 = avma;
    3232        1764 :   for (i=2; i<=n; i++)
    3233             :   {
    3234        1148 :     GEN s = gel(q,i), F = gel(v,i), D = divisorsu_moebius(gel(F,1));
    3235        1148 :     long j, l = lg(D);
    3236        2534 :     for (j = 2; j < l; j++) /* skip 1 */
    3237             :     {
    3238        1386 :       long md = D[j];
    3239        1386 :       GEN pd = gel(q, i / labs(md)); /* p^{i/d} */
    3240        1386 :       s = md > 0? addii(s, pd): subii(s, pd);
    3241             :     }
    3242        1148 :     t = gerepileuptoint(av2, addii(t, diviuexact(s, i)));
    3243             :   }
    3244         616 :   return gerepileuptoint(av, t);
    3245             : }
    3246             : 
    3247             : GEN
    3248         140 : ffnbirred0(GEN p, long n, long flag)
    3249             : {
    3250         140 :   if (typ(p) != t_INT) pari_err_TYPE("ffnbirred", p);
    3251         140 :   if (n <= 0) pari_err_DOMAIN("ffnbirred", "degree", "<=", gen_0, stoi(n));
    3252         140 :   switch(flag)
    3253             :   {
    3254          70 :     case 0: return ffnbirred(p, n);
    3255          70 :     case 1: return ffsumnbirred(p, n);
    3256             :   }
    3257           0 :   pari_err_FLAG("ffnbirred");
    3258             :   return NULL; /* LCOV_EXCL_LINE */
    3259             : }
    3260             : 
    3261             : static void
    3262        2261 : checkmap(GEN m, const char *s)
    3263             : {
    3264        2261 :   if (typ(m)!=t_VEC || lg(m)!=3 || typ(gel(m,1))!=t_FFELT)
    3265           0 :     pari_err_TYPE(s,m);
    3266        2261 : }
    3267             : 
    3268             : GEN
    3269         189 : ffembed(GEN a, GEN b)
    3270             : {
    3271         189 :   pari_sp av = avma;
    3272         189 :   GEN p, Ta, Tb, g, r = NULL;
    3273         189 :   if (typ(a)!=t_FFELT) pari_err_TYPE("ffembed",a);
    3274         189 :   if (typ(b)!=t_FFELT) pari_err_TYPE("ffembed",b);
    3275         189 :   p = FF_p_i(a); g = FF_gen(a);
    3276         189 :   if (!equalii(p, FF_p_i(b))) pari_err_MODULUS("ffembed",a,b);
    3277         189 :   Ta = FF_mod(a);
    3278         189 :   Tb = FF_mod(b);
    3279         189 :   if (degpol(Tb)%degpol(Ta)!=0)
    3280           7 :     pari_err_DOMAIN("ffembed",GENtostr_raw(a),"is not a subfield of",b,a);
    3281         182 :   r = gel(FFX_roots(Ta, b), 1);
    3282         182 :   return gerepilecopy(av, mkvec2(g,r));
    3283             : }
    3284             : 
    3285             : GEN
    3286          91 : ffextend(GEN a, GEN P, long v)
    3287             : {
    3288          91 :   pari_sp av = avma;
    3289             :   long n;
    3290             :   GEN p, T, R, g, m;
    3291          91 :   if (typ(a)!=t_FFELT) pari_err_TYPE("ffextend",a);
    3292          91 :   T = a; p = FF_p_i(a);
    3293          91 :   if (typ(P)!=t_POL || !RgX_is_FpXQX(P,&T,&p)) pari_err_TYPE("ffextend", P);
    3294          49 :   if (!FF_samefield(a, T)) pari_err_MODULUS("ffextend",a,T);
    3295          49 :   if (v < 0) v = varn(P);
    3296          49 :   n = FF_f(T) * degpol(P); R = ffinit(p, n, v); g = ffgen(R, v);
    3297          49 :   m = ffembed(a, g);
    3298          49 :   R = FFX_roots(ffmap(m, P),g);
    3299          49 :   return gerepilecopy(av, mkvec2(gel(R,1), m));
    3300             : }
    3301             : 
    3302             : GEN
    3303          42 : fffrobenius(GEN a, long n)
    3304             : {
    3305          42 :   if (typ(a)!=t_FFELT) pari_err_TYPE("fffrobenius",a);
    3306          42 :   retmkvec2(FF_gen(a), FF_Frobenius(a, n));
    3307             : }
    3308             : 
    3309             : GEN
    3310         133 : ffinvmap(GEN m)
    3311             : {
    3312         133 :   pari_sp av = avma;
    3313             :   long i, l;
    3314         133 :   GEN T, F, a, g, r, f = NULL;
    3315         133 :   checkmap(m, "ffinvmap");
    3316         133 :   a = gel(m,1); r = gel(m,2);
    3317         133 :   if (typ(r) != t_FFELT)
    3318           7 :    pari_err_TYPE("ffinvmap", m);
    3319         126 :   g = FF_gen(a);
    3320         126 :   T = FF_mod(r);
    3321         126 :   F = gel(FFX_factor(T, a), 1);
    3322         126 :   l = lg(F);
    3323         490 :   for(i=1; i<l; i++)
    3324             :   {
    3325         490 :     GEN s = FFX_rem(FF_to_FpXQ_i(r), gel(F, i), a);
    3326         490 :     if (degpol(s)==0 && gequal(constant_coeff(s),g)) { f = gel(F, i); break; }
    3327             :   }
    3328         126 :   if (f==NULL) pari_err_TYPE("ffinvmap", m);
    3329         126 :   if (degpol(f)==1) f = FF_neg_i(gel(f,2));
    3330         126 :   return gerepilecopy(av, mkvec2(FF_gen(r),f));
    3331             : }
    3332             : 
    3333             : static GEN
    3334        1260 : ffpartmapimage(const char *s, GEN r)
    3335             : {
    3336        1260 :    GEN a = NULL, p = NULL;
    3337        1260 :    if (typ(r)==t_POL && degpol(r) >= 1
    3338        1260 :       && RgX_is_FpXQX(r,&a,&p) && a && typ(a)==t_FFELT) return a;
    3339           0 :    pari_err_TYPE(s, r);
    3340             :    return NULL; /* LCOV_EXCL_LINE */
    3341             : }
    3342             : 
    3343             : static GEN
    3344        2709 : ffeltmap_i(GEN m, GEN x)
    3345             : {
    3346        2709 :    GEN r = gel(m,2);
    3347        2709 :    if (!FF_samefield(x, gel(m,1)))
    3348          84 :      pari_err_DOMAIN("ffmap","m","domain does not contain", x, r);
    3349        2625 :    if (typ(r)==t_FFELT)
    3350        1659 :      return FF_map(r, x);
    3351             :    else
    3352         966 :      return FFX_preimage(x, r, ffpartmapimage("ffmap", r));
    3353             : }
    3354             : 
    3355             : static GEN
    3356        4459 : ffmap_i(GEN m, GEN x)
    3357             : {
    3358             :   GEN y;
    3359        4459 :   long i, lx, tx = typ(x);
    3360        4459 :   switch(tx)
    3361             :   {
    3362        2541 :     case t_FFELT:
    3363        2541 :       return ffeltmap_i(m, x);
    3364        1267 :     case t_POL: case t_RFRAC: case t_SER:
    3365             :     case t_VEC: case t_COL: case t_MAT:
    3366        1267 :       y = cgetg_copy(x, &lx);
    3367        1988 :       for (i=1; i<lontyp[tx]; i++) y[i] = x[1];
    3368        4564 :       for (i=lontyp[tx]; i<lx; i++)
    3369             :       {
    3370        3339 :         GEN yi = ffmap_i(m, gel(x,i));
    3371        3297 :         if (!yi) return NULL;
    3372        3297 :         gel(y,i) = yi;
    3373             :       }
    3374        1225 :       return y;
    3375             :   }
    3376         651 :   return gcopy(x);
    3377             : }
    3378             : 
    3379             : GEN
    3380        1036 : ffmap(GEN m, GEN x)
    3381             : {
    3382        1036 :   pari_sp ltop = avma;
    3383             :   GEN y;
    3384        1036 :   checkmap(m, "ffmap");
    3385        1036 :   y = ffmap_i(m, x);
    3386        1036 :   if (y) return y;
    3387          42 :   set_avma(ltop); return cgetg(1,t_VEC);
    3388             : }
    3389             : 
    3390             : static GEN
    3391         252 : ffeltmaprel_i(GEN m, GEN x)
    3392             : {
    3393         252 :    GEN g = gel(m,1), r = gel(m,2);
    3394         252 :    if (!FF_samefield(x, g))
    3395           0 :      pari_err_DOMAIN("ffmap","m","domain does not contain", x, r);
    3396         252 :    if (typ(r)==t_FFELT)
    3397          84 :      retmkpolmod(FF_map(r, x), pol_x(FF_var(g)));
    3398             :    else
    3399         168 :      retmkpolmod(FFX_preimagerel(x, r, ffpartmapimage("ffmap", r)), gcopy(r));
    3400             : }
    3401             : 
    3402             : static GEN
    3403         252 : ffmaprel_i(GEN m, GEN x)
    3404             : {
    3405         252 :   switch(typ(x))
    3406             :   {
    3407         252 :     case t_FFELT:
    3408         252 :       return ffeltmaprel_i(m, x);
    3409           0 :     case t_POL: pari_APPLY_pol_normalized(ffmaprel_i(m, gel(x,i)));
    3410           0 :     case t_SER: pari_APPLY_ser_normalized(ffmaprel_i(m, gel(x,i)));
    3411           0 :     case t_RFRAC: case t_VEC: case t_COL: case t_MAT:
    3412           0 :       pari_APPLY_same(ffmaprel_i(m, gel(x,i)));
    3413             :   }
    3414           0 :   return gcopy(x);
    3415             : }
    3416             : GEN
    3417         252 : ffmaprel(GEN m, GEN x) { checkmap(m, "ffmaprel"); return ffmaprel_i(m, x); }
    3418             : 
    3419             : static void
    3420          84 : err_compo(GEN m, GEN n)
    3421          84 : { pari_err_DOMAIN("ffcompomap","m","domain does not contain codomain of",n,m); }
    3422             : 
    3423             : GEN
    3424         420 : ffcompomap(GEN m, GEN n)
    3425             : {
    3426         420 :   pari_sp av = avma;
    3427         420 :   GEN g = gel(n,1), r, m2, n2;
    3428         420 :   checkmap(m, "ffcompomap");
    3429         420 :   checkmap(n, "ffcompomap");
    3430         420 :   m2 = gel(m,2); n2 = gel(n,2);
    3431         420 :   switch((typ(m2)==t_POL)|((typ(n2)==t_POL)<<1))
    3432             :   {
    3433          84 :     case 0:
    3434          84 :       if (!FF_samefield(gel(m,1),n2)) err_compo(m,n);
    3435          42 :       r = FF_map(gel(m,2), n2);
    3436          42 :       break;
    3437          84 :     case 2:
    3438          84 :       r = ffmap_i(m, n2);
    3439          42 :       if (lg(r) == 1) err_compo(m,n);
    3440          42 :       break;
    3441         168 :     case 1:
    3442         168 :       r = ffeltmap_i(m, n2);
    3443         126 :       if (!r)
    3444             :       {
    3445             :         GEN a, A, R, M;
    3446             :         long dm, dn;
    3447          42 :         a = ffpartmapimage("ffcompomap",m2);
    3448          42 :         A = FF_to_FpXQ_i(FF_neg(n2));
    3449          42 :         setvarn(A, 1);
    3450          42 :         R = deg1pol(gen_1, A, 0);
    3451          42 :         setvarn(R, 0);
    3452          42 :         M = gcopy(m2);
    3453          42 :         setvarn(M, 1);
    3454          42 :         r = polresultant0(R, M, 1, 0);
    3455          42 :         dm = FF_f(gel(m,1)); dn = FF_f(gel(n,1));
    3456          42 :         if (dm % dn || !FFX_ispower(r, dm/dn, a, &r)) err_compo(m,n);
    3457          42 :         setvarn(r, varn(FF_mod(g)));
    3458             :       }
    3459         126 :       break;
    3460          84 :     case 3:
    3461             :     {
    3462             :       GEN M, R, T, p, a;
    3463          84 :       a = ffpartmapimage("ffcompomap",n2);
    3464          84 :       if (!FF_samefield(a, gel(m,1))) err_compo(m,n);
    3465          42 :       p = FF_p_i(gel(n,1));
    3466          42 :       T = FF_mod(gel(n,1));
    3467          42 :       setvarn(T, 1);
    3468          42 :       R = RgX_to_FpXQX(n2,T,p);
    3469          42 :       setvarn(R, 0);
    3470          42 :       M = gcopy(m2);
    3471          42 :       setvarn(M, 1);
    3472          42 :       r = polresultant0(R, M, 1, 0);
    3473          42 :       setvarn(r, varn(n2));
    3474             :     }
    3475             :   }
    3476         252 :   return gerepilecopy(av, mkvec2(g,r));
    3477             : }

Generated by: LCOV version 1.16