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 30387-12623f1693) Lines: 1878 2131 88.1 %
Date: 2025-07-11 09:22:46 Functions: 202 222 91.0 %
Legend: Lines: hit not hit

          Line data    Source code
       1             : /* Copyright (C) 2000-2005  The PARI group.
       2             : 
       3             : This file is part of the PARI/GP package.
       4             : 
       5             : PARI/GP is free software; you can redistribute it and/or modify it under the
       6             : terms of the GNU General Public License as published by the Free Software
       7             : Foundation; either version 2 of the License, or (at your option) any later
       8             : version. It is distributed in the hope that it will be useful, but WITHOUT
       9             : ANY WARRANTY WHATSOEVER.
      10             : 
      11             : Check the License for details. You should have received a copy of it, along
      12             : with the package; see the file 'COPYING'. If not, write to the Free Software
      13             : Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. */
      14             : 
      15             : /***********************************************************************/
      16             : /**                                                                   **/
      17             : /**               ARITHMETIC OPERATIONS ON POLYNOMIALS                **/
      18             : /**                         (third part)                              **/
      19             : /**                                                                   **/
      20             : /***********************************************************************/
      21             : #include "pari.h"
      22             : #include "paripriv.h"
      23             : 
      24             : #define DEBUGLEVEL DEBUGLEVEL_pol
      25             : 
      26             : /************************************************************************
      27             :  **                                                                    **
      28             :  **                      Ring membership                               **
      29             :  **                                                                    **
      30             :  ************************************************************************/
      31             : struct charact {
      32             :   GEN q;
      33             :   int isprime;
      34             : };
      35             : static void
      36        1225 : char_update_prime(struct charact *S, GEN p)
      37             : {
      38        1225 :   if (!S->isprime) { S->isprime = 1; S->q = p; }
      39        1225 :   if (!equalii(p, S->q)) pari_err_MODULUS("characteristic", S->q, p);
      40        1218 : }
      41             : static void
      42        6594 : char_update_int(struct charact *S, GEN n)
      43             : {
      44        6594 :   if (S->isprime)
      45             :   {
      46           7 :     if (dvdii(n, S->q)) return;
      47           7 :     pari_err_MODULUS("characteristic", S->q, n);
      48             :   }
      49        6587 :   S->q = gcdii(S->q, n);
      50             : }
      51             : static void
      52      176946 : charact(struct charact *S, GEN x)
      53             : {
      54      176946 :   const long tx = typ(x);
      55             :   long i, l;
      56      176946 :   switch(tx)
      57             :   {
      58        5145 :     case t_INTMOD:char_update_int(S, gel(x,1)); break;
      59        1134 :     case t_FFELT: char_update_prime(S, gel(x,4)); break;
      60       25711 :     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       25711 :       l = lg(x);
      64      175021 :       for (i=lontyp[tx]; i < l; i++) charact(S,gel(x,i));
      65       25697 :       break;
      66           7 :     case t_LIST:
      67           7 :       x = list_data(x);
      68           7 :       if (x) charact(S, x);
      69           7 :       break;
      70             :   }
      71      176918 : }
      72             : static void
      73        4739 : charact_res(struct charact *S, GEN x)
      74             : {
      75        4739 :   const long tx = typ(x);
      76             :   long i, l;
      77        4739 :   switch(tx)
      78             :   {
      79        1449 :     case t_INTMOD:char_update_int(S, gel(x,1)); break;
      80           0 :     case t_FFELT: char_update_prime(S, gel(x,4)); break;
      81          91 :     case t_PADIC: char_update_prime(S, padic_p(x)); break;
      82        1722 :     case t_COMPLEX: case t_QUAD:
      83             :     case t_POLMOD: case t_POL: case t_SER: case t_RFRAC:
      84             :     case t_VEC: case t_COL: case t_MAT:
      85        1722 :       l = lg(x);
      86        6132 :       for (i=lontyp[tx]; i < l; i++) charact_res(S,gel(x,i));
      87        1722 :       break;
      88           0 :     case t_LIST:
      89           0 :       x = list_data(x);
      90           0 :       if (x) charact_res(S, x);
      91           0 :       break;
      92             :   }
      93        4739 : }
      94             : GEN
      95       27622 : characteristic(GEN x)
      96             : {
      97             :   struct charact S;
      98       27622 :   S.q = gen_0; S.isprime = 0;
      99       27622 :   charact(&S, x); return S.q;
     100             : }
     101             : GEN
     102         329 : residual_characteristic(GEN x)
     103             : {
     104             :   struct charact S;
     105         329 :   S.q = gen_0; S.isprime = 0;
     106         329 :   charact_res(&S, x); return S.q;
     107             : }
     108             : 
     109             : int
     110    70272878 : Rg_is_Fp(GEN x, GEN *pp)
     111             : {
     112             :   GEN mod;
     113    70272878 :   switch(typ(x))
     114             :   {
     115     2482676 :   case t_INTMOD:
     116     2482676 :     mod = gel(x,1);
     117     2482676 :     if (!*pp) *pp = mod;
     118     2341976 :     else if (mod != *pp && !equalii(mod, *pp))
     119             :     {
     120           0 :       if (DEBUGLEVEL) pari_warn(warner,"different moduli in Rg_is_Fp");
     121           0 :       return 0;
     122             :     }
     123     2482676 :     return 1;
     124    56412031 :   case t_INT:
     125    56412031 :     return 1;
     126    11378171 :   default: return 0;
     127             :   }
     128             : }
     129             : 
     130             : int
     131    28008732 : RgX_is_FpX(GEN x, GEN *pp)
     132             : {
     133    28008732 :   long i, lx = lg(x);
     134    86877301 :   for (i=2; i<lx; i++)
     135    70246737 :     if (!Rg_is_Fp(gel(x, i), pp))
     136    11378172 :       return 0;
     137    16630564 :   return 1;
     138             : }
     139             : 
     140             : int
     141           0 : RgV_is_FpV(GEN x, GEN *pp)
     142             : {
     143           0 :   long i, lx = lg(x);
     144           0 :   for (i=1; i<lx; i++)
     145           0 :     if (!Rg_is_Fp(gel(x,i), pp)) return 0;
     146           0 :   return 1;
     147             : }
     148             : 
     149             : int
     150           0 : RgM_is_FpM(GEN x, GEN *pp)
     151             : {
     152           0 :   long i, lx = lg(x);
     153           0 :   for (i=1; i<lx; i++)
     154           0 :     if (!RgV_is_FpV(gel(x, i), pp)) return 0;
     155           0 :   return 1;
     156             : }
     157             : 
     158             : int
     159       60802 : Rg_is_FpXQ(GEN x, GEN *pT, GEN *pp)
     160             : {
     161             :   GEN pol, mod, p;
     162       60802 :   switch(typ(x))
     163             :   {
     164       26131 :   case t_INTMOD:
     165       26131 :     return Rg_is_Fp(x, pp);
     166        8561 :   case t_INT:
     167        8561 :     return 1;
     168          21 :   case t_POL:
     169          21 :     return RgX_is_FpX(x, pp);
     170       21350 :   case t_FFELT:
     171       21350 :     mod = x; p = FF_p_i(x);
     172       21350 :     if (!*pp) *pp = p;
     173       21350 :     if (!*pT) *pT = mod;
     174       19824 :     else if (typ(*pT)!=t_FFELT || !FF_samefield(*pT,mod))
     175             :     {
     176          42 :       if (DEBUGLEVEL) pari_warn(warner,"different moduli in Rg_is_FpXQ");
     177          42 :       return 0;
     178             :     }
     179       21308 :     return 1;
     180        4585 :   case t_POLMOD:
     181        4585 :     mod = gel(x,1); pol = gel(x, 2);
     182        4585 :     if (!RgX_is_FpX(mod, pp)) return 0;
     183        4585 :     if (typ(pol)==t_POL)
     184             :     {
     185        4578 :       if (!RgX_is_FpX(pol, pp)) return 0;
     186             :     }
     187           7 :     else if (!Rg_is_Fp(pol, pp)) return 0;
     188        4585 :     if (!*pT) *pT = mod;
     189        4431 :     else if (mod != *pT && !gequal(mod, *pT))
     190             :     {
     191           0 :       if (DEBUGLEVEL) pari_warn(warner,"different moduli in Rg_is_FpXQ");
     192           0 :       return 0;
     193             :     }
     194        4585 :     return 1;
     195             : 
     196         154 :   default: return 0;
     197             :   }
     198             : }
     199             : 
     200             : int
     201     2021554 : RgX_is_ZXX(GEN x, long *v)
     202             : {
     203             :   long i;
     204     8484666 :   for (i = lg(x)-1; i > 1; i--)
     205             :   {
     206     6463321 :     GEN xi = gel(x,i);
     207     6463321 :     long t = typ(xi), vi;
     208     6463321 :     if (t==t_INT) continue;
     209     1011939 :     if (t!=t_POL || !RgX_is_ZX(xi)) return 0;
     210     1011765 :     vi = varn(xi);
     211     1011765 :     if (*v < 0) *v = vi;
     212         994 :     else if (vi!=*v) return 0;
     213             :   }
     214     2021345 :   return 1;
     215             : }
     216             : 
     217             : int
     218        3381 : RgX_is_FpXQX(GEN x, GEN *pT, GEN *pp)
     219             : {
     220        3381 :   long i, lx = lg(x);
     221       63427 :   for (i = 2; i < lx; i++)
     222       60144 :     if (!Rg_is_FpXQ(gel(x,i), pT, pp)) return 0;
     223        3283 :   return 1;
     224             : }
     225             : 
     226             : /************************************************************************
     227             :  **                                                                    **
     228             :  **                      Ring conversion                               **
     229             :  **                                                                    **
     230             :  ************************************************************************/
     231             : 
     232             : /* p > 0 a t_INT, return lift(x * Mod(1,p)).
     233             :  * If x is an INTMOD, assume modulus is a multiple of p. */
     234             : GEN
     235    52334468 : Rg_to_Fp(GEN x, GEN p)
     236             : {
     237    52334468 :   if (lgefint(p) == 3) return utoi(Rg_to_Fl(x, uel(p,2)));
     238     4555528 :   switch(typ(x))
     239             :   {
     240      289105 :     case t_INT: return modii(x, p);
     241       18790 :     case t_FRAC: {
     242       18790 :       pari_sp av = avma;
     243       18790 :       GEN z = modii(gel(x,1), p);
     244       18790 :       if (z == gen_0) return gen_0;
     245       18785 :       return gc_INT(av, remii(mulii(z, Fp_inv(gel(x,2), p)), p));
     246             :     }
     247          70 :     case t_PADIC: return padic_to_Fp(x, p);
     248     4247567 :     case t_INTMOD: {
     249     4247567 :       GEN q = gel(x,1), a = gel(x,2);
     250     4247567 :       if (equalii(q, p)) return icopy(a);
     251          14 :       if (!dvdii(q,p)) pari_err_MODULUS("Rg_to_Fp", q, p);
     252           0 :       return remii(a, p);
     253             :     }
     254           0 :     default: pari_err_TYPE("Rg_to_Fp",x);
     255             :       return NULL; /* LCOV_EXCL_LINE */
     256             :   }
     257             : }
     258             : /* If x is a POLMOD, assume modulus is a multiple of T. */
     259             : GEN
     260     1291986 : Rg_to_FpXQ(GEN x, GEN T, GEN p)
     261             : {
     262     1291986 :   long ta, tx = typ(x), v = get_FpX_var(T);
     263             :   GEN a, b;
     264     1291986 :   if (is_const_t(tx))
     265             :   {
     266       59182 :     if (tx == t_FFELT)
     267             :     {
     268       17355 :       GEN z = FF_to_FpXQ(x);
     269       17355 :       setvarn(z, v);
     270       17355 :       return z;
     271             :     }
     272       41827 :     return scalar_ZX(degpol(T)? Rg_to_Fp(x, p): gen_0, v);
     273             :   }
     274     1232804 :   switch(tx)
     275             :   {
     276     1230697 :     case t_POLMOD:
     277     1230697 :       b = gel(x,1);
     278     1230697 :       a = gel(x,2); ta = typ(a);
     279     1230697 :       if (is_const_t(ta))
     280        3885 :         return scalar_ZX(degpol(T)? Rg_to_Fp(a, p): gen_0, v);
     281     1226812 :       b = RgX_to_FpX(b, p); if (varn(b) != v) break;
     282     1226812 :       a = RgX_to_FpX(a, p);
     283     1226812 :       if (ZX_equal(b,get_FpX_mod(T)) || signe(FpX_rem(b,T,p))==0)
     284     1226812 :         return FpX_rem(a, T, p);
     285           0 :       break;
     286        2107 :     case t_POL:
     287        2107 :       if (varn(x) != v) break;
     288        2100 :       return FpX_rem(RgX_to_FpX(x,p), T, p);
     289           0 :     case t_RFRAC:
     290           0 :       a = Rg_to_FpXQ(gel(x,1), T,p);
     291           0 :       b = Rg_to_FpXQ(gel(x,2), T,p);
     292           0 :       return FpXQ_div(a,b, T,p);
     293             :   }
     294           7 :   pari_err_TYPE("Rg_to_FpXQ",x);
     295             :   return NULL; /* LCOV_EXCL_LINE */
     296             : }
     297             : GEN
     298     3335720 : RgX_to_FpX(GEN x, GEN p)
     299             : {
     300             :   long i, l;
     301     3335720 :   GEN z = cgetg_copy(x, &l); z[1] = x[1];
     302    14765324 :   for (i = 2; i < l; i++) gel(z,i) = Rg_to_Fp(gel(x,i), p);
     303     3335720 :   return FpX_renormalize(z, l);
     304             : }
     305             : 
     306             : GEN
     307         140 : RgV_to_FpV(GEN x, GEN p)
     308         483 : { pari_APPLY_type(t_VEC, Rg_to_Fp(gel(x,i), p)) }
     309             : 
     310             : GEN
     311     1751090 : RgC_to_FpC(GEN x, GEN p)
     312    28499485 : { pari_APPLY_type(t_COL, Rg_to_Fp(gel(x,i), p)) }
     313             : 
     314             : GEN
     315      222349 : RgM_to_FpM(GEN x, GEN p)
     316     1973397 : { pari_APPLY_same(RgC_to_FpC(gel(x,i), p)) }
     317             : 
     318             : GEN
     319      369001 : RgV_to_Flv(GEN x, ulong p)
     320     1676894 : { pari_APPLY_ulong(Rg_to_Fl(gel(x,i), p)) }
     321             : 
     322             : GEN
     323      118296 : RgM_to_Flm(GEN x, ulong p)
     324      422998 : { pari_APPLY_same(RgV_to_Flv(gel(x,i), p)) }
     325             : 
     326             : GEN
     327        5105 : RgX_to_FpXQX(GEN x, GEN T, GEN p)
     328             : {
     329        5105 :   long i, l = lg(x);
     330        5105 :   GEN z = cgetg(l, t_POL); z[1] = x[1];
     331       43394 :   for (i = 2; i < l; i++) gel(z,i) = Rg_to_FpXQ(gel(x,i), T,p);
     332        5105 :   return FpXQX_renormalize(z, l);
     333             : }
     334             : GEN
     335       49186 : RgX_to_FqX(GEN x, GEN T, GEN p)
     336             : {
     337       49186 :   long i, l = lg(x);
     338       49186 :   GEN z = cgetg(l, t_POL); z[1] = x[1];
     339       49186 :   if (T)
     340       10990 :     for (i = 2; i < l; i++) gel(z,i) = Rg_to_FpXQ(gel(x,i), T, p);
     341             :   else
     342      791394 :     for (i = 2; i < l; i++) gel(z,i) = Rg_to_Fp(gel(x,i), p);
     343       49186 :   return FpXQX_renormalize(z, l);
     344             : }
     345             : 
     346             : GEN
     347      219128 : RgC_to_FqC(GEN x, GEN T, GEN p)
     348             : {
     349      219128 :   long i, l = lg(x);
     350      219128 :   GEN z = cgetg(l, t_COL);
     351      219128 :   if (T)
     352     1430310 :     for (i = 1; i < l; i++) gel(z,i) = Rg_to_FpXQ(gel(x,i), T, p);
     353             :   else
     354           0 :     for (i = 1; i < l; i++) gel(z,i) = Rg_to_Fp(gel(x,i), p);
     355      219128 :   return z;
     356             : }
     357             : 
     358             : GEN
     359       52325 : RgM_to_FqM(GEN x, GEN T, GEN p)
     360      271418 : { pari_APPLY_same(RgC_to_FqC(gel(x, i), T, p)) }
     361             : 
     362             : /* lg(V) > 1 */
     363             : GEN
     364      851487 : FpXV_FpC_mul(GEN V, GEN W, GEN p)
     365             : {
     366      851487 :   pari_sp av = avma;
     367      851487 :   long i, l = lg(V);
     368      851487 :   GEN z = ZX_Z_mul(gel(V,1),gel(W,1));
     369     4201029 :   for(i=2; i<l; i++)
     370             :   {
     371     3349542 :     z = ZX_add(z, ZX_Z_mul(gel(V,i),gel(W,i)));
     372     3349542 :     if ((i & 7) == 0) z = gc_upto(av, z);
     373             :   }
     374      851487 :   return gc_upto(av, FpX_red(z,p));
     375             : }
     376             : 
     377             : GEN
     378       55832 : FqX_Fq_add(GEN y, GEN x, GEN T, GEN p)
     379             : {
     380       55832 :   long i, lz = lg(y);
     381             :   GEN z;
     382       55832 :   if (!T) return FpX_Fp_add(y, x, p);
     383        8666 :   if (lz == 2) return scalarpol(x, varn(y));
     384        7952 :   z = cgetg(lz,t_POL); z[1] = y[1];
     385        7952 :   gel(z,2) = Fq_add(gel(y,2),x, T, p);
     386        7952 :   if (lz == 3) z = FpXX_renormalize(z,lz);
     387             :   else
     388       33145 :     for(i=3;i<lz;i++) gel(z,i) = gcopy(gel(y,i));
     389        7952 :   return z;
     390             : }
     391             : 
     392             : GEN
     393        1059 : FqX_Fq_sub(GEN y, GEN x, GEN T, GEN p)
     394             : {
     395        1059 :   long i, lz = lg(y);
     396             :   GEN z;
     397        1059 :   if (!T) return FpX_Fp_sub(y, x, p);
     398        1059 :   if (lz == 2) return scalarpol(x, varn(y));
     399        1059 :   z = cgetg(lz,t_POL); z[1] = y[1];
     400        1059 :   gel(z,2) = Fq_sub(gel(y,2), x, T, p);
     401        1059 :   if (lz == 3) z = FpXX_renormalize(z,lz);
     402             :   else
     403       10278 :     for(i=3;i<lz;i++) gel(z,i) = gcopy(gel(y,i));
     404        1059 :   return z;
     405             : }
     406             : 
     407             : GEN
     408      149052 : FqX_Fq_mul_to_monic(GEN P, GEN U, GEN T, GEN p)
     409             : {
     410             :   long i, lP;
     411      149052 :   GEN res = cgetg_copy(P, &lP); res[1] = P[1];
     412      918799 :   for(i=2; i<lP-1; i++) gel(res,i) = Fq_mul(U,gel(P,i), T,p);
     413      149052 :   gel(res,lP-1) = gen_1; return res;
     414             : }
     415             : 
     416             : GEN
     417       38189 : FpXQX_normalize(GEN z, GEN T, GEN p)
     418             : {
     419             :   GEN lc;
     420       38189 :   if (lg(z) == 2) return z;
     421       38175 :   lc = leading_coeff(z);
     422       38175 :   if (typ(lc) == t_POL)
     423             :   {
     424        2167 :     if (lg(lc) > 3) /* nonconstant */
     425        1902 :       return FqX_Fq_mul_to_monic(z, Fq_inv(lc,T,p), T,p);
     426             :     /* constant */
     427         265 :     lc = gel(lc,2);
     428         265 :     z = shallowcopy(z);
     429         265 :     gel(z, lg(z)-1) = lc;
     430             :   }
     431             :   /* lc a t_INT */
     432       36273 :   if (equali1(lc)) return z;
     433          87 :   return FqX_Fq_mul_to_monic(z, Fp_inv(lc,p), T,p);
     434             : }
     435             : 
     436             : GEN
     437      390935 : FqX_eval(GEN x, GEN y, GEN T, GEN p)
     438             : {
     439             :   pari_sp av;
     440             :   GEN p1, r;
     441      390935 :   long j, i=lg(x)-1;
     442      390935 :   if (i<=2)
     443       45107 :     return (i==2)? Fq_red(gel(x,2), T, p): gen_0;
     444      345828 :   av=avma; p1=gel(x,i);
     445             :   /* specific attention to sparse polynomials (see poleval)*/
     446             :   /*You've guessed it! It's a copy-paste(tm)*/
     447     1150441 :   for (i--; i>=2; i=j-1)
     448             :   {
     449      805300 :     for (j=i; !signe(gel(x,j)); j--)
     450         686 :       if (j==2)
     451             :       {
     452         490 :         if (i!=j) y = Fq_pow(y,utoipos(i-j+1), T, p);
     453         490 :         return gc_upto(av, Fq_mul(p1,y, T, p));
     454             :       }
     455      804614 :     r = (i==j)? y: Fq_pow(y, utoipos(i-j+1), T, p);
     456      804614 :     p1 = Fq_add(Fq_mul(p1,r,T,p), gel(x,j), T, p);
     457             :   }
     458      345337 :   return gc_upto(av, p1);
     459             : }
     460             : 
     461             : GEN
     462       97321 : FqXY_evalx(GEN Q, GEN x, GEN T, GEN p)
     463             : {
     464       97321 :   long i, lb = lg(Q);
     465             :   GEN z;
     466       97321 :   if (!T) return FpXY_evalx(Q, x, p);
     467       86961 :   z = cgetg(lb, t_POL); z[1] = Q[1];
     468      462945 :   for (i=2; i<lb; i++)
     469             :   {
     470      375984 :     GEN q = gel(Q,i);
     471      375984 :     gel(z,i) = typ(q) == t_INT? modii(q,p): FqX_eval(q, x, T, p);
     472             :   }
     473       86961 :   return FpXQX_renormalize(z, lb);
     474             : }
     475             : 
     476             : /* Q an FpXY, evaluate at (X,Y) = (x,y) */
     477             : GEN
     478       14623 : FqXY_eval(GEN Q, GEN y, GEN x, GEN T, GEN p)
     479             : {
     480       14623 :   pari_sp av = avma;
     481       14623 :   if (!T) return FpXY_eval(Q, y, x, p);
     482         966 :   return gc_upto(av, FqX_eval(FqXY_evalx(Q, x, T, p), y, T, p));
     483             : }
     484             : 
     485             : /* a X^d */
     486             : GEN
     487    13640799 : monomial(GEN a, long d, long v)
     488             : {
     489             :   long i, n;
     490             :   GEN P;
     491    13640799 :   if (d < 0) {
     492          14 :     if (isrationalzero(a)) return pol_0(v);
     493          14 :     retmkrfrac(a, pol_xn(-d, v));
     494             :   }
     495    13640785 :   if (gequal0(a))
     496             :   {
     497       93989 :     if (isexactzero(a)) return scalarpol_shallow(a,v);
     498           0 :     n = d+2; P = cgetg(n+1, t_POL);
     499           0 :     P[1] = evalsigne(0) | evalvarn(v);
     500             :   }
     501             :   else
     502             :   {
     503    13546793 :     n = d+2; P = cgetg(n+1, t_POL);
     504    13546794 :     P[1] = evalsigne(1) | evalvarn(v);
     505             :   }
     506    32923981 :   for (i = 2; i < n; i++) gel(P,i) = gen_0;
     507    13546794 :   gel(P,i) = a; return P;
     508             : }
     509             : GEN
     510      157969 : monomialcopy(GEN a, long d, long v)
     511             : {
     512             :   long i, n;
     513             :   GEN P;
     514      157969 :   if (d < 0) {
     515          14 :     if (isrationalzero(a)) return pol_0(v);
     516          14 :     retmkrfrac(gcopy(a), pol_xn(-d, v));
     517             :   }
     518      157955 :   if (gequal0(a))
     519             :   {
     520          14 :     if (isexactzero(a)) return scalarpol(a,v);
     521           7 :     n = d+2; P = cgetg(n+1, t_POL);
     522           7 :     P[1] = evalsigne(0) | evalvarn(v);
     523             :   }
     524             :   else
     525             :   {
     526      157941 :     n = d+2; P = cgetg(n+1, t_POL);
     527      157941 :     P[1] = evalsigne(1) | evalvarn(v);
     528             :   }
     529      314678 :   for (i = 2; i < n; i++) gel(P,i) = gen_0;
     530      157948 :   gel(P,i) = gcopy(a); return P;
     531             : }
     532             : GEN
     533      325951 : pol_x_powers(long N, long v)
     534             : {
     535      325951 :   GEN L = cgetg(N+1,t_VEC);
     536             :   long i;
     537      789059 :   for (i=1; i<=N; i++) gel(L,i) = pol_xn(i-1, v);
     538      325954 :   return L;
     539             : }
     540             : 
     541             : GEN
     542           0 : FqXQ_powers(GEN x, long l, GEN S, GEN T, GEN p)
     543             : {
     544           0 :   return T ? FpXQXQ_powers(x, l, S, T, p): FpXQ_powers(x, l, S, p);
     545             : }
     546             : 
     547             : GEN
     548           0 : FqXQ_matrix_pow(GEN y, long n, long m, GEN S, GEN T, GEN p)
     549             : {
     550           0 :   return T ? FpXQXQ_matrix_pow(y, n, m, S, T, p): FpXQ_matrix_pow(y, n, m, S, p);
     551             : }
     552             : 
     553             : /*******************************************************************/
     554             : /*                                                                 */
     555             : /*                             Fq                                  */
     556             : /*                                                                 */
     557             : /*******************************************************************/
     558             : 
     559             : GEN
     560    11592890 : Fq_add(GEN x, GEN y, GEN T/*unused*/, GEN p)
     561             : {
     562             :   (void)T;
     563    11592890 :   switch((typ(x)==t_POL)|((typ(y)==t_POL)<<1))
     564             :   {
     565     1143687 :     case 0: return Fp_add(x,y,p);
     566      748136 :     case 1: return FpX_Fp_add(x,y,p);
     567       91991 :     case 2: return FpX_Fp_add(y,x,p);
     568     9609076 :     case 3: return FpX_add(x,y,p);
     569             :   }
     570             :   return NULL;/*LCOV_EXCL_LINE*/
     571             : }
     572             : 
     573             : GEN
     574     8563061 : Fq_sub(GEN x, GEN y, GEN T/*unused*/, GEN p)
     575             : {
     576             :   (void)T;
     577     8563061 :   switch((typ(x)==t_POL)|((typ(y)==t_POL)<<1))
     578             :   {
     579      256368 :     case 0: return Fp_sub(x,y,p);
     580       24540 :     case 1: return FpX_Fp_sub(x,y,p);
     581       23896 :     case 2: return Fp_FpX_sub(x,y,p);
     582     8258257 :     case 3: return FpX_sub(x,y,p);
     583             :   }
     584             :   return NULL;/*LCOV_EXCL_LINE*/
     585             : }
     586             : 
     587             : GEN
     588     1080513 : Fq_neg(GEN x, GEN T/*unused*/, GEN p)
     589             : {
     590             :   (void)T;
     591     1080513 :   return (typ(x)==t_POL)? FpX_neg(x,p): Fp_neg(x,p);
     592             : }
     593             : 
     594             : GEN
     595       81354 : Fq_halve(GEN x, GEN T/*unused*/, GEN p)
     596             : {
     597             :   (void)T;
     598       81354 :   return (typ(x)==t_POL)? FpX_halve(x,p): Fp_halve(x,p);
     599             : }
     600             : 
     601             : /* If T==NULL do not reduce*/
     602             : GEN
     603     8608661 : Fq_mul(GEN x, GEN y, GEN T, GEN p)
     604             : {
     605     8608661 :   switch((typ(x)==t_POL)|((typ(y)==t_POL)<<1))
     606             :   {
     607     1037917 :     case 0: return Fp_mul(x,y,p);
     608      128565 :     case 1: return FpX_Fp_mul(x,y,p);
     609      394686 :     case 2: return FpX_Fp_mul(y,x,p);
     610     7047497 :     case 3: if (T) return FpXQ_mul(x,y,T,p);
     611     4478770 :             else return FpX_mul(x,y,p);
     612             :   }
     613             :   return NULL;/*LCOV_EXCL_LINE*/
     614             : }
     615             : 
     616             : /* If T==NULL do not reduce*/
     617             : GEN
     618      490590 : Fq_mulu(GEN x, ulong y, /*unused*/GEN T, GEN p)
     619             : {
     620             :   (void) T;
     621      490590 :   return typ(x)==t_POL ? FpX_Fp_mul(x,utoi(y),p): Fp_mulu(x, y, p);
     622             : }
     623             : 
     624             : /* y t_INT */
     625             : GEN
     626       44041 : Fq_Fp_mul(GEN x, GEN y, GEN T/*unused*/, GEN p)
     627             : {
     628             :   (void)T;
     629        6822 :   return (typ(x) == t_POL)? FpX_Fp_mul(x,y,p)
     630       50863 :                           : Fp_mul(x,y,p);
     631             : }
     632             : /* If T==NULL do not reduce*/
     633             : GEN
     634      611418 : Fq_sqr(GEN x, GEN T, GEN p)
     635             : {
     636      611418 :   if (typ(x) == t_POL)
     637             :   {
     638       70585 :     if (T) return FpXQ_sqr(x,T,p);
     639           0 :     else return FpX_sqr(x,p);
     640             :   }
     641             :   else
     642      540833 :     return Fp_sqr(x,p);
     643             : }
     644             : 
     645             : GEN
     646           0 : Fq_neg_inv(GEN x, GEN T, GEN p)
     647             : {
     648           0 :   if (typ(x) == t_INT) return Fp_inv(Fp_neg(x,p),p);
     649           0 :   return FpXQ_inv(FpX_neg(x,p),T,p);
     650             : }
     651             : 
     652             : GEN
     653           0 : Fq_invsafe(GEN x, GEN pol, GEN p)
     654             : {
     655           0 :   if (typ(x) == t_INT) return Fp_invsafe(x,p);
     656           0 :   return FpXQ_invsafe(x,pol,p);
     657             : }
     658             : 
     659             : GEN
     660       89312 : Fq_inv(GEN x, GEN pol, GEN p)
     661             : {
     662       89312 :   if (typ(x) == t_INT) return Fp_inv(x,p);
     663       81546 :   return FpXQ_inv(x,pol,p);
     664             : }
     665             : 
     666             : GEN
     667      343791 : Fq_div(GEN x, GEN y, GEN pol, GEN p)
     668             : {
     669      343791 :   switch((typ(x)==t_POL)|((typ(y)==t_POL)<<1))
     670             :   {
     671      318402 :     case 0: return Fp_div(x,y,p);
     672       16702 :     case 1: return FpX_Fp_div(x,y,p);
     673         406 :     case 2: return FpX_Fp_mul(FpXQ_inv(y,pol,p),x,p);
     674        8281 :     case 3: return FpXQ_div(x,y,pol,p);
     675             :   }
     676             :   return NULL;/*LCOV_EXCL_LINE*/
     677             : }
     678             : 
     679             : GEN
     680     1088144 : Fq_pow(GEN x, GEN n, GEN pol, GEN p)
     681             : {
     682     1088144 :   if (typ(x) == t_INT) return Fp_pow(x,n,p);
     683      137457 :   return FpXQ_pow(x,n,pol,p);
     684             : }
     685             : 
     686             : GEN
     687       15050 : Fq_powu(GEN x, ulong n, GEN pol, GEN p)
     688             : {
     689       15050 :   if (typ(x) == t_INT) return Fp_powu(x,n,p);
     690        1267 :   return FpXQ_powu(x,n,pol,p);
     691             : }
     692             : 
     693             : GEN
     694     1892926 : Fq_sqrt(GEN x, GEN T, GEN p)
     695             : {
     696     1892926 :   if (typ(x) == t_INT)
     697             :   {
     698     1825064 :     if (!T || odd(get_FpX_degree(T))) return Fp_sqrt(x,p);
     699        9621 :     x = scalarpol_shallow(x, get_FpX_var(T));
     700             :   }
     701       77483 :   return FpXQ_sqrt(x,T,p);
     702             : }
     703             : GEN
     704      170786 : Fq_sqrtn(GEN x, GEN n, GEN T, GEN p, GEN *zeta)
     705             : {
     706      170786 :   if (typ(x) == t_INT)
     707             :   {
     708             :     long d;
     709      170415 :     if (!T) return Fp_sqrtn(x,n,p,zeta);
     710         126 :     d = get_FpX_degree(T);
     711         126 :     if (ugcdiu(n,d) == 1)
     712             :     {
     713          56 :       if (!zeta) return Fp_sqrtn(x,n,p,NULL);
     714             :       /* gcd(n,p-1)=gcd(n,q-1): same number of solutions in Fp and F_q */
     715          21 :       if (equalii(gcdii(subiu(p,1),n), gcdii(subiu(Fp_powu(p,d,n), 1), n)))
     716          14 :         return Fp_sqrtn(x,n,p,zeta);
     717             :     }
     718          77 :     x = scalarpol(x, get_FpX_var(T)); /* left on stack */
     719             :   }
     720         448 :   return FpXQ_sqrtn(x,n,T,p,zeta);
     721             : }
     722             : 
     723             : struct _Fq_field
     724             : {
     725             :   GEN T, p;
     726             : };
     727             : 
     728             : static GEN
     729      303247 : _Fq_red(void *E, GEN x)
     730      303247 : { struct _Fq_field *s = (struct _Fq_field *)E;
     731      303247 :   return Fq_red(x, s->T, s->p);
     732             : }
     733             : 
     734             : static GEN
     735      362523 : _Fq_add(void *E, GEN x, GEN y)
     736             : {
     737             :   (void) E;
     738      362523 :   switch((typ(x)==t_POL)|((typ(y)==t_POL)<<1))
     739             :   {
     740          14 :     case 0: return addii(x,y);
     741           0 :     case 1: return ZX_Z_add(x,y);
     742       15918 :     case 2: return ZX_Z_add(y,x);
     743      346591 :     default: return ZX_add(x,y);
     744             :   }
     745             : }
     746             : 
     747             : static GEN
     748      315028 : _Fq_neg(void *E, GEN x) { (void) E; return typ(x)==t_POL?ZX_neg(x):negi(x); }
     749             : 
     750             : static GEN
     751      243341 : _Fq_mul(void *E, GEN x, GEN y)
     752             : {
     753             :   (void) E;
     754      243341 :   switch((typ(x)==t_POL)|((typ(y)==t_POL)<<1))
     755             :   {
     756         679 :     case 0: return mulii(x,y);
     757        1085 :     case 1: return ZX_Z_mul(x,y);
     758        1043 :     case 2: return ZX_Z_mul(y,x);
     759      240534 :     default: return ZX_mul(x,y);
     760             :   }
     761             : }
     762             : 
     763             : static GEN
     764        9331 : _Fq_inv(void *E, GEN x)
     765        9331 : { struct _Fq_field *s = (struct _Fq_field *)E;
     766        9331 :   return Fq_inv(x,s->T,s->p);
     767             : }
     768             : 
     769             : static int
     770       38388 : _Fq_equal0(GEN x) { return signe(x)==0; }
     771             : 
     772             : static GEN
     773        4151 : _Fq_s(void *E, long x) { (void) E; return stoi(x); }
     774             : 
     775             : static const struct bb_field Fq_field={_Fq_red,_Fq_add,_Fq_mul,_Fq_neg,
     776             :                                        _Fq_inv,_Fq_equal0,_Fq_s};
     777             : 
     778        4725 : const struct bb_field *get_Fq_field(void **E, GEN T, GEN p)
     779             : {
     780        4725 :   if (!T)
     781           0 :     return get_Fp_field(E, p);
     782             :   else
     783             :   {
     784        4725 :     GEN z = new_chunk(sizeof(struct _Fq_field));
     785        4725 :     struct _Fq_field *e = (struct _Fq_field *) z;
     786        4725 :     e->T = T; e->p  = p; *E = (void*)e;
     787        4725 :     return &Fq_field;
     788             :   }
     789             : }
     790             : 
     791             : /*******************************************************************/
     792             : /*                                                                 */
     793             : /*                             Fq[X]                               */
     794             : /*                                                                 */
     795             : /*******************************************************************/
     796             : /* FpV_red(vecbinomial(n), p) */
     797             : static GEN
     798           0 : vecbinomial_Fp(long n, GEN p)
     799             : {
     800           0 :   GEN C = vecbinomial(n) + 1;
     801           0 :   long k, d = (n + 1) >> 1;
     802           0 :   for (k = d; k >= 1; k--)
     803             :   {
     804           0 :     GEN a = gel(C,k);
     805           0 :     if (cmpii(a, p) < 0) break;
     806           0 :     gel(C,k) = gel(C, n-k) = remii(a, p);
     807             :   }
     808           0 :   return C - 1;
     809             : }
     810             : /* (X+u)^n */
     811             : static GEN
     812         434 : Fp_XpN_powu(GEN u, ulong n, GEN p, long v)
     813             : {
     814             :   pari_sp av;
     815             :   ulong k;
     816             :   GEN B, C, V;
     817         434 :   if (!n) return pol_1(v);
     818         434 :   if (is_pm1(u))
     819         434 :     return Xpm1_powu(n, signe(u), v);
     820           0 :   av = avma;
     821           0 :   V = Fp_powers(u, n, p);
     822           0 :   B = vecbinomial_Fp(n, p);
     823           0 :   C = cgetg(n+3, t_POL);
     824           0 :   C[1] = evalsigne(1)| evalvarn(v);
     825           0 :   for (k=1; k <= n+1; k++)
     826           0 :     gel(C,k+1) = Fp_mul(gel(V,n+2-k), gel(B,k), p);
     827           0 :   return gc_upto(av, C);
     828             : }
     829             : 
     830             : static GEN
     831         700 : FpX_Fp_translate_basecase(GEN P, GEN c, GEN p)
     832             : {
     833         700 :   pari_sp av = avma;
     834             :   GEN Q;
     835             :   long i, k, n;
     836             : 
     837         700 :   if (!signe(P) || !signe(c)) return ZX_copy(P);
     838         560 :   Q = leafcopy(P); n = degpol(P);
     839        1316 :   for (i=1; i<=n; i++)
     840             :   {
     841        2016 :     for (k=n-i; k<n; k++)
     842        1260 :       gel(Q,2+k) = Fp_add(gel(Q,2+k), Fp_mul(c, gel(Q,2+k+1), p), p);
     843             : 
     844         756 :     if (gc_needed(av,2))
     845             :     {
     846           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"FpX_Fp_translate, i = %ld/%ld", i,n);
     847           0 :       Q = gc_GEN(av, Q);
     848             :     }
     849             :   }
     850         560 :   return gc_GEN(av, FpX_renormalize(Q, lg(Q)));
     851             : }
     852             : 
     853             : GEN
     854        1134 : FpX_Fp_translate(GEN P, GEN c, GEN p)
     855             : {
     856        1134 :   pari_sp av = avma;
     857        1134 :   long n = degpol(P);
     858        1134 :   if (n<=3 || 25*(n-3) < expi(p))
     859         700 :     return FpX_Fp_translate_basecase(P, c, p);
     860             :   else
     861             :   {
     862         434 :     long d = n >> 1;
     863         434 :     GEN Q = FpX_Fp_translate(RgX_shift_shallow(P, -d), c, p);
     864         434 :     GEN R = FpX_Fp_translate(RgXn_red_shallow(P, d), c, p);
     865         434 :     GEN S = Fp_XpN_powu(c, d, p, varn(P));
     866         434 :     return gc_upto(av, FpX_add(FpX_mul(Q, S, p), R, p));
     867             :   }
     868             : }
     869             : 
     870             : /* (X+u)^n mod (T,p) */
     871             : static GEN
     872           0 : FpXQX_XpN_powu(GEN u, ulong n, GEN T, GEN p, long v)
     873             : {
     874             :   pari_sp av;
     875             :   ulong k;
     876             :   GEN B, C, V;
     877           0 :   if (!n) return pol_1(v);
     878           0 :   av = avma;
     879           0 :   V = FpXQ_powers(u, n, T, p);
     880           0 :   B = vecbinomial_Fp(n, p);
     881           0 :   C = cgetg(n+3, t_POL);
     882           0 :   C[1] = evalsigne(1)| evalvarn(v);
     883           0 :   for (k=1; k <= n+1; k++)
     884           0 :     gel(C,k+1) = Fq_mul(gel(V,n+2-k), gel(B,k), T, p);
     885           0 :   return gc_upto(av, C);
     886             : }
     887             : 
     888             : static GEN
     889       33887 : FpXQX_FpXQ_translate_basecase(GEN P, GEN c, GEN T, GEN p)
     890             : {
     891       33887 :   pari_sp av = avma;
     892             :   GEN Q;
     893             :   long i, k, n;
     894             : 
     895             :   /* signe works for t_(INT|POL) */
     896       33887 :   if (!signe(P) || !signe(c)) return RgX_copy(P);
     897       33887 :   Q = leafcopy(P); n = degpol(P);
     898      150080 :   for (i=1; i<=n; i++)
     899             :   {
     900      433594 :     for (k=n-i; k<n; k++)
     901      317401 :       gel(Q,2+k) = Fq_add(gel(Q,2+k), Fq_mul(c, gel(Q,2+k+1), T, p), T, p);
     902             : 
     903      116193 :     if (gc_needed(av,2))
     904             :     {
     905           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"FqX_Fq_translate, i = %ld/%ld", i,n);
     906           0 :       Q = gc_GEN(av, Q);
     907             :     }
     908             :   }
     909       33887 :   return gc_GEN(av, FpXQX_renormalize(Q, lg(Q)));
     910             : }
     911             : 
     912             : GEN
     913       33887 : FpXQX_FpXQ_translate(GEN P, GEN c, GEN T, GEN p)
     914             : {
     915       33887 :   pari_sp av = avma;
     916       33887 :   long n = degpol(P);
     917       33887 :   if (n < 220)
     918       33887 :     return FpXQX_FpXQ_translate_basecase(P, c, T, p);
     919             :   else
     920             :   {
     921           0 :     long d = n >> 1;
     922           0 :     GEN Q = FpXQX_FpXQ_translate(RgX_shift_shallow(P, -d), c, T, p);
     923           0 :     GEN R = FpXQX_FpXQ_translate(RgXn_red_shallow(P, d), c, T, p);
     924           0 :     GEN S = FpXQX_XpN_powu(c, d, T, p, varn(P));
     925           0 :     return gc_upto(av, FpXX_add(FpXQX_mul(Q, S, T, p), R, p));
     926             :   }
     927             : }
     928             : 
     929             : GEN
     930       33880 : FqX_Fq_translate(GEN x, GEN y, GEN T, GEN p)
     931             : {
     932       33880 :   if (!T) return FpX_Fp_translate(x,y,p);
     933       33880 :   if (typ(y)==t_INT)
     934             :   {
     935           0 :     pari_sp av = avma;
     936           0 :     y = scalarpol_shallow(y,varn(T));
     937           0 :     return gc_upto(av, FpXQX_FpXQ_translate(x,y,T,p));
     938             :   }
     939       33880 :   return FpXQX_FpXQ_translate(x,y,T,p);
     940             : }
     941             : 
     942             : GEN
     943       40450 : FqV_roots_to_pol(GEN V, GEN T, GEN p, long v)
     944             : {
     945       40450 :   pari_sp ltop = avma;
     946             :   long k;
     947             :   GEN W;
     948       40450 :   if (lgefint(p) == 3)
     949             :   {
     950       31739 :     ulong pp = p[2];
     951       31739 :     GEN Tl = ZX_to_Flx(T, pp);
     952       31743 :     GEN Vl = FqC_to_FlxqC(V, Tl, pp);
     953       31745 :     Tl = FlxqV_roots_to_pol(Vl, Tl, pp, v);
     954       31744 :     return gc_upto(ltop, FlxX_to_ZXX(Tl));
     955             :   }
     956        8711 :   W = cgetg(lg(V),t_VEC);
     957       78117 :   for(k=1; k < lg(V); k++)
     958       69406 :     gel(W,k) = deg1pol_shallow(gen_1,Fq_neg(gel(V,k),T,p),v);
     959        8711 :   return gc_upto(ltop, FpXQXV_prod(W, T, p));
     960             : }
     961             : 
     962             : GEN
     963      109459 : FqV_red(GEN x, GEN T, GEN p)
     964      778034 : { pari_APPLY_type(t_VEC, Fq_red(gel(x,i), T, p)) }
     965             : 
     966             : GEN
     967       24058 : FqC_red(GEN x, GEN T, GEN p)
     968      163384 : { pari_APPLY_type(t_COL, Fq_red(gel(x,i), T, p)) }
     969             : 
     970             : GEN
     971        1701 : FqM_red(GEN x, GEN T, GEN p)
     972        5411 : { pari_APPLY_same(FqC_red(gel(x,i), T, p)) }
     973             : 
     974             : GEN
     975           0 : FqC_add(GEN x, GEN y, GEN T, GEN p)
     976             : {
     977           0 :   if (!T) return FpC_add(x, y, p);
     978           0 :   pari_APPLY_type(t_COL, Fq_add(gel(x,i), gel(y,i), T, p))
     979             : }
     980             : 
     981             : GEN
     982           0 : FqM_add(GEN x, GEN y, GEN T, GEN p)
     983             : {
     984           0 :   if (!T) return FpM_add(x, y, p);
     985           0 :   pari_APPLY_same(FqC_add(gel(x,i), gel(y,i), T, p))
     986             : }
     987             : 
     988             : GEN
     989           0 : FqC_sub(GEN x, GEN y, GEN T, GEN p)
     990             : {
     991           0 :   if (!T) return FpC_sub(x, y, p);
     992           0 :   pari_APPLY_type(t_COL, Fq_sub(gel(x,i), gel(y,i), T, p))
     993             : }
     994             : 
     995             : GEN
     996           0 : FqM_sub(GEN x, GEN y, GEN T, GEN p)
     997             : {
     998           0 :   if (!T) return FpM_sub(x, y, p);
     999           0 :   pari_APPLY_same(FqC_sub(gel(x,i), gel(y,i), T, p))
    1000             : }
    1001             : 
    1002             : GEN
    1003           0 : FqC_Fq_mul(GEN x, GEN y, GEN T, GEN p)
    1004             : {
    1005           0 :   if (!T) return FpC_Fp_mul(x, y, p);
    1006           0 :   pari_APPLY_type(t_COL, Fq_mul(gel(x,i),y,T,p))
    1007             : }
    1008             : 
    1009             : GEN
    1010         105 : FqC_FqV_mul(GEN x, GEN y, GEN T, GEN p)
    1011             : {
    1012         105 :   long i,j, lx=lg(x), ly=lg(y);
    1013             :   GEN z;
    1014         105 :   if (ly==1) return cgetg(1,t_MAT);
    1015         105 :   z = cgetg(ly,t_MAT);
    1016         819 :   for (j=1; j < ly; j++)
    1017             :   {
    1018         714 :     GEN zj = cgetg(lx,t_COL);
    1019        4200 :     for (i=1; i<lx; i++) gel(zj,i) = Fq_mul(gel(x,i),gel(y,j), T, p);
    1020         714 :     gel(z, j) = zj;
    1021             :   }
    1022         105 :   return z;
    1023             : }
    1024             : 
    1025             : GEN
    1026        5467 : FpXC_center(GEN x, GEN p, GEN pov2)
    1027       41476 : { pari_APPLY_type(t_COL, FpX_center(gel(x,i), p, pov2)) }
    1028             : 
    1029             : GEN
    1030      109020 : FqC_to_FlxqC(GEN x, GEN T, ulong p)
    1031      109020 : { long sv = get_Flx_var(T);
    1032     4834755 :   pari_APPLY_type(t_COL,typ(gel(x,i))==t_INT ?
    1033             :                   Z_to_Flx(gel(x,i), p, sv): ZX_to_Flx(gel(x,i), p)) }
    1034             : 
    1035             : GEN
    1036        8708 : FqM_to_FlxqM(GEN x, GEN T, ulong p)
    1037       85985 : { pari_APPLY_same(FqC_to_FlxqC(gel(x,i), T, p)) }
    1038             : 
    1039             : GEN
    1040        1800 : FpXM_center(GEN x, GEN p, GEN pov2)
    1041        7267 : { pari_APPLY_same(FpXC_center(gel(x,i), p, pov2)) }
    1042             : 
    1043             : /*******************************************************************/
    1044             : /*                                                                 */
    1045             : /*                          GENERIC CRT                            */
    1046             : /*                                                                 */
    1047             : /*******************************************************************/
    1048             : static GEN
    1049     9414479 : primelist(forprime_t *S, long n, GEN dB)
    1050             : {
    1051     9414479 :   GEN P = cgetg(n+1, t_VECSMALL);
    1052     9414453 :   long i = 1;
    1053             :   ulong p;
    1054    22385319 :   while (i <= n && (p = u_forprime_next(S)))
    1055    12970866 :     if (!dB || umodiu(dB, p)) P[i++] = p;
    1056     9414448 :   return P;
    1057             : }
    1058             : 
    1059             : void
    1060     8826386 : gen_inccrt_i(const char *str, GEN worker, GEN dB, long n, long mmin,
    1061             :              forprime_t *S, GEN *pH, GEN *pmod, GEN crt(GEN, GEN, GEN*),
    1062             :              GEN center(GEN, GEN, GEN))
    1063             : {
    1064     8826386 :   long m = mmin? minss(mmin, n): usqrt(n);
    1065             :   GEN  H, P, mod;
    1066             :   pari_timer ti;
    1067     8826384 :   if (DEBUGLEVEL > 4)
    1068             :   {
    1069           0 :     timer_start(&ti);
    1070           0 :     err_printf("%s: nb primes: %ld\n",str, n);
    1071             :   }
    1072     8826380 :   if (m == 1)
    1073             :   {
    1074     8510391 :     GEN P = primelist(S, n, dB);
    1075     8510351 :     GEN done = closure_callgen1(worker, P);
    1076     8510363 :     H = gel(done,1);
    1077     8510363 :     mod = gel(done,2);
    1078     8510363 :     if (!*pH && center) H = center(H, mod, shifti(mod,-1));
    1079     8510305 :     if (DEBUGLEVEL>4) timer_printf(&ti,"%s: modular", str);
    1080             :   }
    1081             :   else
    1082             :   {
    1083      315989 :     long i, s = (n+m-1)/m, r = m - (m*s-n), di = 0;
    1084             :     struct pari_mt pt;
    1085      315989 :     long pending = 0;
    1086      315989 :     H = cgetg(m+1, t_VEC); P = cgetg(m+1, t_VEC);
    1087      315989 :     mt_queue_start_lim(&pt, worker, m);
    1088     1286075 :     for (i=1; i<=m || pending; i++)
    1089             :     {
    1090             :       GEN done;
    1091      970085 :       GEN pr = i <= m ? mkvec(primelist(S, i<=r ? s: s-1, dB)): NULL;
    1092      970087 :       mt_queue_submit(&pt, i, pr);
    1093      970088 :       done = mt_queue_get(&pt, NULL, &pending);
    1094      970088 :       if (done)
    1095             :       {
    1096      904095 :         di++;
    1097      904095 :         gel(H, di) = gel(done,1);
    1098      904095 :         gel(P, di) = gel(done,2);
    1099      904095 :         if (DEBUGLEVEL>5) err_printf("%ld%% ",100*di/m);
    1100             :       }
    1101             :     }
    1102      315990 :     mt_queue_end(&pt);
    1103      315990 :     if (DEBUGLEVEL>5) err_printf("\n");
    1104      315990 :     if (DEBUGLEVEL>4) timer_printf(&ti,"%s: modular", str);
    1105      315990 :     H = crt(H, P, &mod);
    1106      315990 :     if (DEBUGLEVEL>4) timer_printf(&ti,"%s: chinese", str);
    1107             :   }
    1108     8826295 :   if (*pH) H = crt(mkvec2(*pH, H), mkvec2(*pmod, mod), &mod);
    1109     8826295 :   *pH = H; *pmod = mod;
    1110     8826295 : }
    1111             : void
    1112     3073116 : gen_inccrt(const char *str, GEN worker, GEN dB, long n, long mmin,
    1113             :            forprime_t *S, GEN *pH, GEN *pmod, GEN crt(GEN, GEN, GEN*),
    1114             :            GEN center(GEN, GEN, GEN))
    1115             : {
    1116     3073116 :   pari_sp av = avma;
    1117     3073116 :   gen_inccrt_i(str, worker, dB, n, mmin, S, pH, pmod, crt, center);
    1118     3073078 :   (void)gc_all(av, 2, pH, pmod);
    1119     3073203 : }
    1120             : 
    1121             : GEN
    1122     2285278 : gen_crt(const char *str, GEN worker, forprime_t *S, GEN dB, ulong bound, long mmin, GEN *pmod,
    1123             :         GEN crt(GEN, GEN, GEN*), GEN center(GEN, GEN, GEN))
    1124             : {
    1125     2285278 :   GEN mod = gen_1, H = NULL;
    1126             :   ulong e;
    1127             : 
    1128     2285278 :   bound++;
    1129     4570619 :   while (bound > (e = expi(mod)))
    1130             :   {
    1131     2285232 :     long n = (bound - e) / expu(S->p) + 1;
    1132     2285256 :     gen_inccrt(str, worker, dB, n, mmin, S, &H, &mod, crt, center);
    1133             :   }
    1134     2285329 :   if (pmod) *pmod = mod;
    1135     2285329 :   return H;
    1136             : }
    1137             : 
    1138             : /*******************************************************************/
    1139             : /*                                                                 */
    1140             : /*                          MODULAR GCD                            */
    1141             : /*                                                                 */
    1142             : /*******************************************************************/
    1143             : /* return z = a mod q, b mod p (p,q) = 1; qinv = 1/q mod p; a in ]-q,q] */
    1144             : static GEN
    1145     5162002 : Fl_chinese_coprime(GEN a, ulong b, GEN q, ulong p, ulong qinv, GEN pq, GEN pq2)
    1146             : {
    1147     5162002 :   ulong d, amod = umodiu(a, p);
    1148     5161982 :   pari_sp av = avma;
    1149             :   GEN ax;
    1150             : 
    1151     5161982 :   if (b == amod) return NULL;
    1152     2126105 :   d = Fl_mul(Fl_sub(b, amod, p), qinv, p); /* != 0 */
    1153     2126822 :   if (d >= 1 + (p>>1))
    1154     1037715 :     ax = subii(a, mului(p-d, q));
    1155             :   else
    1156             :   {
    1157     1089107 :     ax = addii(a, mului(d, q)); /* in ]0, pq[ assuming a in ]-q,q[ */
    1158     1088869 :     if (cmpii(ax,pq2) > 0) ax = subii(ax,pq);
    1159             :   }
    1160     2126261 :   return gc_INT(av, ax);
    1161             : }
    1162             : GEN
    1163         406 : Z_init_CRT(ulong Hp, ulong p) { return stoi(Fl_center(Hp, p, p>>1)); }
    1164             : GEN
    1165       32487 : ZX_init_CRT(GEN Hp, ulong p, long v)
    1166             : {
    1167       32487 :   long i, l = lg(Hp), lim = (long)(p>>1);
    1168       32487 :   GEN H = cgetg(l, t_POL);
    1169       32487 :   H[1] = evalsigne(1) | evalvarn(v);
    1170      801138 :   for (i=2; i<l; i++)
    1171      768651 :     gel(H,i) = stoi(Fl_center(Hp[i], p, lim));
    1172       32487 :   return ZX_renormalize(H,l);
    1173             : }
    1174             : 
    1175             : GEN
    1176        5978 : ZM_init_CRT(GEN Hp, ulong p)
    1177             : {
    1178        5978 :   long i,j, m, l = lg(Hp), lim = (long)(p>>1);
    1179        5978 :   GEN c, cp, H = cgetg(l, t_MAT);
    1180        5978 :   if (l==1) return H;
    1181        5978 :   m = lgcols(Hp);
    1182       20223 :   for (j=1; j<l; j++)
    1183             :   {
    1184       14245 :     cp = gel(Hp,j);
    1185       14245 :     c = cgetg(m, t_COL);
    1186       14245 :     gel(H,j) = c;
    1187      169316 :     for (i=1; i<m; i++) gel(c,i) = stoi(Fl_center(cp[i],p, lim));
    1188             :   }
    1189        5978 :   return H;
    1190             : }
    1191             : 
    1192             : int
    1193        7742 : Z_incremental_CRT(GEN *H, ulong Hp, GEN *ptq, ulong p)
    1194             : {
    1195        7742 :   GEN h, q = *ptq, qp = muliu(q,p);
    1196        7742 :   ulong qinv = Fl_inv(umodiu(q,p), p);
    1197        7742 :   int stable = 1;
    1198        7742 :   h = Fl_chinese_coprime(*H,Hp,q,p,qinv,qp,shifti(qp,-1));
    1199        7742 :   if (h) { *H = h; stable = 0; }
    1200        7742 :   *ptq = qp; return stable;
    1201             : }
    1202             : 
    1203             : static int
    1204      148375 : ZX_incremental_CRT_raw(GEN *ptH, GEN Hp, GEN q, GEN qp, ulong p)
    1205             : {
    1206      148375 :   GEN H = *ptH, h, qp2 = shifti(qp,-1);
    1207      148370 :   ulong qinv = Fl_inv(umodiu(q,p), p);
    1208      148380 :   long i, l = lg(H), lp = lg(Hp);
    1209      148380 :   int stable = 1;
    1210             : 
    1211      148380 :   if (l < lp)
    1212             :   { /* degree increases */
    1213           0 :     GEN x = cgetg(lp, t_POL);
    1214           0 :     for (i=1; i<l; i++)  x[i] = H[i];
    1215           0 :     for (   ; i<lp; i++) gel(x,i) = gen_0;
    1216           0 :     *ptH = H = x;
    1217           0 :     stable = 0;
    1218      148380 :   } else if (l > lp)
    1219             :   { /* degree decreases */
    1220           0 :     GEN x = cgetg(l, t_VECSMALL);
    1221           0 :     for (i=1; i<lp; i++)  x[i] = Hp[i];
    1222           0 :     for (   ; i<l; i++) x[i] = 0;
    1223           0 :     Hp = x; lp = l;
    1224             :   }
    1225     4938885 :   for (i=2; i<lp; i++)
    1226             :   {
    1227     4790595 :     h = Fl_chinese_coprime(gel(H,i),Hp[i],q,p,qinv,qp,qp2);
    1228     4790505 :     if (h) { gel(H,i) = h; stable = 0; }
    1229             :   }
    1230      148290 :   (void)ZX_renormalize(H,lp);
    1231      148377 :   return stable;
    1232             : }
    1233             : 
    1234             : int
    1235           0 : ZX_incremental_CRT(GEN *ptH, GEN Hp, GEN *ptq, ulong p)
    1236             : {
    1237           0 :   GEN q = *ptq, qp = muliu(q,p);
    1238           0 :   int stable = ZX_incremental_CRT_raw(ptH, Hp, q, qp, p);
    1239           0 :   *ptq = qp; return stable;
    1240             : }
    1241             : 
    1242             : int
    1243        7787 : ZM_incremental_CRT(GEN *pH, GEN Hp, GEN *ptq, ulong p)
    1244             : {
    1245        7787 :   GEN h, H = *pH, q = *ptq, qp = muliu(q, p), qp2 = shifti(qp,-1);
    1246        7787 :   ulong qinv = Fl_inv(umodiu(q,p), p);
    1247        7787 :   long i,j, l = lg(H), m = lgcols(H);
    1248        7787 :   int stable = 1;
    1249       27451 :   for (j=1; j<l; j++)
    1250      205516 :     for (i=1; i<m; i++)
    1251             :     {
    1252      185852 :       h = Fl_chinese_coprime(gcoeff(H,i,j), coeff(Hp,i,j),q,p,qinv,qp,qp2);
    1253      185852 :       if (h) { gcoeff(H,i,j) = h; stable = 0; }
    1254             :     }
    1255        7787 :   *ptq = qp; return stable;
    1256             : }
    1257             : 
    1258             : GEN
    1259         679 : ZXM_init_CRT(GEN Hp, long deg, ulong p)
    1260             : {
    1261             :   long i, j, k;
    1262             :   GEN H;
    1263         679 :   long m, l = lg(Hp), lim = (long)(p>>1), n;
    1264         679 :   H = cgetg(l, t_MAT);
    1265         679 :   if (l==1) return H;
    1266         679 :   m = lgcols(Hp);
    1267         679 :   n = deg + 3;
    1268        2268 :   for (j=1; j<l; j++)
    1269             :   {
    1270        1589 :     GEN cp = gel(Hp,j);
    1271        1589 :     GEN c = cgetg(m, t_COL);
    1272        1589 :     gel(H,j) = c;
    1273       24465 :     for (i=1; i<m; i++)
    1274             :     {
    1275       22876 :       GEN dp = gel(cp, i);
    1276       22876 :       long l = lg(dp);
    1277       22876 :       GEN d = cgetg(n, t_POL);
    1278       22876 :       gel(c, i) = d;
    1279       22876 :       d[1] = dp[1] | evalsigne(1);
    1280       46459 :       for (k=2; k<l; k++)
    1281       23583 :         gel(d,k) = stoi(Fl_center(dp[k], p, lim));
    1282       45493 :       for (   ; k<n; k++)
    1283       22617 :         gel(d,k) = gen_0;
    1284             :     }
    1285             :   }
    1286         679 :   return H;
    1287             : }
    1288             : 
    1289             : int
    1290         653 : ZXM_incremental_CRT(GEN *pH, GEN Hp, GEN *ptq, ulong p)
    1291             : {
    1292         653 :   GEN v, H = *pH, q = *ptq, qp = muliu(q, p), qp2 = shifti(qp,-1);
    1293         653 :   ulong qinv = Fl_inv(umodiu(q,p), p);
    1294         653 :   long i,j,k, l = lg(H), m = lgcols(H), n = lg(gmael(H,1,1));
    1295         653 :   int stable = 1;
    1296        2225 :   for (j=1; j<l; j++)
    1297       90418 :     for (i=1; i<m; i++)
    1298             :     {
    1299       88846 :       GEN h = gmael(H,j,i), hp = gmael(Hp,j,i);
    1300       88846 :       long lh = lg(hp);
    1301      246641 :       for (k=2; k<lh; k++)
    1302             :       {
    1303      157795 :         v = Fl_chinese_coprime(gel(h,k),uel(hp,k),q,p,qinv,qp,qp2);
    1304      157795 :         if (v) { gel(h,k) = v; stable = 0; }
    1305             :       }
    1306      108763 :       for (; k<n; k++)
    1307             :       {
    1308       19917 :         v = Fl_chinese_coprime(gel(h,k),0,q,p,qinv,qp,qp2);
    1309       19917 :         if (v) { gel(h,k) = v; stable = 0; }
    1310             :       }
    1311             :     }
    1312         653 :   *ptq = qp; return stable;
    1313             : }
    1314             : 
    1315             : /* record the degrees of Euclidean remainders (make them as large as
    1316             :  * possible : smaller values correspond to a degenerate sequence) */
    1317             : static void
    1318       23741 : Flx_resultant_set_dglist(GEN a, GEN b, GEN dglist, ulong p)
    1319             : {
    1320             :   long da,db,dc, ind;
    1321       23741 :   pari_sp av = avma;
    1322             : 
    1323       23741 :   if (lgpol(a)==0 || lgpol(b)==0) return;
    1324       22474 :   da = degpol(a);
    1325       22474 :   db = degpol(b);
    1326       22474 :   if (db > da)
    1327           0 :   { swapspec(a,b, da,db); }
    1328       22474 :   else if (!da) return;
    1329       22474 :   ind = 0;
    1330      145766 :   while (db)
    1331             :   {
    1332      123292 :     GEN c = Flx_rem(a,b, p);
    1333      123291 :     a = b; b = c; dc = degpol(c);
    1334      123290 :     if (dc < 0) break;
    1335             : 
    1336      123290 :     ind++;
    1337      123290 :     if (dc > dglist[ind]) dglist[ind] = dc;
    1338      123290 :     if (gc_needed(av,2))
    1339             :     {
    1340           0 :       if (DEBUGMEM>1) pari_warn(warnmem,"Flx_resultant_all");
    1341           0 :       (void)gc_all(av, 2, &a,&b);
    1342             :     }
    1343      123292 :     db = dc; /* = degpol(b) */
    1344             :   }
    1345       22474 :   if (ind+1 > lg(dglist)) setlg(dglist,ind+1);
    1346       22474 :   set_avma(av);
    1347             : }
    1348             : /* assuming the PRS finishes on a degree 1 polynomial C0 + C1X, with
    1349             :  * "generic" degree sequence as given by dglist, set *Ci and return
    1350             :  * resultant(a,b). Modular version of Collins's subresultant */
    1351             : static ulong
    1352     2089628 : Flx_resultant_all(GEN a, GEN b, long *C0, long *C1, GEN dglist, ulong p)
    1353             : {
    1354             :   long da,db,dc, ind;
    1355     2089628 :   ulong lb, res, g = 1UL, h = 1UL, ca = 1UL, cb = 1UL;
    1356     2089628 :   int s = 1;
    1357     2089628 :   pari_sp av = avma;
    1358             : 
    1359     2089628 :   *C0 = 1; *C1 = 0;
    1360     2089628 :   if (lgpol(a)==0 || lgpol(b)==0) return 0;
    1361     2080125 :   da = degpol(a);
    1362     2080115 :   db = degpol(b);
    1363     2080082 :   if (db > da)
    1364             :   {
    1365           0 :     swapspec(a,b, da,db);
    1366           0 :     if (both_odd(da,db)) s = -s;
    1367             :   }
    1368     2080082 :   else if (!da) return 1; /* = a[2] ^ db, since 0 <= db <= da = 0 */
    1369     2080082 :   ind = 0;
    1370    19813574 :   while (db)
    1371             :   { /* sub-resultant algo., applied to ca * a and cb * b, ca,cb scalars,
    1372             :      * da = deg a, db = deg b */
    1373    17737980 :     GEN c = Flx_rem(a,b, p);
    1374    17623078 :     long delta = da - db;
    1375             : 
    1376    17623078 :     if (both_odd(da,db)) s = -s;
    1377    17621320 :     lb = Fl_mul(b[db+2], cb, p);
    1378    17653802 :     a = b; b = c; dc = degpol(c);
    1379    17663124 :     ind++;
    1380    17663124 :     if (dc != dglist[ind]) return gc_ulong(av,0); /* degenerates */
    1381    17658148 :     if (g == h)
    1382             :     { /* frequent */
    1383    17598186 :       ulong cc = Fl_mul(ca, Fl_powu(Fl_div(lb,g,p), delta+1, p), p);
    1384    17675353 :       ca = cb;
    1385    17675353 :       cb = cc;
    1386             :     }
    1387             :     else
    1388             :     {
    1389       59962 :       ulong cc = Fl_mul(ca, Fl_powu(lb, delta+1, p), p);
    1390       59964 :       ulong ghdelta = Fl_mul(g, Fl_powu(h, delta, p), p);
    1391       59965 :       ca = cb;
    1392       59965 :       cb = Fl_div(cc, ghdelta, p);
    1393             :     }
    1394    17736000 :     da = db; /* = degpol(a) */
    1395    17736000 :     db = dc; /* = degpol(b) */
    1396             : 
    1397    17736000 :     g = lb;
    1398    17736000 :     if (delta == 1)
    1399    17635326 :       h = g; /* frequent */
    1400             :     else
    1401      100674 :       h = Fl_mul(h, Fl_powu(Fl_div(g,h,p), delta, p), p);
    1402             : 
    1403    17735354 :     if (gc_needed(av,2))
    1404             :     {
    1405           0 :       if (DEBUGMEM>1) pari_warn(warnmem,"Flx_resultant_all");
    1406           0 :       (void)gc_all(av, 2, &a,&b);
    1407             :     }
    1408             :   }
    1409     2075594 :   if (da > 1) return 0; /* Failure */
    1410             :   /* last nonconstant polynomial has degree 1 */
    1411     2075594 :   *C0 = Fl_mul(ca, a[2], p);
    1412     2075537 :   *C1 = Fl_mul(ca, a[3], p);
    1413     2075529 :   res = Fl_mul(cb, b[2], p);
    1414     2075503 :   if (s == -1) res = p - res;
    1415     2075503 :   return gc_ulong(av,res);
    1416             : }
    1417             : 
    1418             : /* Q a vector of polynomials representing B in Fp[X][Y], evaluate at X = x,
    1419             :  * Return 0 in case of degree drop. */
    1420             : static GEN
    1421     2113548 : FlxY_evalx_drop(GEN Q, ulong x, ulong p)
    1422             : {
    1423             :   GEN z;
    1424     2113548 :   long i, lb = lg(Q);
    1425     2113548 :   ulong leadz = Flx_eval(leading_coeff(Q), x, p);
    1426     2113252 :   long vs=mael(Q,2,1);
    1427     2113252 :   if (!leadz) return zero_Flx(vs);
    1428             : 
    1429     2102592 :   z = cgetg(lb, t_VECSMALL); z[1] = vs;
    1430    20080798 :   for (i=2; i<lb-1; i++) z[i] = Flx_eval(gel(Q,i), x, p);
    1431     2102152 :   z[i] = leadz; return z;
    1432             : }
    1433             : 
    1434             : GEN
    1435        2072 : FpXY_FpXQ_evaly(GEN Q, GEN y, GEN T, GEN p, long vx)
    1436             : {
    1437        2072 :   pari_sp av = avma;
    1438        2072 :   long i, lb = lg(Q);
    1439             :   GEN z;
    1440        2072 :   if (lb == 2) return pol_0(vx);
    1441        2072 :   z = gel(Q, lb-1);
    1442        2072 :   if (lb == 3 || !signe(y)) return typ(z)==t_INT? scalar_ZX(z, vx): ZX_copy(z);
    1443             : 
    1444        2072 :   if (typ(z) == t_INT) z = scalar_ZX_shallow(z, vx);
    1445       48636 :   for (i=lb-2; i>=2; i--)
    1446             :   {
    1447       46564 :     GEN c = gel(Q,i);
    1448       46564 :     z = FqX_Fq_mul(z, y, T, p);
    1449       46564 :     z = typ(c) == t_INT? FqX_Fq_add(z,c,T,p): FqX_add(z,c,T,p);
    1450             :   }
    1451        2072 :   return gc_upto(av, z);
    1452             : }
    1453             : 
    1454             : static GEN
    1455     1303290 : ZX_norml1(GEN x)
    1456             : {
    1457     1303290 :   long i, l = lg(x);
    1458             :   GEN s;
    1459             : 
    1460     1303290 :   if (l == 2) return gen_0;
    1461     1210694 :   s = gel(x, l-1); /* != 0 */
    1462     2726305 :   for (i = l-2; i > 1; i--) {
    1463     1515617 :     GEN xi = gel(x,i);
    1464     1515617 :     if (!signe(xi)) continue;
    1465     1224391 :     s = addii_sign(s,1, xi,1);
    1466             :   }
    1467     1210688 :   return s;
    1468             : }
    1469             : /* x >= 0, y != 0, return x + |y| */
    1470             : static GEN
    1471       25559 : addii_abs(GEN x, GEN y)
    1472             : {
    1473       25559 :   if (!signe(x)) return absi_shallow(y);
    1474       16048 :   return addii_sign(x,1, y,1);
    1475             : }
    1476             : 
    1477             : /* x a ZX, return sum_{i >= k} |x[i]| binomial(i, k) */
    1478             : static GEN
    1479       31650 : ZX_norml1_1(GEN x, long k)
    1480             : {
    1481       31650 :   long i, d = degpol(x);
    1482             :   GEN s, C; /* = binomial(i, k) */
    1483             : 
    1484       31649 :   if (!d || k > d) return gen_0;
    1485       31650 :   s = absi_shallow(gel(x, k+2)); /* may be 0 */
    1486       31651 :   C = gen_1;
    1487       68055 :   for (i = k+1; i <= d; i++) {
    1488       36412 :     GEN xi = gel(x,i+2);
    1489       36412 :     if (k) C = diviuexact(muliu(C, i), i-k);
    1490       36413 :     if (signe(xi)) s = addii_abs(s, mulii(C, xi));
    1491             :   }
    1492       31643 :   return s;
    1493             : }
    1494             : /* x has non-negative real coefficients */
    1495             : static GEN
    1496        3283 : RgX_norml1_1(GEN x, long k)
    1497             : {
    1498        3283 :   long i, d = degpol(x);
    1499             :   GEN s, C; /* = binomial(i, k) */
    1500             : 
    1501        3283 :   if (!d || k > d) return gen_0;
    1502        3283 :   s = gel(x, k+2); /* may be 0 */
    1503        3283 :   C = gen_1;
    1504        9198 :   for (i = k+1; i <= d; i++) {
    1505        5915 :     GEN xi = gel(x,i+2);
    1506        5915 :     if (k) C = diviuexact(muliu(C, i), i-k);
    1507        5915 :     if (!gequal0(xi)) s = gadd(s, gmul(C, xi));
    1508             :   }
    1509        3283 :   return s;
    1510             : }
    1511             : 
    1512             : /* N_2(A)^2 */
    1513             : static GEN
    1514        9019 : sqrN2(GEN A, long prec)
    1515             : {
    1516        9019 :   pari_sp av = avma;
    1517        9019 :   long i, l = lg(A);
    1518        9019 :   GEN a = gen_0;
    1519       43727 :   for (i = 2; i < l; i++)
    1520             :   {
    1521       34708 :     a = gadd(a, gabs(gnorm(gel(A,i)), prec));
    1522       34708 :     if (gc_needed(av,1))
    1523             :     {
    1524           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"RgX_RgXY_ResBound i = %ld",i);
    1525           0 :       a = gc_upto(av, a);
    1526             :     }
    1527             :   }
    1528        9019 :   return a;
    1529             : }
    1530             : /* Interpolate at roots of 1 and use Hadamard bound for univariate resultant:
    1531             :  *   bound = N_2(A)^degpol B N_2(B)^degpol(A),  where
    1532             :  *     N_2(A) = sqrt(sum (N_1(Ai))^2)
    1533             :  * Return e such that Res(A, B) < 2^e */
    1534             : static GEN
    1535        8165 : RgX_RgXY_ResBound(GEN A, GEN B, long prec)
    1536             : {
    1537        8165 :   pari_sp av = avma;
    1538        8165 :   GEN b = gen_0, bnd;
    1539        8165 :   long i, lB = lg(B);
    1540       31747 :   for (i=2; i<lB; i++)
    1541             :   {
    1542       23582 :     GEN t = gel(B,i);
    1543       23582 :     if (typ(t) == t_POL) t = gnorml1(t, prec);
    1544       23582 :     b = gadd(b, gabs(gsqr(t), prec));
    1545       23582 :     if (gc_needed(av,1))
    1546             :     {
    1547           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"RgX_RgXY_ResBound i = %ld",i);
    1548           0 :       b = gc_upto(av, b);
    1549             :     }
    1550             :   }
    1551        8165 :   bnd = gsqrt(gmul(gpowgs(sqrN2(A,prec), degpol(B)),
    1552             :                    gpowgs(b, degpol(A))), prec);
    1553        8165 :   return gc_upto(av, bnd);
    1554             : }
    1555             : /* A,B in C[X] return RgX_RgXY_ResBound(A, B(x+y)) */
    1556             : static GEN
    1557         854 : RgX_RgXY_ResBound_1(GEN A, GEN B, long prec)
    1558             : {
    1559         854 :   pari_sp av = avma, av2;
    1560         854 :   GEN b = gen_0, bnd;
    1561         854 :   long i, lB = lg(B);
    1562         854 :   B = shallowcopy(B);
    1563        4137 :   for (i=2; i<lB; i++) gel(B,i) = gabs(gel(B,i), prec);
    1564         854 :   av2 = avma;
    1565        4137 :   for (i=2; i<lB; i++)
    1566             :   {
    1567        3283 :     b = gadd(b, gsqr(RgX_norml1_1(B, i-2)));
    1568        3283 :     if (gc_needed(av2,1))
    1569             :     {
    1570           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"RgX_RgXY_ResBound i = %ld",i);
    1571           0 :       b = gc_upto(av2, b);
    1572             :     }
    1573             :   }
    1574         854 :   bnd = gsqrt(gmul(gpowgs(sqrN2(A,prec), degpol(B)),
    1575             :                    gpowgs(b, degpol(A))), prec);
    1576         854 :   return gc_upto(av, bnd);
    1577             : }
    1578             : 
    1579             : /* log2 N_2(A)^2 */
    1580             : static double
    1581      176984 : log2N2(GEN A)
    1582             : {
    1583      176984 :   pari_sp av = avma;
    1584      176984 :   long i, l = lg(A);
    1585      176984 :   GEN a = gen_0;
    1586     1336965 :   for (i=2; i < l; i++)
    1587             :   {
    1588     1159987 :     a = addii(a, sqri(gel(A,i)));
    1589     1159984 :     if (gc_needed(av,1))
    1590             :     {
    1591           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"ZX_ZXY_ResBound i = %ld",i);
    1592           0 :       a = gc_upto(av, a);
    1593             :     }
    1594             :   }
    1595      176978 :   return gc_double(av, dbllog2(a));
    1596             : }
    1597             : /* Interpolate at roots of 1 and use Hadamard bound for univariate resultant:
    1598             :  *   bound = N_2(A)^degpol B N_2(B)^degpol(A),  where
    1599             :  *     N_2(A) = sqrt(sum (N_1(Ai))^2)
    1600             :  * Return e such that Res(A, B) < 2^e */
    1601             : 
    1602             : static double
    1603     2188192 : resbound(GEN B)
    1604             : {
    1605     2188192 :   pari_sp av = avma;
    1606     2188192 :   long i, lB = lg(B);
    1607     2188192 :   GEN b = gen_0;
    1608     9744617 :   for (i=2; i<lB; i++)
    1609             :   {
    1610     7556567 :     GEN t = gel(B,i);
    1611     7556567 :     if (typ(t) == t_POL) t = ZX_norml1(t);
    1612     7556562 :     b = addii(b, sqri(t));
    1613     7556424 :     if (gc_needed(av,1))
    1614             :     {
    1615           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"ZX_ZXY_ResBound i = %ld",i);
    1616           0 :       b = gc_upto(av, b);
    1617             :     }
    1618             :   }
    1619     2188050 :   return gc_double(av, dbllog2(b));
    1620             : }
    1621             : 
    1622             : ulong
    1623      166902 : ZX_ZXY_ResBound(GEN A, GEN B, GEN dB)
    1624             : {
    1625      166902 :   pari_sp av = avma;
    1626      166902 :   double logb = resbound(B);
    1627             :   long i;
    1628      166898 :   if (dB) logb -= 2 * dbllog2(dB);
    1629      166898 :   i = (long)((degpol(B) * log2N2(A) + degpol(A) * logb) / 2);
    1630      166896 :   return gc_ulong(av, (i <= 0)? 1: 1 + (ulong)i);
    1631             : }
    1632             : static ulong
    1633     1010652 : ZXX_ResBound(GEN A, GEN B)
    1634             : {
    1635     1010652 :   pari_sp av = avma;
    1636     1010652 :   double loga  = resbound(A), logb = resbound(B);
    1637     1010643 :   long i = (long)((degpol(B) * loga + degpol(A) * logb) / 2);
    1638     1010646 :   return gc_ulong(av, (i <= 0)? 1: 1 + (ulong)i);
    1639             : }
    1640             : 
    1641             : /* A,B ZX. Return ZX_ZXY_ResBound(A(x), B(x+y)) */
    1642             : static ulong
    1643       10085 : ZX_ZXY_ResBound_1(GEN A, GEN B)
    1644             : {
    1645       10085 :   pari_sp av = avma;
    1646       10085 :   GEN b = gen_0;
    1647       10085 :   long i, lB = lg(B);
    1648       41735 :   for (i=2; i<lB; i++)
    1649             :   {
    1650       31651 :     b = addii(b, sqri(ZX_norml1_1(B, i-2)));
    1651       31650 :     if (gc_needed(av,1))
    1652             :     {
    1653           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"ZX_ZXY_ResBound i = %ld",i);
    1654           0 :       b = gc_upto(av, b);
    1655             :     }
    1656             :   }
    1657       10084 :   i = (long)((degpol(B) * log2N2(A) + degpol(A) * dbllog2(b)) / 2);
    1658       10086 :   return gc_ulong(av, (i <= 0)? 1: 1 + (ulong)i);
    1659             : }
    1660             : /* special case B = A' */
    1661             : static ulong
    1662     1134913 : ZX_discbound(GEN A)
    1663             : {
    1664     1134913 :   pari_sp av = avma;
    1665     1134913 :   GEN a = gen_0, b = gen_0;
    1666     1134913 :   long i , lA = lg(A), dA = degpol(A);
    1667             :   double loga, logb;
    1668     6772037 :   for (i = 2; i < lA; i++)
    1669             :   {
    1670     5637331 :     GEN c = sqri(gel(A,i));
    1671     5637031 :     a = addii(a, c);
    1672     5637114 :     if (i > 2) b = addii(b, mulii(c, sqru(i-2)));
    1673     5637174 :     if (gc_needed(av,1))
    1674             :     {
    1675           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"ZX_discbound i = %ld",i);
    1676           0 :       (void)gc_all(av, 2, &a, &b);
    1677             :     }
    1678             :   }
    1679     1134706 :   loga = dbllog2(a);
    1680     1134817 :   logb = dbllog2(b); set_avma(av);
    1681     1134839 :   i = (long)(((dA-1) * loga + dA * logb) / 2);
    1682     1134839 :   return (i <= 0)? 1: 1 + (ulong)i;
    1683             : }
    1684             : 
    1685             : /* return Res(a(Y), b(n,Y)) over Fp. la = leading_coeff(a) [for efficiency] */
    1686             : static ulong
    1687     5540077 : Flx_FlxY_eval_resultant(GEN a, GEN b, ulong n, ulong p, ulong pi, ulong la)
    1688             : {
    1689     5540077 :   GEN ev = FlxY_evalx_pre(b, n, p, pi);
    1690     5540445 :   long drop = lg(b) - lg(ev);
    1691     5540445 :   ulong r = Flx_resultant_pre(a, ev, p, pi);
    1692     5539884 :   if (drop && la != 1) r = Fl_mul(r, Fl_powu_pre(la, drop, p, pi), p);
    1693     5539896 :   return r;
    1694             : }
    1695             : /* return Res(a(Y), b(n,Y)) over Fp. la = leading_coeff(a) [for efficiency] */
    1696             : static ulong
    1697     4387505 : FlxY_eval_resultant(GEN a, GEN b, ulong n, ulong p, ulong pi, GEN la, GEN lb)
    1698             : {
    1699     4387505 :   GEN av = FlxY_evalx_pre(a, n, p, pi);
    1700     4387497 :   GEN bv = FlxY_evalx_pre(b, n, p, pi);
    1701     4387504 :   long lav = lgpol(av), lbv = lgpol(bv), dropa, dropb;
    1702             :   ulong r;
    1703     4387487 :   if (lav==0 && lbv==0) return 1UL;
    1704     4387480 :   dropa = lgpol(a) - lav;
    1705     4387474 :   dropb = lgpol(b) - lbv;
    1706     4387473 :   r = Flx_resultant_pre(av, bv, p, pi);
    1707     4387481 :   if (dropa)
    1708             :   { /* multiply by ((-1)^deg B lc(B))^(deg A - deg a) */
    1709          37 :     ulong c = Flx_eval_pre(lb, n,p ,pi); /* lc(B) */
    1710          37 :     if (odd(degpol(b))) c = p - c;
    1711          37 :     c = Fl_powu(c, dropa, p);
    1712          37 :     if (c != 1UL) r = Fl_mul(r, c, p);
    1713             :   }
    1714     4387444 :   else if (dropb)
    1715             :   { /* multiply by lc(A)^(deg B - deg b) */
    1716           7 :     ulong c = Flx_eval_pre(la, n,p ,pi); /* lc(B) */
    1717           7 :     c = Fl_powu(c, dropb, p);
    1718           7 :     if (c != 1UL) r = Fl_mul(r, c, p);
    1719             :   }
    1720     4387481 :   return r;
    1721             : }
    1722             : 
    1723             : static GEN
    1724         284 : FpX_FpXY_eval_resultant(GEN a, GEN b, GEN n, GEN p, GEN la, long db, long vX)
    1725             : {
    1726         284 :   GEN ev = FpXY_evaly(b, n, p, vX);
    1727         284 :   long drop = db-degpol(ev);
    1728         284 :   GEN r = FpX_resultant(a, ev, p);
    1729         284 :   if (drop && !gequal1(la)) r = Fp_mul(r, Fp_powu(la, drop,p),p);
    1730         284 :   return r;
    1731             : }
    1732             : 
    1733             : /* assume dres := deg(Res_X(a,b), Y) <= deg(a,X) * deg(b,Y) < p */
    1734             : /* Return a Fly */
    1735             : static GEN
    1736      368517 : Flx_FlxY_resultant_polint(GEN a, GEN b, ulong p, ulong pi, long dres, long sx)
    1737             : {
    1738             :   long i;
    1739      368517 :   ulong n, la = Flx_lead(a);
    1740      368516 :   GEN  x = cgetg(dres+2, t_VECSMALL);
    1741      368518 :   GEN  y = cgetg(dres+2, t_VECSMALL);
    1742             :  /* Evaluate at dres+ 1 points: 0 (if dres even) and +/- n, so that P_n(X) =
    1743             :   * P_{-n}(-X), where P_i is Lagrange polynomial: P_i(j) = delta_{i,j} */
    1744     2957681 :   for (i=0,n = 1; i < dres; n++)
    1745             :   {
    1746     2589170 :     x[++i] = n;   y[i] = Flx_FlxY_eval_resultant(a,b, x[i], p,pi,la);
    1747     2589071 :     x[++i] = p-n; y[i] = Flx_FlxY_eval_resultant(a,b, x[i], p,pi,la);
    1748             :   }
    1749      368511 :   if (i == dres)
    1750             :   {
    1751      363005 :     x[++i] = 0;   y[i] = Flx_FlxY_eval_resultant(a,b, x[i], p,pi,la);
    1752             :   }
    1753      368513 :   return Flv_polint(x,y, p, sx);
    1754             : }
    1755             : 
    1756             : /* assume dres := deg(Res_X(a,b), Y) <= deg(a,X) * deg(b,Y) < p */
    1757             : /* Return a Fly */
    1758             : static GEN
    1759     1118164 : FlxX_resultant_polint(GEN a, GEN b, ulong p, ulong pi, long dres, long sx)
    1760             : {
    1761             :   long i;
    1762             :   ulong n;
    1763     1118164 :   GEN la = leading_coeff(a), lb = leading_coeff(b);
    1764     1118164 :   GEN x = cgetg(dres+2, t_VECSMALL);
    1765     1118164 :   GEN y = cgetg(dres+2, t_VECSMALL);
    1766             :  /* Evaluate at dres+ 1 points: 0 (if dres even) and +/- n, so that P_n(X) =
    1767             :   * P_{-n}(-X), where P_i is Lagrange polynomial: P_i(j) = delta_{i,j} */
    1768     3018210 :   for (i=0,n = 1; i < dres; n++)
    1769             :   {
    1770     1900046 :     x[++i] = n;   y[i] = FlxY_eval_resultant(a,b, x[i], p,pi, la,lb);
    1771     1900033 :     x[++i] = p-n; y[i] = FlxY_eval_resultant(a,b, x[i], p,pi, la,lb);
    1772             :   }
    1773     1118164 :   if (i == dres)
    1774             :   {
    1775      587496 :     x[++i] = 0;   y[i] = FlxY_eval_resultant(a,b, x[i], p,pi, la,lb);
    1776             :   }
    1777     1118165 :   return Flv_polint(x,y, p, sx);
    1778             : }
    1779             : 
    1780             : static GEN
    1781        7633 : FlxX_pseudorem(GEN x, GEN y, ulong p, ulong pi)
    1782             : {
    1783        7633 :   long vx = varn(x), dx, dy, dz, i, lx, dp;
    1784        7633 :   pari_sp av = avma, av2;
    1785             : 
    1786        7633 :   if (!signe(y)) pari_err_INV("FlxX_pseudorem",y);
    1787        7633 :   (void)new_chunk(2);
    1788        7633 :   dx=degpol(x); x = RgX_recip_i(x)+2;
    1789        7635 :   dy=degpol(y); y = RgX_recip_i(y)+2; dz=dx-dy; dp = dz+1;
    1790        7635 :   av2 = avma;
    1791             :   for (;;)
    1792             :   {
    1793       62605 :     gel(x,0) = Flx_neg(gel(x,0), p); dp--;
    1794      234612 :     for (i=1; i<=dy; i++)
    1795      171747 :       gel(x,i) = Flx_add( Flx_mul_pre(gel(y,0), gel(x,i), p, pi),
    1796      171983 :                           Flx_mul_pre(gel(x,0), gel(y,i), p, pi), p );
    1797     1140882 :     for (   ; i<=dx; i++)
    1798     1078981 :       gel(x,i) = Flx_mul_pre(gel(y,0), gel(x,i), p, pi);
    1799       66587 :     do { x++; dx--; } while (dx >= 0 && lg(gel(x,0))==2);
    1800       61901 :     if (dx < dy) break;
    1801       54265 :     if (gc_needed(av2,1))
    1802             :     {
    1803           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"FlxX_pseudorem dx = %ld >= %ld",dx,dy);
    1804           0 :       gc_slice(av2,x,dx+1);
    1805             :     }
    1806             :   }
    1807        7636 :   if (dx < 0) return zero_Flx(0);
    1808        7636 :   lx = dx+3; x -= 2;
    1809        7636 :   x[0]=evaltyp(t_POL) | _evallg(lx);
    1810        7636 :   x[1]=evalsigne(1) | evalvarn(vx);
    1811        7636 :   x = RgX_recip_i(x);
    1812        7637 :   if (dp)
    1813             :   { /* multiply by y[0]^dp   [beware dummy vars from FpX_FpXY_resultant] */
    1814        1995 :     GEN t = Flx_powu_pre(gel(y,0), dp, p, pi);
    1815        7983 :     for (i=2; i<lx; i++) gel(x,i) = Flx_mul_pre(gel(x,i), t, p, pi);
    1816             :   }
    1817        7636 :   return gc_GEN(av, x);
    1818             : }
    1819             : 
    1820             : /* return a Flx */
    1821             : static GEN
    1822        2553 : FlxX_resultant_subres(GEN u, GEN v, ulong p, ulong pi, long sx)
    1823             : {
    1824        2553 :   pari_sp av = avma, av2;
    1825             :   long degq, dx, dy, du, dv, dr, signh;
    1826             :   GEN z, g, h, r, p1;
    1827             : 
    1828        2553 :   dx = degpol(u); dy = degpol(v); signh = 1;
    1829        2555 :   if (dx < dy)
    1830             :   {
    1831           7 :     swap(u,v); lswap(dx,dy);
    1832           7 :     if (both_odd(dx, dy)) signh = -signh;
    1833             :   }
    1834        2555 :   if (dy < 0) return zero_Flx(sx);
    1835        2555 :   if (dy==0) return gc_upto(av, Flx_powu_pre(gel(v,2),dx,p,pi));
    1836             : 
    1837        2555 :   g = h = pol1_Flx(sx); av2 = avma;
    1838             :   for(;;)
    1839             :   {
    1840        7633 :     r = FlxX_pseudorem(u,v,p,pi); dr = lg(r);
    1841        7636 :     if (dr == 2) { set_avma(av); return zero_Flx(sx); }
    1842        7636 :     du = degpol(u); dv = degpol(v); degq = du-dv;
    1843        7636 :     u = v; p1 = g; g = leading_coeff(u);
    1844        7636 :     switch(degq)
    1845             :     {
    1846           0 :       case 0: break;
    1847        5627 :       case 1:
    1848        5627 :         p1 = Flx_mul_pre(h,p1, p, pi); h = g; break;
    1849        2009 :       default:
    1850        2009 :         p1 = Flx_mul_pre(Flx_powu_pre(h,degq,p,pi), p1, p, pi);
    1851        2008 :         h = Flx_div_pre(Flx_powu_pre(g,degq,p,pi),
    1852        2008 :                         Flx_powu_pre(h,degq-1,p,pi), p, pi);
    1853             :     }
    1854        7633 :     if (both_odd(du,dv)) signh = -signh;
    1855        7631 :     v = FlxY_Flx_div(r, p1, p);
    1856        7631 :     if (dr==3) break;
    1857        5078 :     if (gc_needed(av2,1))
    1858             :     {
    1859           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"FlxX_resultant, dr = %ld",dr);
    1860           0 :       (void)gc_all(av2,4, &u, &v, &g, &h);
    1861             :     }
    1862             :   }
    1863        2553 :   z = gel(v,2);
    1864        2553 :   if (dv > 1) z = Flx_div_pre(Flx_powu_pre(z,dv,p,pi),
    1865           0 :                               Flx_powu_pre(h,dv-1,p,pi), p, pi);
    1866        2553 :   if (signh < 0) z = Flx_neg(z,p);
    1867        2553 :   return gc_upto(av, z);
    1868             : }
    1869             : 
    1870             : /* Return a Flx*/
    1871             : GEN
    1872           0 : FlxX_resultant_pre(GEN a, GEN b, ulong p, ulong pi, long sx)
    1873             : {
    1874           0 :   pari_sp ltop = avma;
    1875           0 :   long da = degpol(a), db = degpol(b);
    1876             :   ulong dres;
    1877             :   GEN z;
    1878           0 :   if (da<0 || db<0) return pol0_Flx(sx);
    1879           0 :   dres = FlxY_degreex(a)*db+FlxY_degreex(b)*da;
    1880           0 :   z = dres >= p ? FlxX_resultant_subres(a, b, p, pi, sx)
    1881           0 :                 : FlxX_resultant_polint(a, b, p, pi, dres, sx);
    1882           0 :   return gc_upto(ltop, z);
    1883             : }
    1884             : 
    1885             : GEN
    1886           0 : FlxX_resultant(GEN a, GEN b, ulong p, long sx)
    1887           0 : { return FlxX_resultant_pre(a, b, p, SMALL_ULONG(p)? 0: get_Fl_red(p), sx); }
    1888             : 
    1889             : /* Warning:
    1890             :  * This function switches between valid and invalid variable ordering*/
    1891             : static GEN
    1892        6163 : FlxY_to_FlyX(GEN b, long sv)
    1893             : {
    1894        6163 :   long i, n=-1;
    1895        6163 :   long sw = b[1]&VARNBITS;
    1896       21049 :   for(i=2;i<lg(b);i++) n = maxss(n,lgpol(gel(b,i)));
    1897        6163 :   return Flm_to_FlxX(Flm_transpose(FlxX_to_Flm(b,n)),sv,sw);
    1898             : }
    1899             : 
    1900             : /* Return a Fly*/
    1901             : GEN
    1902        6163 : Flx_FlxY_resultant(GEN a, GEN b, ulong p)
    1903             : {
    1904        6163 :   pari_sp ltop=avma;
    1905        6163 :   long dres = degpol(a)*degpol(b);
    1906        6163 :   long sx=a[1], sy=b[1]&VARNBITS;
    1907        6163 :   ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    1908             :   GEN z;
    1909        6163 :   b = FlxY_to_FlyX(b,sx);
    1910        6164 :   if ((ulong)dres >= p)
    1911        2554 :     z = FlxX_resultant_subres(Fly_to_FlxY(a, sy), b, p, pi, sy);
    1912             :   else
    1913        3610 :     z = Flx_FlxY_resultant_polint(a, b, p, pi, (ulong)dres, sy);
    1914        6165 :   return gc_upto(ltop,z);
    1915             : }
    1916             : 
    1917             : /* Return a t_POL in variable vc whose coeffs are the coeffs of b in
    1918             :  * variable v; vc must have higher priority than all variables occuring in b. */
    1919             : GEN
    1920      146884 : swap_vars(GEN b, long v, long vc)
    1921             : {
    1922      146884 :   long i, n = RgX_degree(b, v);
    1923             :   GEN c, x;
    1924      146884 :   if (n < 0) return pol_0(vc);
    1925      146884 :   c = cgetg(n+3, t_POL); x = c + 2;
    1926      146883 :   c[1] = evalsigne(1) | evalvarn(vc);
    1927      971224 :   for (i = 0; i <= n; i++) gel(x,i) = polcoef_i(b, i, v);
    1928      146882 :   return c;
    1929             : }
    1930             : 
    1931             : /* assume varn(b) << varn(a) */
    1932             : /* return a FpY*/
    1933             : GEN
    1934          15 : FpX_FpXY_resultant(GEN a, GEN b, GEN p)
    1935             : {
    1936          15 :   long i,n,dres, db, vY = varn(b), vX = varn(a);
    1937             :   GEN la,x,y;
    1938             : 
    1939          15 :   if (lgefint(p) == 3)
    1940             :   {
    1941           0 :     ulong pp = uel(p,2);
    1942           0 :     b = ZXX_to_FlxX(b, pp, vX);
    1943           0 :     a = ZX_to_Flx(a, pp);
    1944           0 :     x = Flx_FlxY_resultant(a, b, pp);
    1945           0 :     return Flx_to_ZX(x);
    1946             :   }
    1947          15 :   db = RgXY_degreex(b);
    1948          15 :   dres = degpol(a)*degpol(b);
    1949          15 :   la = leading_coeff(a);
    1950          15 :   x = cgetg(dres+2, t_VEC);
    1951          15 :   y = cgetg(dres+2, t_VEC);
    1952             :  /* Evaluate at dres+ 1 points: 0 (if dres even) and +/- n, so that P_n(X) =
    1953             :   * P_{-n}(-X), where P_i is Lagrange polynomial: P_i(j) = delta_{i,j} */
    1954         157 :   for (i=0,n = 1; i < dres; n++)
    1955             :   {
    1956         142 :     gel(x,++i) = utoipos(n);
    1957         142 :     gel(y,i) = FpX_FpXY_eval_resultant(a,b,gel(x,i),p,la,db,vY);
    1958         142 :     gel(x,++i) = subiu(p,n);
    1959         142 :     gel(y,i) = FpX_FpXY_eval_resultant(a,b,gel(x,i),p,la,db,vY);
    1960             :   }
    1961          15 :   if (i == dres)
    1962             :   {
    1963           0 :     gel(x,++i) = gen_0;
    1964           0 :     gel(y,i) = FpX_FpXY_eval_resultant(a,b, gel(x,i), p,la,db,vY);
    1965             :   }
    1966          15 :   return FpV_polint(x,y, p, vY);
    1967             : }
    1968             : 
    1969             : GEN
    1970         191 : FpX_composedsum(GEN P, GEN Q, GEN p)
    1971             : {
    1972         191 :   pari_sp av = avma;
    1973         191 :   if (lgefint(p)==3)
    1974             :   {
    1975           0 :     ulong pp = p[2];
    1976           0 :     GEN z = Flx_composedsum(ZX_to_Flx(P, pp), ZX_to_Flx(Q, pp), pp);
    1977           0 :     return gc_upto(av, Flx_to_ZX(z));
    1978             :   }
    1979             :   else
    1980             :   {
    1981         191 :     long n = 1+ degpol(P)*degpol(Q);
    1982         191 :     GEN Pl = FpX_invLaplace(FpX_Newton(P,n,p), p);
    1983         191 :     GEN Ql = FpX_invLaplace(FpX_Newton(Q,n,p), p);
    1984         191 :     GEN L = FpX_Laplace(FpXn_mul(Pl, Ql, n, p), p);
    1985         191 :     GEN lead = Fp_mul(Fp_powu(leading_coeff(P),degpol(Q), p),
    1986         191 :         Fp_powu(leading_coeff(Q),degpol(P), p), p);
    1987         191 :     GEN R = FpX_fromNewton(L, p);
    1988         191 :     return gc_upto(av, FpX_Fp_mul(R, lead, p));
    1989             :   }
    1990             : }
    1991             : 
    1992             : GEN
    1993           0 : FpX_composedprod(GEN P, GEN Q, GEN p)
    1994             : {
    1995           0 :   pari_sp av = avma;
    1996           0 :   if (lgefint(p)==3)
    1997             :   {
    1998           0 :     ulong pp = p[2];
    1999           0 :     GEN z = Flx_composedprod(ZX_to_Flx(P, pp), ZX_to_Flx(Q, pp), pp);
    2000           0 :     return gc_upto(av, Flx_to_ZX(z));
    2001             :   }
    2002             :   else
    2003             :   {
    2004           0 :     long n = 1+ degpol(P)*degpol(Q);
    2005           0 :     GEN L = FpX_convol(FpX_Newton(P,n,p), FpX_Newton(Q,n,p), p);
    2006           0 :     return gc_upto(av,FpX_fromNewton(L, p));
    2007             :   }
    2008             : }
    2009             : 
    2010             : static GEN
    2011         191 : _FpX_composedsum(void *E, GEN a, GEN b)
    2012         191 : { return FpX_composedsum(a,b, (GEN)E); }
    2013             : 
    2014             : GEN
    2015        1637 : FpXV_composedsum(GEN V, GEN p)
    2016             : {
    2017        1637 :   if (lgefint(p)==3)
    2018             :   {
    2019           0 :     ulong pp = p[2];
    2020           0 :     return Flx_to_ZX(FlxV_composedsum(ZXV_to_FlxV(V, pp), pp));
    2021             :   }
    2022        1637 :   return gen_product(V, (void *)p, &_FpX_composedsum);
    2023             : }
    2024             : 
    2025             : /* 0, 1, -1, 2, -2, ... */
    2026             : #define next_lambda(a) (a>0 ? -a : 1-a)
    2027             : 
    2028             : /* Assume A in Z[Y], B in Q[Y][X], B squarefree in (Q[Y]/(A))[X] and
    2029             :  * Res_Y(A, B) in Z[X]. Find a small lambda (start from *lambda, use
    2030             :  * next_lambda successively) such that C(X) = Res_Y(A(Y), B(X + lambda Y))
    2031             :  * is squarefree, reset *lambda to the chosen value and return C. Set LERS to
    2032             :  * the Last nonconstant polynomial in the Euclidean Remainder Sequence */
    2033             : static GEN
    2034       22421 : ZX_ZXY_resultant_LERS(GEN A, GEN B0, long *plambda, GEN *LERS)
    2035             : {
    2036             :   ulong bound, dp;
    2037       22421 :   pari_sp av = avma, av2 = 0;
    2038       22421 :   long lambda = *plambda, degA = degpol(A), dres = degA*degpol(B0);
    2039             :   long stable, checksqfree, i,n, cnt, degB;
    2040       22421 :   long v, vX = varn(B0), vY = varn(A); /* vY < vX */
    2041             :   GEN x, y, dglist, B, q, a, b, ev, H, H0, H1, Hp, H0p, H1p, C0, C1;
    2042             :   forprime_t S;
    2043             : 
    2044       22421 :   if (degA == 1)
    2045             :   {
    2046        1260 :     GEN a1 = gel(A,3), a0 = gel(A,2);
    2047        1260 :     B = lambda? RgX_Rg_translate(B0, monomial(stoi(lambda), 1, vY)): B0;
    2048        1260 :     H = gsubst(B, vY, gdiv(gneg(a0),a1));
    2049        1260 :    if (!equali1(a1)) H = RgX_Rg_mul(H, powiu(a1, poldegree(B,vY)));
    2050        1260 :     *LERS = mkvec2(scalarpol_shallow(a0,vX), scalarpol_shallow(a1,vX));
    2051        1260 :     return gc_all(av, 2, &H, LERS);
    2052             :   }
    2053             : 
    2054       21161 :   dglist = Hp = H0p = H1p = C0 = C1 = NULL; /* gcc -Wall */
    2055       21161 :   C0 = cgetg(dres+2, t_VECSMALL);
    2056       21161 :   C1 = cgetg(dres+2, t_VECSMALL);
    2057       21161 :   dglist = cgetg(dres+1, t_VECSMALL);
    2058       21161 :   x = cgetg(dres+2, t_VECSMALL);
    2059       21160 :   y = cgetg(dres+2, t_VECSMALL);
    2060       21160 :   B0 = leafcopy(B0);
    2061       21160 :   A = leafcopy(A);
    2062       21161 :   B = B0;
    2063       21161 :   v = fetch_var_higher(); setvarn(A,v);
    2064             :   /* make sure p large enough */
    2065       22320 : INIT:
    2066             :   /* always except the first time */
    2067       22320 :   if (av2) { set_avma(av2); lambda = next_lambda(lambda); }
    2068       22320 :   if (lambda) B = RgX_Rg_translate(B0, monomial(stoi(lambda), 1, vY));
    2069       22320 :   B = swap_vars(B, vY, v);
    2070             :   /* B0(lambda v + x, v) */
    2071       22320 :   if (DEBUGLEVEL>4) err_printf("Trying lambda = %ld\n", lambda);
    2072       22320 :   av2 = avma;
    2073             : 
    2074       22320 :   if (degA <= 3)
    2075             :   { /* sub-resultant faster for small degrees */
    2076       11319 :     H = RgX_resultant_all(A,B,&q);
    2077       11319 :     if (typ(q) != t_POL || degpol(q)!=1) goto INIT;
    2078       10374 :     H0 = gel(q,2);
    2079       10374 :     if (typ(H0) == t_POL) setvarn(H0,vX); else H0 = scalarpol(H0,vX);
    2080       10374 :     H1 = gel(q,3);
    2081       10374 :     if (typ(H1) == t_POL) setvarn(H1,vX); else H1 = scalarpol(H1,vX);
    2082       10374 :     if (!ZX_is_squarefree(H)) goto INIT;
    2083       10332 :     goto END;
    2084             :   }
    2085             : 
    2086       11001 :   H = H0 = H1 = NULL;
    2087       11001 :   degB = degpol(B);
    2088       11001 :   bound = ZX_ZXY_ResBound(A, B, NULL);
    2089       11000 :   if (DEBUGLEVEL>4) err_printf("bound for resultant coeffs: 2^%ld\n",bound);
    2090       11000 :   dp = 1;
    2091       11000 :   init_modular_big(&S);
    2092       11000 :   for(cnt = 0, checksqfree = 1;;)
    2093       49459 :   {
    2094       60459 :     ulong p = u_forprime_next(&S);
    2095             :     GEN Hi;
    2096       60458 :     a = ZX_to_Flx(A, p);
    2097       60460 :     b = ZXX_to_FlxX(B, p, varn(A));
    2098       60458 :     if (degpol(a) < degA || degpol(b) < degB) continue; /* p | lc(A)lc(B) */
    2099       60458 :     if (checksqfree)
    2100             :     { /* find degree list for generic Euclidean Remainder Sequence */
    2101       11000 :       long goal = minss(degpol(a), degpol(b)); /* longest possible */
    2102       74267 :       for (n=1; n <= goal; n++) dglist[n] = 0;
    2103       11001 :       setlg(dglist, 1);
    2104       24154 :       for (n=0; n <= dres; n++)
    2105             :       {
    2106       23741 :         ev = FlxY_evalx_drop(b, n, p);
    2107       23741 :         Flx_resultant_set_dglist(a, ev, dglist, p);
    2108       23741 :         if (lg(dglist)-1 == goal) break;
    2109             :       }
    2110             :       /* last pol in ERS has degree > 1 ? */
    2111       11001 :       goal = lg(dglist)-1;
    2112       11001 :       if (degpol(B) == 1) { if (!goal) goto INIT; }
    2113             :       else
    2114             :       {
    2115       10938 :         if (goal <= 1) goto INIT;
    2116       10854 :         if (dglist[goal] != 0 || dglist[goal-1] != 1) goto INIT;
    2117             :       }
    2118       10917 :       if (DEBUGLEVEL>4)
    2119           0 :         err_printf("Degree list for ERS (trials: %ld) = %Ps\n",n+1,dglist);
    2120             :     }
    2121             : 
    2122     2150230 :     for (i=0,n = 0; i <= dres; n++)
    2123             :     {
    2124     2089846 :       ev = FlxY_evalx_drop(b, n, p);
    2125     2089584 :       x[++i] = n; y[i] = Flx_resultant_all(a, ev, C0+i, C1+i, dglist, p);
    2126     2089855 :       if (!C1[i]) i--; /* C1(i) = 0. No way to recover C0(i) */
    2127             :     }
    2128       60384 :     Hi = Flv_Flm_polint(x, mkvec3(y,C0,C1), p, 0);
    2129       60377 :     Hp = gel(Hi,1); H0p = gel(Hi,2); H1p = gel(Hi,3);
    2130       60377 :     if (!H && degpol(Hp) != dres) continue;
    2131       60377 :     if (dp != 1) Hp = Flx_Fl_mul(Hp, Fl_powu(Fl_inv(dp,p), degA, p), p);
    2132       60377 :     if (checksqfree) {
    2133       10917 :       if (!Flx_is_squarefree(Hp, p)) goto INIT;
    2134       10829 :       if (DEBUGLEVEL>4) err_printf("Final lambda = %ld\n", lambda);
    2135       10829 :       checksqfree = 0;
    2136             :     }
    2137             : 
    2138       60289 :     if (!H)
    2139             :     { /* initialize */
    2140       10829 :       q = utoipos(p); stable = 0;
    2141       10829 :       H = ZX_init_CRT(Hp, p,vX);
    2142       10829 :       H0= ZX_init_CRT(H0p, p,vX);
    2143       10829 :       H1= ZX_init_CRT(H1p, p,vX);
    2144             :     }
    2145             :     else
    2146             :     {
    2147       49460 :       GEN qp = muliu(q,p);
    2148       49459 :       stable  = ZX_incremental_CRT_raw(&H, Hp, q,qp, p)
    2149       49460 :               & ZX_incremental_CRT_raw(&H0,H0p, q,qp, p)
    2150       49459 :               & ZX_incremental_CRT_raw(&H1,H1p, q,qp, p);
    2151       49459 :       q = qp;
    2152             :     }
    2153             :     /* could make it probabilistic for H ? [e.g if stable twice, etc]
    2154             :      * Probabilistic anyway for H0, H1 */
    2155       60288 :     if (DEBUGLEVEL>5 && (stable ||  ++cnt==100))
    2156           0 :     { cnt=0; err_printf("%ld%%%s ",100*expi(q)/bound,stable?"s":""); }
    2157       60288 :     if (stable && (ulong)expi(q) >= bound) break; /* DONE */
    2158       49459 :     if (gc_needed(av,2))
    2159             :     {
    2160           0 :       if (DEBUGMEM>1) pari_warn(warnmem,"ZX_ZXY_rnfequation");
    2161           0 :       (void)gc_all(av2, 4, &H, &q, &H0, &H1);
    2162             :     }
    2163             :   }
    2164       21161 : END:
    2165       21161 :   if (DEBUGLEVEL>5) err_printf(" done\n");
    2166       21161 :   setvarn(H, vX); (void)delete_var();
    2167       21161 :   *LERS = mkvec2(H0,H1);
    2168       21161 :   *plambda = lambda; return gc_all(av, 2, &H, LERS);
    2169             : }
    2170             : 
    2171             : GEN
    2172       60214 : ZX_ZXY_resultant_all(GEN A, GEN B, long *plambda, GEN *LERS)
    2173             : {
    2174       60214 :   if (LERS)
    2175             :   {
    2176       22421 :     if (!plambda)
    2177           0 :       pari_err_BUG("ZX_ZXY_resultant_all [LERS != NULL needs lambda]");
    2178       22421 :     return ZX_ZXY_resultant_LERS(A, B, plambda, LERS);
    2179             :   }
    2180       37793 :   return ZX_ZXY_rnfequation(A, B, plambda);
    2181             : }
    2182             : 
    2183             : /* If lambda = NULL, return caract(Mod(A, T)), T,A in Z[X].
    2184             :  * Otherwise find a small lambda such that caract (Mod(A + lambda X, T)) is
    2185             :  * squarefree */
    2186             : GEN
    2187       22594 : ZXQ_charpoly_sqf(GEN A, GEN T, long *lambda, long v)
    2188             : {
    2189       22594 :   pari_sp av = avma;
    2190             :   GEN R, a;
    2191             :   long dA;
    2192             :   int delvar;
    2193             : 
    2194       22594 :   if (v < 0) v = 0;
    2195       22594 :   switch (typ(A))
    2196             :   {
    2197       22594 :     case t_POL: dA = degpol(A); if (dA > 0) break;
    2198           0 :       A = constant_coeff(A);
    2199           0 :     default:
    2200           0 :       if (lambda) { A = scalar_ZX_shallow(A,varn(T)); dA = 0; break;}
    2201           0 :       return gc_upto(av, gpowgs(gsub(pol_x(v), A), degpol(T)));
    2202             :   }
    2203       22594 :   delvar = 0;
    2204       22594 :   if (varncmp(varn(T), 0) <= 0)
    2205             :   {
    2206        3681 :     long v0 = fetch_var(); delvar = 1;
    2207        3681 :     T = leafcopy(T); setvarn(T,v0);
    2208        3681 :     A = leafcopy(A); setvarn(A,v0);
    2209             :   }
    2210       22594 :   R = ZX_ZXY_rnfequation(T, deg1pol_shallow(gen_1, gneg_i(A), 0), lambda);
    2211       22594 :   if (delvar) (void)delete_var();
    2212       22594 :   setvarn(R, v); a = leading_coeff(T);
    2213       22594 :   if (!gequal1(a)) R = gdiv(R, powiu(a, dA));
    2214       22594 :   return gc_upto(av, R);
    2215             : }
    2216             : 
    2217             : /* charpoly(Mod(A,T)), A may be in Q[X], but assume T and result are integral */
    2218             : GEN
    2219     1247365 : ZXQ_charpoly(GEN A, GEN T, long v)
    2220             : {
    2221     1247365 :   return (degpol(T) < 16) ? RgXQ_charpoly_i(A,T,v): ZXQ_charpoly_sqf(A,T, NULL, v);
    2222             : }
    2223             : 
    2224             : GEN
    2225        9772 : QXQ_charpoly(GEN A, GEN T, long v)
    2226             : {
    2227        9772 :   pari_sp av = avma;
    2228        9772 :   GEN den, B = Q_remove_denom(A, &den);
    2229        9772 :   GEN P = ZXQ_charpoly(B, T, v);
    2230        9772 :   return gc_GEN(av, den ? RgX_rescale(P, ginv(den)): P);
    2231             : }
    2232             : 
    2233             : static ulong
    2234     3864991 : ZX_resultant_prime(GEN a, GEN b, GEN dB, long degA, long degB, ulong p)
    2235             : {
    2236     3864991 :   pari_sp av = avma;
    2237     3864991 :   long dropa = degA - degpol(a), dropb = degB - degpol(b);
    2238             :   ulong H, dp;
    2239     3864899 :   if (dropa && dropb) return 0; /* p | lc(A), p | lc(B) */
    2240     3864899 :   H = Flx_resultant(a, b, p);
    2241     3864641 :   if (dropa)
    2242             :   { /* multiply by ((-1)^deg B lc(B))^(deg A - deg a) */
    2243           0 :     ulong c = b[degB+2]; /* lc(B) */
    2244           0 :     if (odd(degB)) c = p - c;
    2245           0 :     c = Fl_powu(c, dropa, p);
    2246           0 :     if (c != 1) H = Fl_mul(H, c, p);
    2247             :   }
    2248     3864641 :   else if (dropb)
    2249             :   { /* multiply by lc(A)^(deg B - deg b) */
    2250           0 :     ulong c = a[degA+2]; /* lc(A) */
    2251           0 :     c = Fl_powu(c, dropb, p);
    2252           0 :     if (c != 1) H = Fl_mul(H, c, p);
    2253             :   }
    2254     3864645 :   dp = dB ? umodiu(dB, p): 1;
    2255     3864645 :   if (dp != 1) H = Fl_mul(H, Fl_powu(Fl_inv(dp,p), degA, p), p);
    2256     3864647 :   return gc_ulong(av, H);
    2257             : }
    2258             : 
    2259             : /* If B=NULL, assume B=A' */
    2260             : static GEN
    2261     1495318 : ZX_resultant_slice(GEN A, GEN B, GEN dB, GEN P, GEN *mod)
    2262             : {
    2263     1495318 :   pari_sp av = avma, av2;
    2264     1495318 :   long degA, degB, i, n = lg(P)-1;
    2265             :   GEN H, T;
    2266             : 
    2267     1495318 :   degA = degpol(A);
    2268     1495317 :   degB = B? degpol(B): degA - 1;
    2269     1495315 :   if (n == 1)
    2270             :   {
    2271      811315 :     ulong Hp, p = uel(P,1);
    2272      811315 :     GEN a = ZX_to_Flx(A, p), b = B? ZX_to_Flx(B, p): Flx_deriv(a, p);
    2273      811330 :     Hp = ZX_resultant_prime(a, b, dB, degA, degB, p);
    2274      811356 :     set_avma(av); *mod = utoipos(p); return utoi(Hp);
    2275             :   }
    2276      684000 :   T = ZV_producttree(P);
    2277      683997 :   A = ZX_nv_mod_tree(A, P, T);
    2278      683996 :   if (B) B = ZX_nv_mod_tree(B, P, T);
    2279      683995 :   H = cgetg(n+1, t_VECSMALL); av2 = avma;
    2280     3737348 :   for(i=1; i <= n; i++, set_avma(av2))
    2281             :   {
    2282     3053356 :     ulong p = P[i];
    2283     3053356 :     GEN a = gel(A,i), b = B? gel(B,i): Flx_deriv(a, p);
    2284     3053662 :     H[i] = ZX_resultant_prime(a, b, dB, degA, degB, p);
    2285             :   }
    2286      683992 :   H = ZV_chinese_tree(H, P, T, ZV_chinesetree(P,T));
    2287      683997 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2288             : }
    2289             : 
    2290             : GEN
    2291     1495326 : ZX_resultant_worker(GEN P, GEN A, GEN B, GEN dB)
    2292             : {
    2293     1495326 :   GEN V = cgetg(3, t_VEC);
    2294     1495317 :   if (typ(B) == t_INT) B = NULL;
    2295     1495317 :   if (!signe(dB)) dB = NULL;
    2296     1495317 :   gel(V,1) = ZX_resultant_slice(A, B, dB, P, &gel(V,2));
    2297     1495342 :   return V;
    2298             : }
    2299             : 
    2300             : /* Compute Res(A, B/dB) in Z, assuming A,B in Z[X], dB in Z or NULL (= 1)
    2301             :  * If B=NULL, take B = A' and assume deg A > 1 and 'bound' is set */
    2302             : GEN
    2303     1350874 : ZX_resultant_all(GEN A, GEN B, GEN dB, ulong bound)
    2304             : {
    2305     1350874 :   pari_sp av = avma;
    2306             :   forprime_t S;
    2307             :   GEN  H, worker;
    2308     1350874 :   if (!B && degpol(A)==2)
    2309             :   {
    2310      114099 :     GEN a = gel(A,4), b = gel(A,3), c = gel(A,2);
    2311      114099 :     H = mulii(a, subii(shifti(mulii(a, c), 2), sqri(b)));
    2312      114086 :     if (dB) H = diviiexact(H, sqri(dB));
    2313      114086 :     return gc_INT(av, H);
    2314             :   }
    2315     1236773 :   if (B)
    2316             :   {
    2317      153986 :     long a = degpol(A), b = degpol(B);
    2318      153986 :     if (a < 0 || b < 0) return gen_0;
    2319      153956 :     if (!a) return powiu(gel(A,2), b);
    2320      153956 :     if (!b) return powiu(gel(B,2), a);
    2321      153331 :     if (minss(a, b) <= 1)
    2322             :     {
    2323       76626 :       H = RgX_resultant_all(A, B, NULL);
    2324       76626 :       if (dB) H = diviiexact(H, powiu(dB, a));
    2325       76626 :       return gc_INT(av, H);
    2326             :     }
    2327       76705 :     if (!bound) bound = ZX_ZXY_ResBound(A, B, dB);
    2328             :   }
    2329     1159500 :   worker = snm_closure(is_entry("_ZX_resultant_worker"),
    2330             :                        mkvec3(A, B? B: gen_0, dB? dB: gen_0));
    2331     1159566 :   init_modular_big(&S);
    2332     1159520 :   H = gen_crt("ZX_resultant_all", worker, &S, dB, bound, 0, NULL,
    2333             :               ZV_chinese_center, Fp_center);
    2334     1159567 :   return gc_INT(av, H);
    2335             : }
    2336             : 
    2337             : /* A0 and B0 in Q[X] */
    2338             : GEN
    2339          56 : QX_resultant(GEN A0, GEN B0)
    2340             : {
    2341             :   GEN s, a, b, A, B;
    2342          56 :   pari_sp av = avma;
    2343             : 
    2344          56 :   A = Q_primitive_part(A0, &a);
    2345          56 :   B = Q_primitive_part(B0, &b);
    2346          56 :   s = ZX_resultant(A, B);
    2347          56 :   if (!signe(s)) { set_avma(av); return gen_0; }
    2348          56 :   if (a) s = gmul(s, gpowgs(a,degpol(B)));
    2349          56 :   if (b) s = gmul(s, gpowgs(b,degpol(A)));
    2350          56 :   return gc_upto(av, s);
    2351             : }
    2352             : 
    2353             : GEN
    2354       56077 : ZX_resultant(GEN A, GEN B) { return ZX_resultant_all(A,B,NULL,0); }
    2355             : 
    2356             : GEN
    2357           0 : QXQ_intnorm(GEN A, GEN B)
    2358             : {
    2359             :   GEN c, n, R, lB;
    2360           0 :   long dA = degpol(A), dB = degpol(B);
    2361           0 :   pari_sp av = avma;
    2362           0 :   if (dA < 0) return gen_0;
    2363           0 :   A = Q_primitive_part(A, &c);
    2364           0 :   if (!c || typ(c) == t_INT) {
    2365           0 :     n = c;
    2366           0 :     R = ZX_resultant(B, A);
    2367             :   } else {
    2368           0 :     n = gel(c,1);
    2369           0 :     R = ZX_resultant_all(B, A, gel(c,2), 0);
    2370             :   }
    2371           0 :   if (n && !equali1(n)) R = mulii(R, powiu(n, dB));
    2372           0 :   lB = leading_coeff(B);
    2373           0 :   if (!equali1(lB)) R = diviiexact(R, powiu(lB, dA));
    2374           0 :   return gc_INT(av, R);
    2375             : }
    2376             : 
    2377             : GEN
    2378       19418 : QXQ_norm(GEN A, GEN B)
    2379             : {
    2380             :   GEN c, R, lB;
    2381       19418 :   long dA = degpol(A), dB = degpol(B);
    2382       19418 :   pari_sp av = avma;
    2383       19418 :   if (dA < 0) return gen_0;
    2384       19418 :   A = Q_primitive_part(A, &c);
    2385       19418 :   R = ZX_resultant(B, A);
    2386       19418 :   if (c) R = gmul(R, gpowgs(c, dB));
    2387       19418 :   lB = leading_coeff(B);
    2388       19418 :   if (!equali1(lB)) R = gdiv(R, gpowgs(lB, dA));
    2389       19418 :   return gc_upto(av, R);
    2390             : }
    2391             : 
    2392             : /* assume x has integral coefficients */
    2393             : GEN
    2394     1200231 : ZX_disc_all(GEN x, ulong bound)
    2395             : {
    2396     1200231 :   pari_sp av = avma;
    2397     1200231 :   long s, d = degpol(x);
    2398             :   GEN l, R;
    2399             : 
    2400     1200225 :   if (d <= 1) return d == 1? gen_1: gen_0;
    2401     1196932 :   s = (d & 2) ? -1: 1;
    2402     1196932 :   l = leading_coeff(x);
    2403     1196933 :   if (!bound) bound = ZX_discbound(x);
    2404     1196858 :   R = ZX_resultant_all(x, NULL, NULL, bound);
    2405     1196930 :   if (is_pm1(l))
    2406     1017891 :   { if (signe(l) < 0) s = -s; }
    2407             :   else
    2408      179037 :     R = diviiexact(R,l);
    2409     1196928 :   if (s == -1) togglesign_safe(&R);
    2410     1196923 :   return gc_INT(av,R);
    2411             : }
    2412             : 
    2413             : GEN
    2414     1138163 : ZX_disc(GEN x) { return ZX_disc_all(x,0); }
    2415             : 
    2416             : static GEN
    2417       11008 : ZXQX_resultant_prime(GEN a, GEN b, GEN dB, long degA, long degB, GEN T, ulong p)
    2418             : {
    2419       11008 :   pari_sp av = avma;
    2420       11008 :   long dropa = degA - degpol(a), dropb = degB - degpol(b);
    2421             :   GEN H, dp;
    2422       11008 :   if (dropa && dropb) return pol0_Flx(T[1]); /* p | lc(A), p | lc(B) */
    2423       11008 :   H = FlxqX_saferesultant(a, b, T, p);
    2424       11007 :   if (!H) return NULL;
    2425       11007 :   if (dropa)
    2426             :   { /* multiply by ((-1)^deg B lc(B))^(deg A - deg a) */
    2427           0 :     GEN c = gel(b,degB+2); /* lc(B) */
    2428           0 :     if (odd(degB)) c = Flx_neg(c, p);
    2429           0 :     c = Flxq_powu(c, dropa, T, p);
    2430           0 :     if (!Flx_equal1(c)) H = Flxq_mul(H, c, T, p);
    2431             :   }
    2432       11007 :   else if (dropb)
    2433             :   { /* multiply by lc(A)^(deg B - deg b) */
    2434           0 :     GEN c = gel(a,degA+2); /* lc(A) */
    2435           0 :     c = Flxq_powu(c, dropb, T, p);
    2436           0 :     if (!Flx_equal1(c)) H = Flxq_mul(H, c, T, p);
    2437             :   }
    2438       11007 :   dp = dB ? ZX_to_Flx(dB, p): pol1_Flx(T[1]);
    2439       11007 :   if (!Flx_equal1(dp))
    2440             :   {
    2441           0 :     GEN idp = Flxq_invsafe(dp, T, p);
    2442           0 :     if (!idp) return NULL;
    2443           0 :     H = Flxq_mul(H, Flxq_powu(idp, degA, T, p), T, p);
    2444             :   }
    2445       11008 :   return gc_leaf(av, H);
    2446             : }
    2447             : 
    2448             : /* If B=NULL, assume B=A' */
    2449             : static GEN
    2450        4911 : ZXQX_resultant_slice(GEN A, GEN B, GEN U, GEN dB, GEN P, GEN *mod)
    2451             : {
    2452        4911 :   pari_sp av = avma;
    2453        4911 :   long degA, degB, i, n = lg(P)-1;
    2454             :   GEN H, T;
    2455        4911 :   long v = varn(U), redo = 0;
    2456             : 
    2457        4911 :   degA = degpol(A);
    2458        4911 :   degB = B? degpol(B): degA - 1;
    2459        4911 :   if (n == 1)
    2460             :   {
    2461        3177 :     ulong p = uel(P,1);
    2462        3177 :     GEN a = ZXX_to_FlxX(A, p, v), b = B? ZXX_to_FlxX(B, p, v): FlxX_deriv(a, p);
    2463        3177 :     GEN u = ZX_to_Flx(U, p);
    2464        3177 :     GEN Hp = ZXQX_resultant_prime(a, b, dB, degA, degB, u, p);
    2465        3177 :     if (!Hp) { set_avma(av); *mod = gen_1; return pol_0(v); }
    2466        3177 :     Hp = gc_upto(av, Flx_to_ZX(Hp)); *mod = utoipos(p); return Hp;
    2467             :   }
    2468        1734 :   T = ZV_producttree(P);
    2469        1734 :   A = ZXX_nv_mod_tree(A, P, T, v);
    2470        1734 :   if (B) B = ZXX_nv_mod_tree(B, P, T, v);
    2471        1734 :   U = ZX_nv_mod_tree(U, P, T);
    2472        1734 :   H = cgetg(n+1, t_VEC);
    2473        9566 :   for(i=1; i <= n; i++)
    2474             :   {
    2475        7832 :     ulong p = P[i];
    2476        7832 :     GEN a = gel(A,i), b = B? gel(B,i): FlxX_deriv(a, p), u = gel(U, i);
    2477        7831 :     GEN h = ZXQX_resultant_prime(a, b, dB, degA, degB, u, p);
    2478        7832 :     if (!h)
    2479             :     {
    2480           0 :       gel(H,i) = pol_0(v);
    2481           0 :       P[i] = 1; redo = 1;
    2482             :     }
    2483             :     else
    2484        7832 :       gel(H,i) = h;
    2485             :   }
    2486        1734 :   if (redo) T = ZV_producttree(P);
    2487        1734 :   H = nxV_chinese_center_tree(H, P, T, ZV_chinesetree(P, T));
    2488        1734 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2489             : }
    2490             : 
    2491             : GEN
    2492        4911 : ZXQX_resultant_worker(GEN P, GEN A, GEN B, GEN T, GEN dB)
    2493             : {
    2494        4911 :   GEN V = cgetg(3, t_VEC);
    2495        4911 :   if (isintzero(B)) B = NULL;
    2496        4911 :   if (!signe(dB)) dB = NULL;
    2497        4911 :   gel(V,1) = ZXQX_resultant_slice(A, B, T, dB, P, &gel(V,2));
    2498        4911 :   return V;
    2499             : }
    2500             : 
    2501             : static ulong
    2502        4315 : ZXQX_resultant_bound_i(GEN nf, GEN A, GEN B, GEN (*f)(GEN,GEN,long))
    2503             : {
    2504        4315 :   pari_sp av = avma;
    2505        4315 :   GEN r, M = nf_L2_bound(nf, NULL, &r);
    2506        4315 :   long v = nf_get_varn(nf), i, l = lg(r);
    2507        4315 :   GEN a = cgetg(l, t_COL);
    2508       13334 :   for (i = 1; i < l; i++)
    2509        9019 :     gel(a, i) = f(gsubst(A, v, gel(r,i)), gsubst(B, v, gel(r,i)), DEFAULTPREC);
    2510        4315 :   return gc_ulong(av, (ulong) dbllog2(gmul(M,RgC_fpnorml2(a, DEFAULTPREC))));
    2511             : }
    2512             : static ulong
    2513        4000 : ZXQX_resultant_bound(GEN nf, GEN A, GEN B)
    2514        4000 : { return ZXQX_resultant_bound_i(nf, A, B, &RgX_RgXY_ResBound); }
    2515             : 
    2516             : static GEN
    2517          56 : _ZXQ_powu(GEN x, ulong u, GEN T)
    2518          56 : { return typ(x) == t_INT? powiu(x, u): ZXQ_powu(x, u, T); }
    2519             : 
    2520             : /* Compute Res(A, B/dB) in Z[X]/T, assuming A,B in Z[X,Y], dB in Z or NULL (= 1)
    2521             :  * If B=NULL, take B = A' and assume deg A > 1 */
    2522             : static GEN
    2523        3997 : ZXQX_resultant_all(GEN A, GEN B, GEN T, GEN dB, ulong bound)
    2524             : {
    2525        3997 :   pari_sp av = avma;
    2526             :   forprime_t S;
    2527             :   GEN  H, worker;
    2528        3997 :   if (B)
    2529             :   {
    2530          63 :     long a = degpol(A), b = degpol(B);
    2531          63 :     if (a < 0 || b < 0) return gen_0;
    2532          63 :     if (!a) return _ZXQ_powu(gel(A,2), b, T);
    2533          63 :     if (!b) return _ZXQ_powu(gel(B,2), a, T);
    2534             :   } else
    2535        3934 :     if (!bound) B = RgX_deriv(A);
    2536        3997 :   if (!bound) bound = ZXQX_resultant_bound(nfinit(T, DEFAULTPREC), A, B);
    2537        3997 :   worker = snm_closure(is_entry("_ZXQX_resultant_worker"),
    2538             :                        mkvec4(A, B? B: gen_0, T, dB? dB: gen_0));
    2539        3997 :   init_modular_big(&S);
    2540        3997 :   H = gen_crt("ZXQX_resultant_all", worker, &S, dB, bound, 0, NULL,
    2541             :               nxV_chinese_center, FpX_center);
    2542        3997 :   if (DEBUGLEVEL)
    2543           0 :     err_printf("ZXQX_resultant_all: a priori bound: %lu, a posteriori: %lu\n",
    2544             :                bound, expi(gsupnorm(H, DEFAULTPREC)));
    2545        3997 :   return gc_upto(av, H);
    2546             : }
    2547             : 
    2548             : GEN
    2549         119 : nfX_resultant(GEN nf, GEN x, GEN y)
    2550             : {
    2551         119 :   pari_sp av = avma;
    2552         119 :   GEN cx, cy, D, T = nf_get_pol(nf);
    2553         119 :   long dx = degpol(x), dy = degpol(y);
    2554         119 :   if (dx < 0 || dy < 0) return gen_0;
    2555         119 :   x = Q_primitive_part(x, &cx); if (cx) cx = gpowgs(cx, dy);
    2556         119 :   y = Q_primitive_part(y, &cy); if (cy) cy = gpowgs(cy, dx);
    2557         119 :   if (!dx)      D = _ZXQ_powu(gel(x,2), dy, T);
    2558         119 :   else if (!dy) D = _ZXQ_powu(gel(y,2), dx, T);
    2559             :   else
    2560             :   {
    2561          63 :     ulong bound = ZXQX_resultant_bound(nf, x, y);
    2562          63 :     D = ZXQX_resultant_all(x, y, T, NULL, bound);
    2563             :   }
    2564         119 :   cx = mul_content(cx, cy); if (cx) D = gmul(D, cx);
    2565         119 :   return gc_upto(av, D);
    2566             : }
    2567             : 
    2568             : static GEN
    2569         252 : to_ZX(GEN a, long v) { return typ(a)==t_INT? scalarpol(a,v): a; }
    2570             : 
    2571             : static GEN
    2572        3934 : ZXQX_disc_all(GEN x, GEN T, ulong bound)
    2573             : {
    2574        3934 :   pari_sp av = avma;
    2575        3934 :   long s, d = degpol(x), v = varn(T);
    2576             :   GEN l, R;
    2577             : 
    2578        3934 :   if (d <= 1) return d == 1? pol_1(v): pol_0(v);
    2579        3934 :   s = (d & 2) ? -1: 1;
    2580        3934 :   l = leading_coeff(x);
    2581        3934 :   R = ZXQX_resultant_all(x, NULL, T, NULL, bound);
    2582        3934 :   if (!gequal1(l)) R = QXQ_div(R, to_ZX(l,v), T);
    2583        3934 :   if (s == -1) R = RgX_neg(R);
    2584        3934 :   return gc_upto(av, R);
    2585             : }
    2586             : 
    2587             : GEN
    2588           7 : QX_disc(GEN x)
    2589             : {
    2590           7 :   pari_sp av = avma;
    2591           7 :   GEN c, d = ZX_disc( Q_primitive_part(x, &c) );
    2592           7 :   if (c) d = gmul(d, gpowgs(c, 2*degpol(x) - 2));
    2593           7 :   return gc_upto(av, d);
    2594             : }
    2595             : 
    2596             : GEN
    2597        4165 : nfX_disc(GEN nf, GEN x)
    2598             : {
    2599        4165 :   pari_sp av = avma;
    2600        4165 :   GEN c, D, T = nf_get_pol(nf);
    2601             :   ulong bound;
    2602        4165 :   long d = degpol(x), v = varn(T);
    2603        4165 :   if (d <= 1) return d == 1? pol_1(v): pol_0(v);
    2604        3934 :   x = Q_primitive_part(x, &c);
    2605        3934 :   bound = ZXQX_resultant_bound(nf, x, RgX_deriv(x));
    2606        3934 :   D = ZXQX_disc_all(x, T, bound);
    2607        3934 :   if (c) D = gmul(D, gpowgs(c, 2*d - 2));
    2608        3934 :   return gc_upto(av, D);
    2609             : }
    2610             : 
    2611             : GEN
    2612      846035 : QXQ_mul(GEN x, GEN y, GEN T)
    2613             : {
    2614      846035 :   GEN dx, nx = Q_primitive_part(x, &dx);
    2615      846034 :   GEN dy, ny = Q_primitive_part(y, &dy);
    2616      846032 :   GEN z = ZXQ_mul(nx, ny, T);
    2617      846032 :   if (dx || dy)
    2618             :   {
    2619      843232 :     GEN d = dx ? dy ? gmul(dx, dy): dx : dy;
    2620      843232 :     if (!gequal1(d)) z = ZX_Q_mul(z, d);
    2621             :   }
    2622      846035 :   return z;
    2623             : }
    2624             : 
    2625             : GEN
    2626      407043 : QXQ_sqr(GEN x, GEN T)
    2627             : {
    2628      407043 :   GEN dx, nx = Q_primitive_part(x, &dx);
    2629      407043 :   GEN z = ZXQ_sqr(nx, T);
    2630      407043 :   if (dx)
    2631      405307 :     z = ZX_Q_mul(z, gsqr(dx));
    2632      407043 :   return z;
    2633             : }
    2634             : 
    2635             : static GEN
    2636      212912 : QXQ_inv_slice(GEN A, GEN B, GEN P, GEN *mod)
    2637             : {
    2638      212912 :   pari_sp av = avma;
    2639      212912 :   long i, n = lg(P)-1, v = varn(A), redo = 0;
    2640             :   GEN H, T;
    2641      212912 :   if (n == 1)
    2642             :   {
    2643      165824 :     ulong p = uel(P,1);
    2644      165824 :     GEN a = ZX_to_Flx(A, p), b = ZX_to_Flx(B, p);
    2645      165824 :     GEN U = Flxq_invsafe(a, b, p);
    2646      165824 :     if (!U)
    2647             :     {
    2648          24 :       set_avma(av);
    2649          24 :       *mod = gen_1; return pol_0(v);
    2650             :     }
    2651      165800 :     H = gc_GEN(av, Flx_to_ZX(U));
    2652      165800 :     *mod = utoipos(p); return H;
    2653             :   }
    2654       47088 :   T = ZV_producttree(P);
    2655       47088 :   A = ZX_nv_mod_tree(A, P, T);
    2656       47088 :   B = ZX_nv_mod_tree(B, P, T);
    2657       47088 :   H = cgetg(n+1, t_VEC);
    2658      238087 :   for(i=1; i <= n; i++)
    2659             :   {
    2660      190999 :     ulong p = P[i];
    2661      190999 :     GEN a = gel(A,i), b = gel(B,i);
    2662      190999 :     GEN U = Flxq_invsafe(a, b, p);
    2663      190999 :     if (!U)
    2664             :     {
    2665         601 :       gel(H,i) = pol_0(v);
    2666         601 :       P[i] = 1; redo = 1;
    2667             :     }
    2668             :     else
    2669      190398 :       gel(H,i) = U;
    2670             :   }
    2671       47088 :   if (redo) T = ZV_producttree(P);
    2672       47088 :   H = nxV_chinese_center_tree(H, P, T, ZV_chinesetree(P, T));
    2673       47088 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2674             : }
    2675             : 
    2676             : GEN
    2677      212912 : QXQ_inv_worker(GEN P, GEN A, GEN B)
    2678             : {
    2679      212912 :   GEN V = cgetg(3, t_VEC);
    2680      212912 :   gel(V,1) = QXQ_inv_slice(A, B, P, &gel(V,2));
    2681      212912 :   return V;
    2682             : }
    2683             : 
    2684             : /* lift(1 / Mod(A,B)). B a ZX, A a scalar or a QX */
    2685             : GEN
    2686      146111 : QXQ_inv(GEN A, GEN B)
    2687             : {
    2688             :   GEN D, Ap, Bp;
    2689             :   ulong pp;
    2690      146111 :   pari_sp av2, av = avma;
    2691             :   forprime_t S;
    2692      146111 :   GEN worker, U, H = NULL, mod = gen_1;
    2693             :   pari_timer ti;
    2694             :   long k, dA, dB;
    2695      146111 :   if (is_scalar_t(typ(A))) return scalarpol(ginv(A), varn(B));
    2696             :   /* A a QX, B a ZX */
    2697      146111 :   A = Q_primitive_part(A, &D);
    2698      146111 :   dA = degpol(A); dB= degpol(B);
    2699             :   /* A, B in Z[X] */
    2700      146111 :   init_modular_small(&S);
    2701             :   do {
    2702      146111 :     pp = u_forprime_next(&S);
    2703      146111 :     Ap = ZX_to_Flx(A, pp);
    2704      146111 :     Bp = ZX_to_Flx(B, pp);
    2705      146111 :   } while (degpol(Ap) != dA || degpol(Bp) != dB);
    2706      146111 :   if (degpol(Flx_gcd(Ap, Bp, pp)) != 0 && degpol(ZX_gcd(A,B))!=0)
    2707          14 :     pari_err_INV("QXQ_inv",mkpolmod(A,B));
    2708      146097 :   worker = snm_closure(is_entry("_QXQ_inv_worker"), mkvec2(A, B));
    2709      146097 :   av2 = avma;
    2710      146097 :   for (k = 1; ;k *= 2)
    2711       42591 :   {
    2712             :     GEN res, b, N, den;
    2713      188688 :     gen_inccrt_i("QXQ_inv", worker, NULL, (k+1)>>1, 0, &S, &H, &mod,
    2714             :                  nxV_chinese_center, FpX_center);
    2715      188688 :     (void)gc_all(av2, 2, &H, &mod);
    2716      188688 :     b = sqrti(shifti(mod,-1));
    2717      188688 :     if (DEBUGLEVEL>5) timer_start(&ti);
    2718      188688 :     U = FpX_ratlift(H, mod, b, b, NULL);
    2719      188688 :     if (DEBUGLEVEL>5) timer_printf(&ti,"QXQ_inv: ratlift");
    2720      194434 :     if (!U) continue;
    2721      151843 :     N = Q_remove_denom(U, &den); if (!den) den = gen_1;
    2722      151843 :     res = Flx_rem(Flx_Fl_sub(Flx_mul(Ap, ZX_to_Flx(N,pp), pp),
    2723             :                   umodiu(den, pp), pp), Bp, pp);
    2724      151843 :     if (degpol(res) >= 0) continue;
    2725      146097 :     res = ZX_Z_sub(ZX_mul(A, N), den);
    2726      146097 :     res = ZX_is_monic(B) ? ZX_rem(res, B): RgX_pseudorem(res, B);
    2727      146097 :     if (DEBUGLEVEL>5) timer_printf(&ti,"QXQ_inv: final check");
    2728      146097 :     if (degpol(res)<0)
    2729             :     {
    2730      146097 :       if (D) U = RgX_Rg_div(U, D);
    2731      146097 :       return gc_GEN(av, U);
    2732             :     }
    2733             :   }
    2734             : }
    2735             : 
    2736             : static GEN
    2737      121107 : QXQ_div_slice(GEN A, GEN B, GEN C, GEN P, GEN *mod)
    2738             : {
    2739      121107 :   pari_sp av = avma;
    2740      121107 :   long i, n = lg(P)-1, v = varn(A), redo = 0;
    2741             :   GEN H, T;
    2742      121107 :   if (n == 1)
    2743             :   {
    2744       44701 :     ulong p = uel(P,1);
    2745       44701 :     GEN a = ZX_to_Flx(A, p), b = ZX_to_Flx(B, p), c = ZX_to_Flx(C, p);
    2746       44701 :     GEN bi = Flxq_invsafe(b, c, p), U;
    2747       44701 :     if (!bi)
    2748             :     {
    2749           0 :       set_avma(av);
    2750           0 :       *mod = gen_1; return pol_0(v);
    2751             :     }
    2752       44701 :     U = Flxq_mul(a, bi, c, p);
    2753       44701 :     H = gc_GEN(av, Flx_to_ZX(U));
    2754       44701 :     *mod = utoipos(p); return H;
    2755             :   }
    2756       76406 :   T = ZV_producttree(P);
    2757       76406 :   A = ZX_nv_mod_tree(A, P, T);
    2758       76406 :   B = ZX_nv_mod_tree(B, P, T);
    2759       76406 :   C = ZX_nv_mod_tree(C, P, T);
    2760       76406 :   H = cgetg(n+1, t_VEC);
    2761      337448 :   for(i=1; i <= n; i++)
    2762             :   {
    2763      261042 :     ulong p = P[i];
    2764      261042 :     GEN a = gel(A,i), b = gel(B,i), c = gel(C, i);
    2765      261042 :     GEN bi = Flxq_invsafe(b, c, p);
    2766      261042 :     if (!bi)
    2767             :     {
    2768           4 :       gel(H,i) = pol_0(v);
    2769           4 :       P[i] = 1; redo = 1;
    2770             :     }
    2771             :     else
    2772      261038 :       gel(H,i) = Flxq_mul(a, bi, c, p);
    2773             :   }
    2774       76406 :   if (redo) T = ZV_producttree(P);
    2775       76406 :   H = nxV_chinese_center_tree(H, P, T, ZV_chinesetree(P, T));
    2776       76406 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2777             : }
    2778             : 
    2779             : GEN
    2780      121107 : QXQ_div_worker(GEN P, GEN A, GEN B, GEN C)
    2781             : {
    2782      121107 :   GEN V = cgetg(3, t_VEC);
    2783      121107 :   gel(V,1) = QXQ_div_slice(A, B, C, P, &gel(V,2));
    2784      121107 :   return V;
    2785             : }
    2786             : 
    2787             : /* lift(Mod(A/B, C)). C a ZX, A, B a scalar or a QX */
    2788             : GEN
    2789       33207 : QXQ_div(GEN A, GEN B, GEN C)
    2790             : {
    2791             :   GEN DA, DB, Ap, Bp, Cp;
    2792             :   ulong pp;
    2793       33207 :   pari_sp av2, av = avma;
    2794             :   forprime_t S;
    2795       33207 :   GEN worker, U, H = NULL, mod = gen_1;
    2796             :   pari_timer ti;
    2797             :   long k, dA, dB, dC;
    2798       33207 :   if (is_scalar_t(typ(A))) return scalarpol(ginv(A), varn(B));
    2799             :   /* A a QX, B a ZX */
    2800       33207 :   A = Q_primitive_part(A, &DA);
    2801       33207 :   B = Q_primitive_part(B, &DB);
    2802       33207 :   dA = degpol(A); dB = degpol(B); dC = degpol(C);
    2803             :   /* A, B in Z[X] */
    2804       33207 :   init_modular_small(&S);
    2805             :   do {
    2806       33207 :     pp = u_forprime_next(&S);
    2807       33207 :     Ap = ZX_to_Flx(A, pp);
    2808       33207 :     Bp = ZX_to_Flx(B, pp);
    2809       33207 :     Cp = ZX_to_Flx(C, pp);
    2810       33207 :   } while (degpol(Ap) != dA || degpol(Bp) != dB || degpol(Cp) != dC);
    2811       33207 :   if (degpol(Flx_gcd(Bp, Cp, pp)) != 0 && degpol(ZX_gcd(B,C))!=0)
    2812           0 :     pari_err_INV("QXQ_div",mkpolmod(B,C));
    2813       33207 :   worker = snm_closure(is_entry("_QXQ_div_worker"), mkvec3(A, B, C));
    2814       33207 :   av2 = avma;
    2815       33207 :   for (k = 1; ;k *= 2)
    2816       46720 :   {
    2817             :     GEN res, b, N, den;
    2818       79927 :     gen_inccrt_i("QXQ_div", worker, NULL, (k+1)>>1, 0, &S, &H, &mod,
    2819             :                  nxV_chinese_center, FpX_center);
    2820       79927 :     (void)gc_all(av2, 2, &H, &mod);
    2821       79927 :     b = sqrti(shifti(mod,-1));
    2822       79927 :     if (DEBUGLEVEL>5) timer_start(&ti);
    2823       79927 :     U = FpX_ratlift(H, mod, b, b, NULL);
    2824       79927 :     if (DEBUGLEVEL>5) timer_printf(&ti,"QXQ_div: ratlift");
    2825       90556 :     if (!U) continue;
    2826       43836 :     N = Q_remove_denom(U, &den); if (!den) den = gen_1;
    2827       43836 :     res = Flx_rem(Flx_sub(Flx_mul(Bp, ZX_to_Flx(N,pp), pp),
    2828             :                           Flx_Fl_mul(Ap, umodiu(den, pp), pp), pp), Cp, pp);
    2829       43836 :     if (degpol(res) >= 0) continue;
    2830       33207 :     res = ZX_sub(ZX_mul(B, N), ZX_Z_mul(A,den));
    2831       33207 :     res = ZX_is_monic(C) ? ZX_rem(res, C): RgX_pseudorem(res, C);
    2832       33207 :     if (DEBUGLEVEL>5) timer_printf(&ti,"QXQ_div: final check");
    2833       33207 :     if (degpol(res)<0)
    2834             :     {
    2835       33207 :       if (DA && DB) U = RgX_Rg_mul(U, gdiv(DA,DB));
    2836       28069 :       else if (DA) U = RgX_Rg_mul(U, DA);
    2837       15981 :       else if (DB) U = RgX_Rg_div(U, DB);
    2838       33207 :       return gc_GEN(av, U);
    2839             :     }
    2840             :   }
    2841             : }
    2842             : 
    2843             : /************************************************************************
    2844             :  *                                                                      *
    2845             :  *                           ZXQ_minpoly                                *
    2846             :  *                                                                      *
    2847             :  ************************************************************************/
    2848             : 
    2849             : static GEN
    2850        3523 : ZXQ_minpoly_slice(GEN A, GEN B, long d, GEN P, GEN *mod)
    2851             : {
    2852        3523 :   pari_sp av = avma;
    2853        3523 :   long i, n = lg(P)-1, v = evalvarn(varn(B));
    2854             :   GEN H, T;
    2855        3523 :   if (n == 1)
    2856             :   {
    2857         716 :     ulong p = uel(P,1);
    2858         716 :     GEN a = ZX_to_Flx(A, p), b = ZX_to_Flx(B, p);
    2859         716 :     GEN Hp = Flxq_minpoly(a, b, p);
    2860         716 :     if (degpol(Hp) != d) { p = 1; Hp = pol0_Flx(v); }
    2861         716 :     H = gc_upto(av, Flx_to_ZX(Hp));
    2862         716 :     *mod = utoipos(p); return H;
    2863             :   }
    2864        2807 :   T = ZV_producttree(P);
    2865        2807 :   A = ZX_nv_mod_tree(A, P, T);
    2866        2807 :   B = ZX_nv_mod_tree(B, P, T);
    2867        2807 :   H = cgetg(n+1, t_VEC);
    2868       16838 :   for(i=1; i <= n; i++)
    2869             :   {
    2870       14031 :     ulong p = P[i];
    2871       14031 :     GEN a = gel(A,i), b = gel(B,i);
    2872       14031 :     GEN m = Flxq_minpoly(a, b, p);
    2873       14031 :     if (degpol(m) != d) { P[i] = 1; m = pol0_Flx(v); }
    2874       14031 :     gel(H, i) = m;
    2875             :   }
    2876        2807 :   H = nxV_chinese_center_tree(H, P, T, ZV_chinesetree(P, T));
    2877        2807 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2878             : }
    2879             : 
    2880             : GEN
    2881        3523 : ZXQ_minpoly_worker(GEN P, GEN A, GEN B, long d)
    2882             : {
    2883        3523 :   GEN V = cgetg(3, t_VEC);
    2884        3523 :   gel(V,1) = ZXQ_minpoly_slice(A, B, d, P, &gel(V,2));
    2885        3523 :   return V;
    2886             : }
    2887             : 
    2888             : GEN
    2889        1701 : ZXQ_minpoly(GEN A, GEN B, long d, ulong bound)
    2890             : {
    2891        1701 :   pari_sp av = avma;
    2892             :   GEN worker, H, dB;
    2893             :   forprime_t S;
    2894        1701 :   B = Q_remove_denom(B, &dB);
    2895        1701 :   worker = strtoclosure("_ZXQ_minpoly_worker", 3, A, B, stoi(d));
    2896        1701 :   init_modular_big(&S);
    2897        1701 :   H = gen_crt("ZXQ_minpoly", worker, &S, dB, bound, 0, NULL,
    2898             :                nxV_chinese_center, FpX_center_i);
    2899        1701 :   return gc_GEN(av, H);
    2900             : }
    2901             : 
    2902             : /************************************************************************
    2903             :  *                                                                      *
    2904             :  *                   ZX_ZXY_resultant                                   *
    2905             :  *                                                                      *
    2906             :  ************************************************************************/
    2907             : 
    2908             : static GEN
    2909      364908 : ZX_ZXY_resultant_prime(GEN a, GEN b, ulong dp, ulong p,
    2910             :                        long degA, long degB, long dres, long sX)
    2911             : {
    2912      364908 :   pari_sp av = avma;
    2913      364908 :   long dropa = degA - degpol(a), dropb = degB - degpol(b);
    2914      364907 :   ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    2915      364907 :   GEN Hp = Flx_FlxY_resultant_polint(a, b, p, pi, dres, sX);
    2916      364910 :   if (dropa && dropb)
    2917           0 :     Hp = zero_Flx(sX);
    2918             :   else {
    2919      364910 :     if (dropa)
    2920             :     { /* multiply by ((-1)^deg B lc(B))^(deg A - deg a) */
    2921           0 :       GEN c = gel(b,degB+2); /* lc(B) */
    2922           0 :       if (odd(degB)) c = Flx_neg(c, p);
    2923           0 :       if (!Flx_equal1(c)) {
    2924           0 :         c = Flx_powu_pre(c, dropa, p, pi);
    2925           0 :         if (!Flx_equal1(c)) Hp = Flx_mul_pre(Hp, c, p, pi);
    2926             :       }
    2927             :     }
    2928      364910 :     else if (dropb)
    2929             :     { /* multiply by lc(A)^(deg B - deg b) */
    2930           0 :       ulong c = uel(a, degA+2); /* lc(A) */
    2931           0 :       c = Fl_powu(c, dropb, p);
    2932           0 :       if (c != 1) Hp = Flx_Fl_mul_pre(Hp, c, p, pi);
    2933             :     }
    2934             :   }
    2935      364910 :   if (dp != 1) Hp = Flx_Fl_mul_pre(Hp, Fl_powu_pre(Fl_inv(dp,p), degA, p, pi), p, pi);
    2936      364910 :   return gc_leaf(av, Hp);
    2937             : }
    2938             : 
    2939             : static GEN
    2940      124962 : ZX_ZXY_resultant_slice(GEN A, GEN B, GEN dB, long degA, long degB, long dres,
    2941             :                        GEN P, GEN *mod, long sX, long vY)
    2942             : {
    2943      124962 :   pari_sp av = avma;
    2944      124962 :   long i, n = lg(P)-1;
    2945             :   GEN H, T, D;
    2946      124962 :   if (n == 1)
    2947             :   {
    2948       40164 :     ulong p = uel(P,1);
    2949       40164 :     ulong dp = dB ? umodiu(dB, p): 1;
    2950       40164 :     GEN a = ZX_to_Flx(A, p), b = ZXX_to_FlxX(B, p, vY);
    2951       40164 :     GEN Hp = ZX_ZXY_resultant_prime(a, b, dp, p, degA, degB, dres, sX);
    2952       40165 :     H = gc_upto(av, Flx_to_ZX(Hp));
    2953       40165 :     *mod = utoipos(p); return H;
    2954             :   }
    2955       84798 :   T = ZV_producttree(P);
    2956       84798 :   A = ZX_nv_mod_tree(A, P, T);
    2957       84798 :   B = ZXX_nv_mod_tree(B, P, T, vY);
    2958       84798 :   D = dB ? Z_ZV_mod_tree(dB, P, T): NULL;
    2959       84798 :   H = cgetg(n+1, t_VEC);
    2960      364208 :   for(i=1; i <= n; i++)
    2961             :   {
    2962      279410 :     ulong p = P[i];
    2963      279410 :     GEN a = gel(A,i), b = gel(B,i);
    2964      279410 :     ulong dp = D ? uel(D, i): 1;
    2965      279410 :     gel(H,i) = ZX_ZXY_resultant_prime(a, b, dp, p, degA, degB, dres, sX);
    2966             :   }
    2967       84798 :   H = nxV_chinese_center_tree(H, P, T, ZV_chinesetree(P, T));
    2968       84798 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2969             : }
    2970             : 
    2971             : GEN
    2972      124962 : ZX_ZXY_resultant_worker(GEN P, GEN A, GEN B, GEN dB, GEN v)
    2973             : {
    2974      124962 :   GEN V = cgetg(3, t_VEC);
    2975      124962 :   if (isintzero(dB)) dB = NULL;
    2976      124962 :   gel(V,1) = ZX_ZXY_resultant_slice(A, B, dB, v[1], v[2], v[3], P, &gel(V,2), v[4], v[5]);
    2977      124963 :   return V;
    2978             : }
    2979             : 
    2980             : GEN
    2981       79195 : ZX_ZXY_resultant(GEN A, GEN B)
    2982             : {
    2983       79195 :   pari_sp av = avma;
    2984             :   forprime_t S;
    2985             :   ulong bound;
    2986       79195 :   long v = fetch_var_higher();
    2987       79195 :   long degA = degpol(A), degB, dres = degA * degpol(B);
    2988       79195 :   long vX = varn(B), vY = varn(A); /* assume vY has lower priority */
    2989       79195 :   long sX = evalvarn(vX);
    2990             :   GEN worker, H, dB;
    2991       79195 :   B = Q_remove_denom(B, &dB);
    2992       79195 :   if (!dB) B = leafcopy(B);
    2993       79195 :   A = leafcopy(A); setvarn(A,v);
    2994       79195 :   B = swap_vars(B, vY, v); degB = degpol(B);
    2995       79196 :   bound = ZX_ZXY_ResBound(A, B, dB);
    2996       79193 :   if (DEBUGLEVEL>4) err_printf("bound for resultant coeffs: 2^%ld\n",bound);
    2997      158389 :   worker = snm_closure(is_entry("_ZX_ZXY_resultant_worker"),
    2998       79196 :                        mkvec4(A, B, dB? dB: gen_0,
    2999             :                               mkvecsmall5(degA, degB, dres, sX, vY)));
    3000       79195 :   init_modular_big(&S);
    3001       79195 :   H = gen_crt("ZX_ZXY_resultant_all", worker, &S, dB, bound, 0, NULL,
    3002             :                nxV_chinese_center, FpX_center_i);
    3003       79196 :   setvarn(H, vX); (void)delete_var();
    3004       79196 :   return gc_GEN(av, H);
    3005             : }
    3006             : 
    3007             : static GEN
    3008     1118164 : ZXX_resultant_prime(GEN a, GEN b, ulong p, long degA, long degB, long dres, long sX)
    3009             : {
    3010     1118164 :   pari_sp av = avma;
    3011     1118164 :   long dropa = degA - degpol(a), dropb = degB - degpol(b);
    3012     1118164 :   ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    3013     1118164 :   GEN Hp = FlxX_resultant_polint(a, b, p, pi, dres, sX);
    3014     1118162 :   if (dropa && dropb)
    3015           0 :     Hp = zero_Flx(sX);
    3016             :   else {
    3017     1118162 :     if (dropa)
    3018             :     { /* multiply by ((-1)^deg B lc(B))^(deg A - deg a) */
    3019           0 :       GEN c = gel(b,degB+2); /* lc(B) */
    3020           0 :       if (odd(degB)) c = Flx_neg(c, p);
    3021           0 :       if (!Flx_equal1(c)) {
    3022           0 :         c = Flx_powu_pre(c, dropa, p, pi);
    3023           0 :         if (!Flx_equal1(c)) Hp = Flx_mul_pre(Hp, c, p, pi);
    3024             :       }
    3025             :     }
    3026     1118162 :     else if (dropb)
    3027             :     { /* multiply by lc(A)^(deg B - deg b) */
    3028           0 :       ulong c = uel(a, degA+2); /* lc(A) */
    3029           0 :       c = Fl_powu(c, dropb, p);
    3030           0 :       if (c != 1) Hp = Flx_Fl_mul_pre(Hp, c, p, pi);
    3031             :     }
    3032             :   }
    3033     1118162 :   return gc_leaf(av, Hp);
    3034             : }
    3035             : 
    3036             : static GEN
    3037     1015937 : ZXX_resultant_slice(GEN A, GEN B, long degA, long degB, long dres,
    3038             :                        GEN P, GEN *mod, long sX, long vY)
    3039             : {
    3040     1015937 :   pari_sp av = avma;
    3041     1015937 :   long i, n = lg(P)-1;
    3042             :   GEN H, T;
    3043     1015937 :   if (n == 1)
    3044             :   {
    3045      931915 :     ulong p = uel(P,1);
    3046      931915 :     GEN a = ZXX_to_FlxX(A, p, vY), b = ZXX_to_FlxX(B, p, vY);
    3047      931914 :     GEN Hp = ZXX_resultant_prime(a, b, p, degA, degB, dres, sX);
    3048      931912 :     H = gc_upto(av, Flx_to_ZX(Hp));
    3049      931916 :     *mod = utoipos(p); return H;
    3050             :   }
    3051       84022 :   T = ZV_producttree(P);
    3052       84022 :   A = ZXX_nv_mod_tree(A, P, T, vY);
    3053       84022 :   B = ZXX_nv_mod_tree(B, P, T, vY);
    3054       84022 :   H = cgetg(n+1, t_VEC);
    3055      270272 :   for(i=1; i <= n; i++)
    3056             :   {
    3057      186250 :     ulong p = P[i];
    3058      186250 :     GEN a = gel(A,i), b = gel(B,i);
    3059      186250 :     gel(H,i) = ZXX_resultant_prime(a, b, p, degA, degB, dres, sX);
    3060             :   }
    3061       84022 :   H = nxV_chinese_center_tree(H, P, T, ZV_chinesetree(P, T));
    3062       84022 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    3063             : }
    3064             : 
    3065             : GEN
    3066     1015937 : ZXX_resultant_worker(GEN P, GEN A, GEN B, GEN v)
    3067             : {
    3068     1015937 :   GEN V = cgetg(3, t_VEC);
    3069     1015937 :   gel(V,1) = ZXX_resultant_slice(A, B, v[1], v[2], v[3], P, &gel(V,2), v[4], v[5]);
    3070     1015938 :   return V;
    3071             : }
    3072             : 
    3073             : GEN
    3074     1010652 : ZXX_resultant(GEN A, GEN B, long vX)
    3075             : {
    3076     1010652 :   pari_sp av = avma;
    3077             :   forprime_t S;
    3078             :   ulong bound;
    3079     1010652 :   long degA = degpol(A), degB = degpol(B), dres = degA * RgXY_degreex(B) + RgXY_degreex(A)*degB;
    3080     1010652 :   long vY = varn(A), sX = evalvarn(vX);
    3081             :   GEN worker, H;
    3082     1010652 :   bound = ZXX_ResBound(A, B);
    3083     1010648 :   if (DEBUGLEVEL>4) err_printf("bound for resultant coeffs: 2^%ld\n",bound);
    3084     1010648 :   worker = snm_closure(is_entry("_ZXX_resultant_worker"),
    3085             :                        mkvec3(A, B, mkvecsmall5(degA, degB, dres, sX, vY)));
    3086     1010655 :   init_modular_big(&S);
    3087     1010654 :   H = gen_crt("ZXX_resultant", worker, &S, NULL, bound, 0, NULL, nxV_chinese_center, FpX_center_i);
    3088     1010655 :   return gc_GEN(av, H);
    3089             : }
    3090             : 
    3091             : static long
    3092       40523 : ZX_ZXY_rnfequation_lambda(GEN A, GEN B0, long lambda)
    3093             : {
    3094       40523 :   pari_sp av = avma;
    3095       40523 :   long degA = degpol(A), degB, dres = degA*degpol(B0);
    3096       40523 :   long v = fetch_var_higher();
    3097       40523 :   long vX = varn(B0), vY = varn(A); /* assume vY has lower priority */
    3098       40523 :   long sX = evalvarn(vX);
    3099             :   GEN dB, B, a, b, Hp;
    3100             :   forprime_t S;
    3101             : 
    3102       40523 :   B0 = Q_remove_denom(B0, &dB);
    3103       40523 :   if (!dB) B0 = leafcopy(B0);
    3104       40523 :   A = leafcopy(A);
    3105       40523 :   B = B0;
    3106       40523 :   setvarn(A,v);
    3107       45335 : INIT:
    3108       45335 :   if (lambda) B = RgX_Rg_translate(B0, monomial(stoi(lambda), 1, vY));
    3109       45335 :   B = swap_vars(B, vY, v);
    3110             :   /* B0(lambda v + x, v) */
    3111       45334 :   if (DEBUGLEVEL>4) err_printf("Trying lambda = %ld\n", lambda);
    3112             : 
    3113       45334 :   degB = degpol(B);
    3114       45334 :   init_modular_big(&S);
    3115             :   while (1)
    3116           0 :   {
    3117       45334 :     ulong p = u_forprime_next(&S);
    3118       45334 :     ulong dp = dB ? umodiu(dB, p): 1;
    3119       45334 :     if (!dp) continue;
    3120       45334 :     a = ZX_to_Flx(A, p);
    3121       45335 :     b = ZXX_to_FlxX(B, p, v);
    3122       45335 :     Hp = ZX_ZXY_resultant_prime(a, b, dp, p, degA, degB, dres, sX);
    3123       45335 :     if (degpol(Hp) != dres) continue;
    3124       45335 :     if (dp != 1) Hp = Flx_Fl_mul(Hp, Fl_powu(Fl_inv(dp,p), degA, p), p);
    3125       45335 :     if (!Flx_is_squarefree(Hp, p)) { lambda = next_lambda(lambda); goto INIT; }
    3126       40522 :     if (DEBUGLEVEL>4) err_printf("Final lambda = %ld\n", lambda);
    3127       40522 :     (void)delete_var(); return gc_long(av,lambda);
    3128             :   }
    3129             : }
    3130             : 
    3131             : GEN
    3132       60562 : ZX_ZXY_rnfequation(GEN A, GEN B, long *lambda)
    3133             : {
    3134       60562 :   if (lambda)
    3135             :   {
    3136       40523 :     *lambda = ZX_ZXY_rnfequation_lambda(A, B, *lambda);
    3137       40522 :     if (*lambda) B = RgX_Rg_translate(B, monomial(stoi(*lambda), 1, varn(A)));
    3138             :   }
    3139       60561 :   return ZX_ZXY_resultant(A,B);
    3140             : }
    3141             : 
    3142             : static GEN
    3143       10350 : ZX_composedsum_slice(GEN A, GEN B, GEN P, GEN *mod)
    3144             : {
    3145       10350 :   pari_sp av = avma;
    3146       10350 :   long i, n = lg(P)-1;
    3147             :   GEN H, T;
    3148       10350 :   if (n == 1)
    3149             :   {
    3150        9848 :     ulong p = uel(P,1);
    3151        9848 :     GEN a = ZX_to_Flx(A, p), b = ZX_to_Flx(B, p);
    3152        9845 :     GEN Hp = Flx_composedsum(a, b, p);
    3153        9849 :     H = gc_upto(av, Flx_to_ZX(Hp));
    3154        9847 :     *mod = utoipos(p); return H;
    3155             :   }
    3156         502 :   T = ZV_producttree(P);
    3157         502 :   A = ZX_nv_mod_tree(A, P, T);
    3158         502 :   B = ZX_nv_mod_tree(B, P, T);
    3159         502 :   H = cgetg(n+1, t_VEC);
    3160        4526 :   for(i=1; i <= n; i++)
    3161             :   {
    3162        4024 :     ulong p = P[i];
    3163        4024 :     GEN a = gel(A,i), b = gel(B,i);
    3164        4024 :     gel(H,i) = Flx_composedsum(a, b, p);
    3165             :   }
    3166         502 :   H = nxV_chinese_center_tree(H, P, T, ZV_chinesetree(P, T));
    3167         502 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    3168             : }
    3169             : 
    3170             : GEN
    3171       10352 : ZX_composedsum_worker(GEN P, GEN A, GEN B)
    3172             : {
    3173       10352 :   GEN V = cgetg(3, t_VEC);
    3174       10350 :   gel(V,1) = ZX_composedsum_slice(A, B, P, &gel(V,2));
    3175       10350 :   return V;
    3176             : }
    3177             : 
    3178             : static GEN
    3179       10085 : ZX_composedsum_i(GEN A, GEN B, GEN lead)
    3180             : {
    3181       10085 :   pari_sp av = avma;
    3182             :   forprime_t S;
    3183             :   ulong bound;
    3184             :   GEN H, worker, mod;
    3185       10085 :   if (degpol(A) < degpol(B)) swap(A, B);
    3186       10085 :   if (!lead) lead  = mulii(leading_coeff(A),leading_coeff(B));
    3187       10085 :   bound = ZX_ZXY_ResBound_1(A, B);
    3188       10086 :   worker = snm_closure(is_entry("_ZX_composedsum_worker"), mkvec2(A,B));
    3189       10087 :   init_modular_big(&S);
    3190       10087 :   H = gen_crt("ZX_composedsum", worker, &S, lead, bound, 0, &mod,
    3191             :               nxV_chinese_center, FpX_center);
    3192       10086 :   return gc_upto(av, H);
    3193             : }
    3194             : 
    3195             : static long
    3196        9696 : ZX_compositum_lambda(GEN A, GEN B, GEN lead, long lambda)
    3197             : {
    3198        9696 :   pari_sp av = avma;
    3199             :   forprime_t S;
    3200             :   ulong p;
    3201        9696 :   init_modular_big(&S);
    3202        9696 :   p = u_forprime_next(&S);
    3203             :   while (1)
    3204         112 :   {
    3205             :     GEN Hp, a;
    3206        9808 :     if (DEBUGLEVEL>4) err_printf("Trying lambda = %ld\n", lambda);
    3207        9808 :     if (lead && dvdiu(lead,p)) { p = u_forprime_next(&S); continue; }
    3208        9802 :     a = ZX_to_Flx(ZX_rescale(A, stoi(-lambda)), p);
    3209        9804 :     Hp = Flx_composedsum(a, ZX_to_Flx(B, p), p);
    3210        9806 :     if (!Flx_is_squarefree(Hp, p)) { lambda = next_lambda(lambda); continue; }
    3211        9698 :     if (DEBUGLEVEL>4) err_printf("Final lambda = %ld\n", lambda);
    3212        9698 :     return gc_long(av, lambda);
    3213             :   }
    3214             : }
    3215             : 
    3216             : GEN
    3217        9698 : ZX_compositum(GEN A, GEN B, long *lambda)
    3218             : {
    3219        9698 :   GEN lead  = mulii(leading_coeff(A),leading_coeff(B));
    3220        9696 :   if (lambda)
    3221             :   {
    3222        9696 :     *lambda = ZX_compositum_lambda(A, B, lead, *lambda);
    3223        9698 :     A = ZX_rescale(A, stoi(-*lambda));
    3224             :   }
    3225        9700 :   return ZX_composedsum_i(A, B, lead);
    3226             : }
    3227             : 
    3228             : GEN
    3229         385 : ZX_composedsum(GEN A, GEN B)
    3230         385 : { return ZX_composedsum_i(A, B, NULL); }
    3231             : 
    3232             : static GEN
    3233         359 : ZXQX_composedsum_slice(GEN A, GEN B, GEN C, GEN P, GEN *mod)
    3234             : {
    3235         359 :   pari_sp av = avma;
    3236         359 :   long i, n = lg(P)-1, dC = degpol(C), v = varn(C);
    3237             :   GEN H, T;
    3238         359 :   if (n == 1)
    3239             :   {
    3240         181 :     ulong p = uel(P,1);
    3241         181 :     GEN a = ZXX_to_FlxX(A, p, v), b = ZXX_to_FlxX(B, p, v);
    3242         181 :     GEN c = ZX_to_Flx(C, p);
    3243         181 :     GEN Hp = FlxX_to_Flm(FlxqX_composedsum(a, b, c, p), dC);
    3244         181 :     H = gc_upto(av, Flm_to_ZM(Hp));
    3245         181 :     *mod = utoipos(p); return H;
    3246             :   }
    3247         178 :   T = ZV_producttree(P);
    3248         178 :   A = ZXX_nv_mod_tree(A, P, T, v);
    3249         178 :   B = ZXX_nv_mod_tree(B, P, T, v);
    3250         178 :   C = ZX_nv_mod_tree(C, P, T);
    3251         178 :   H = cgetg(n+1, t_VEC);
    3252         660 :   for(i=1; i <= n; i++)
    3253             :   {
    3254         482 :     ulong p = P[i];
    3255         482 :     GEN a = gel(A,i), b = gel(B,i), c = gel(C,i);
    3256         482 :     gel(H,i) = FlxX_to_Flm(FlxqX_composedsum(a, b, c, p), dC);
    3257             :   }
    3258         178 :   H = nmV_chinese_center_tree_seq(H, P, T, ZV_chinesetree(P, T));
    3259         178 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    3260             : }
    3261             : 
    3262             : GEN
    3263         359 : ZXQX_composedsum_worker(GEN P, GEN A, GEN B, GEN C)
    3264             : {
    3265         359 :   GEN V = cgetg(3, t_VEC);
    3266         359 :   gel(V,1) = ZXQX_composedsum_slice(A, B, C, P, &gel(V,2));
    3267         359 :   return V;
    3268             : }
    3269             : 
    3270             : static GEN
    3271         315 : ZXQX_composedsum(GEN A, GEN B, GEN T, ulong bound)
    3272             : {
    3273         315 :   pari_sp av = avma;
    3274             :   forprime_t S;
    3275             :   GEN H, worker, mod;
    3276         315 :   GEN lead = mulii(Q_content(leading_coeff(A)), Q_content(leading_coeff(B)));
    3277         315 :   worker = snm_closure(is_entry("_ZXQX_composedsum_worker")
    3278             :                       , mkvec3(A,B,T));
    3279         315 :   init_modular_big(&S);
    3280         315 :   H = gen_crt("ZXQX_composedsum", worker, &S, lead, bound, 0, &mod,
    3281             :               nmV_chinese_center, FpM_center);
    3282         315 :   if (DEBUGLEVEL > 4)
    3283           0 :     err_printf("nfcompositum: a priori bound: %lu, a posteriori: %lu\n",
    3284             :                bound, expi(gsupnorm(H, DEFAULTPREC)));
    3285         315 :   return gc_GEN(av, RgM_to_RgXX(H, varn(A), varn(T)));
    3286             : }
    3287             : 
    3288             : static long
    3289         315 : ZXQX_composedsum_bound(GEN nf, GEN A, GEN B)
    3290         315 : { return ZXQX_resultant_bound_i(nf, A, B, &RgX_RgXY_ResBound_1); }
    3291             : 
    3292             : GEN
    3293         315 : nf_direct_compositum(GEN nf, GEN A, GEN B)
    3294             : {
    3295         315 :   ulong bnd = ZXQX_composedsum_bound(nf, A, B);
    3296         315 :   return ZXQX_composedsum(A, B, nf_get_pol(nf), bnd);
    3297             : }
    3298             : 
    3299             : /************************************************************************
    3300             :  *                                                                      *
    3301             :  *                   IRREDUCIBLE POLYNOMIAL / Fp                        *
    3302             :  *                                                                      *
    3303             :  ************************************************************************/
    3304             : 
    3305             : /* irreducible (unitary) polynomial of degree n over Fp */
    3306             : GEN
    3307           0 : ffinit_rand(GEN p,long n)
    3308             : {
    3309           0 :   for(;;) {
    3310           0 :     pari_sp av = avma;
    3311           0 :     GEN pol = ZX_add(pol_xn(n, 0), random_FpX(n-1,0, p));
    3312           0 :     if (FpX_is_irred(pol, p)) return pol;
    3313           0 :     set_avma(av);
    3314             :   }
    3315             : }
    3316             : 
    3317             : /* return an extension of degree 2^l of F_2, assume l > 0
    3318             :  * Not stack clean. */
    3319             : static GEN
    3320         608 : ffinit_Artin_Schreier_2(long l)
    3321             : {
    3322             :   GEN Q, T, S;
    3323             :   long i, v;
    3324             : 
    3325         608 :   if (l == 1) return mkvecsmall4(0,1,1,1); /*x^2 + x + 1*/
    3326         559 :   v = fetch_var_higher();
    3327         559 :   S = mkvecsmall5(0, 0, 0, 1, 1); /* y(y^2 + y) */
    3328         559 :   Q = mkpoln(3, pol1_Flx(0), pol1_Flx(0), S); /* x^2 + x + y(y^2+y) */
    3329         559 :   setvarn(Q, v);
    3330             : 
    3331             :   /* x^4+x+1, irred over F_2, minimal polynomial of a root of Q */
    3332         559 :   T = mkvecsmalln(6,evalvarn(v),1UL,1UL,0UL,0UL,1UL);
    3333             :   /* Q = x^2 + x + a(y) irred. over K = F2[y] / (T(y))
    3334             :    * ==> x^2 + x + a(y) b irred. over K for any root b of Q
    3335             :    * ==> x^2 + x + (b^2+b)b */
    3336        3091 :   for (i=2; i<l; i++) T = Flx_FlxY_resultant(T, Q, 2); /* minpoly(b) / F2*/
    3337         560 :   (void)delete_var(); T[1] = 0; return T;
    3338             : }
    3339             : 
    3340             : /* return an extension of degree p^l of F_p, assume l > 0
    3341             :  * Not stack clean. */
    3342             : GEN
    3343         965 : ffinit_Artin_Schreier(ulong p, long l)
    3344             : {
    3345             :   long i, v;
    3346             :   GEN Q, R, S, T, xp;
    3347         965 :   if (p==2) return ffinit_Artin_Schreier_2(l);
    3348         357 :   xp = polxn_Flx(p,0); /* x^p */
    3349         357 :   T = Flx_sub(xp, mkvecsmall3(0,1,1),p); /* x^p - x - 1 */
    3350         357 :   if (l == 1) return T;
    3351             : 
    3352           7 :   v = evalvarn(fetch_var_higher());
    3353           7 :   xp[1] = v;
    3354           7 :   R = Flx_sub(polxn_Flx(2*p-1,0), polxn_Flx(p,0),p);
    3355           7 :   S = Flx_sub(xp, polx_Flx(0), p);
    3356           7 :   Q = FlxX_Flx_sub(Flx_to_FlxX(S, v), R, p); /* x^p - x - (y^(2p-1)-y^p) */
    3357          14 :   for (i = 2; i <= l; ++i) T = Flx_FlxY_resultant(T, Q, p);
    3358           7 :   (void)delete_var(); T[1] = 0; return T;
    3359             : }
    3360             : 
    3361             : static long
    3362      149719 : flinit_check(ulong p, long n, long l)
    3363             : {
    3364             :   ulong q;
    3365      149719 :   if (!uisprime(n)) return 0;
    3366      102496 :   q = p % n; if (!q) return 0;
    3367       99885 :   return ugcd((n-1)/Fl_order(q, n-1, n), l) == 1;
    3368             : }
    3369             : 
    3370             : static GEN
    3371       31944 : flinit(ulong p, long l)
    3372             : {
    3373       31944 :   ulong n = 1+l;
    3374       96782 :   while (!flinit_check(p,n,l)) n += l;
    3375       31944 :   if (DEBUGLEVEL>=4) err_printf("FFInit: using polsubcyclo(%ld, %ld)\n",n,l);
    3376       31944 :   return ZX_to_Flx(polsubcyclo(n,l,0), p);
    3377             : }
    3378             : 
    3379             : static GEN
    3380       28999 : ffinit_fact_Flx(ulong p, long n)
    3381             : {
    3382       28999 :   GEN P, F = factoru_pow(n), Fp = gel(F,1), Fe = gel(F,2), Fm = gel(F,3);
    3383       28999 :   long i, l = lg(Fm);
    3384       28999 :   P = cgetg(l, t_VEC);
    3385       61909 :   for (i = 1; i < l; i++)
    3386       32909 :     gel(P,i) = p==uel(Fp,i) ? ffinit_Artin_Schreier(p, Fe[i])
    3387       32909 :                             : flinit(p, uel(Fm,i));
    3388       29000 :   return FlxV_composedsum(P, p);
    3389             : }
    3390             : 
    3391             : static GEN
    3392       52944 : init_Flxq_i(ulong p, long n, long sv)
    3393             : {
    3394             :   GEN P;
    3395       52944 :   if (!odd(p) && p != 2) pari_err_PRIME("ffinit", utoi(p));
    3396       52937 :   if (n == 1) return polx_Flx(sv);
    3397       52937 :   if (flinit_check(p, n+1, n))
    3398             :   {
    3399       23938 :     P = const_vecsmall(n+2,1);
    3400       23938 :     P[1] = sv; return P;
    3401             :   }
    3402       28999 :   P = ffinit_fact_Flx(p,n);
    3403       29000 :   P[1] = sv; return P;
    3404             : }
    3405             : 
    3406             : GEN
    3407           0 : init_Flxq(ulong p, long n, long v)
    3408             : {
    3409           0 :   pari_sp av = avma;
    3410           0 :   return gc_upto(av, init_Flxq_i(p, n, v));
    3411             : }
    3412             : 
    3413             : /* check if polsubcyclo(n,l,0) is irreducible modulo p */
    3414             : static long
    3415        8207 : fpinit_check(GEN p, long n, long l)
    3416             : {
    3417             :   ulong q;
    3418        8207 :   if (!uisprime(n)) return 0;
    3419        4842 :   q = umodiu(p,n); if (!q) return 0;
    3420        4842 :   return ugcd((n-1)/Fl_order(q, n-1, n), l) == 1;
    3421             : }
    3422             : 
    3423             : /* let k=2 if p%4==1, and k=4 else and assume k*p does not divide l.
    3424             :  * Return an irreducible polynomial of degree l over F_p.
    3425             :  * Variant of Adleman and Lenstra "Finding irreducible polynomials over
    3426             :  * finite fields", ACM, 1986 (5) 350--355.
    3427             :  * Not stack clean */
    3428             : static GEN
    3429        1828 : fpinit(GEN p, long l)
    3430             : {
    3431        1828 :   ulong n = 1+l;
    3432        6168 :   while (!fpinit_check(p,n,l)) n += l;
    3433        1828 :   if (DEBUGLEVEL>=4) err_printf("FFInit: using polsubcyclo(%ld, %ld)\n",n,l);
    3434        1828 :   return FpX_red(polsubcyclo(n,l,0),p);
    3435             : }
    3436             : 
    3437             : static GEN
    3438        1637 : ffinit_fact(GEN p, long n)
    3439             : {
    3440        1637 :   GEN P, F = factoru_pow(n), Fp = gel(F,1), Fe = gel(F,2), Fm = gel(F,3);
    3441        1637 :   long i, l = lg(Fm);
    3442        1637 :   P = cgetg(l, t_VEC);
    3443        3465 :   for (i = 1; i < l; ++i)
    3444        3656 :     gel(P,i) = absequaliu(p, Fp[i]) ?
    3445           0 :                  Flx_to_ZX(ffinit_Artin_Schreier(Fp[i], Fe[i]))
    3446        1828 :                : fpinit(p, Fm[i]);
    3447        1637 :   return FpXV_composedsum(P, p);
    3448             : }
    3449             : 
    3450             : static GEN
    3451       55249 : init_Fq_i(GEN p, long n, long v)
    3452             : {
    3453             :   GEN P;
    3454       55249 :   if (n <= 0) pari_err_DOMAIN("ffinit", "degree", "<=", gen_0, stoi(n));
    3455       55249 :   if (typ(p) != t_INT) pari_err_TYPE("ffinit",p);
    3456       55249 :   if (cmpiu(p, 2) < 0) pari_err_PRIME("ffinit",p);
    3457       55242 :   if (v < 0) v = 0;
    3458       55242 :   if (n == 1) return pol_x(v);
    3459       54990 :   if (lgefint(p) == 3)
    3460       52944 :     return Flx_to_ZX(init_Flxq_i(p[2], n, evalvarn(v)));
    3461        2046 :   if (!mpodd(p)) pari_err_PRIME("ffinit", p);
    3462        2039 :   if (fpinit_check(p, n+1, n)) return polcyclo(n+1, v);
    3463        1637 :   P = ffinit_fact(p,n);
    3464        1637 :   setvarn(P, v); return P;
    3465             : }
    3466             : GEN
    3467       54682 : init_Fq(GEN p, long n, long v)
    3468             : {
    3469       54682 :   pari_sp av = avma;
    3470       54682 :   return gc_upto(av, init_Fq_i(p, n, v));
    3471             : }
    3472             : GEN
    3473         567 : ffinit(GEN p, long n, long v)
    3474             : {
    3475         567 :   pari_sp av = avma;
    3476         567 :   return gc_upto(av, FpX_to_mod(init_Fq_i(p, n, v), p));
    3477             : }
    3478             : 
    3479             : GEN
    3480        3178 : ffnbirred(GEN p, long n)
    3481             : {
    3482        3178 :   pari_sp av = avma;
    3483        3178 :   GEN s = powiu(p,n), F = factoru(n), D = divisorsu_moebius(gel(F, 1));
    3484        3178 :   long j, l = lg(D);
    3485        6797 :   for (j = 2; j < l; j++) /* skip d = 1 */
    3486             :   {
    3487        3619 :     long md = D[j]; /* mu(d) * d, d squarefree */
    3488        3619 :     GEN pd = powiu(p, n / labs(md)); /* p^{n/d} */
    3489        3619 :     s = md > 0? addii(s, pd): subii(s,pd);
    3490             :   }
    3491        3178 :   return gc_INT(av, diviuexact(s, n));
    3492             : }
    3493             : 
    3494             : GEN
    3495         616 : ffsumnbirred(GEN p, long n)
    3496             : {
    3497         616 :   pari_sp av = avma, av2;
    3498         616 :   GEN q, t = p, v = vecfactoru_i(1, n);
    3499             :   long i;
    3500         616 :   q = cgetg(n+1,t_VEC); gel(q,1) = p;
    3501        1764 :   for (i=2; i<=n; i++) gel(q,i) = mulii(gel(q,i-1), p);
    3502         616 :   av2 = avma;
    3503        1764 :   for (i=2; i<=n; i++)
    3504             :   {
    3505        1148 :     GEN s = gel(q,i), F = gel(v,i), D = divisorsu_moebius(gel(F,1));
    3506        1148 :     long j, l = lg(D);
    3507        2534 :     for (j = 2; j < l; j++) /* skip 1 */
    3508             :     {
    3509        1386 :       long md = D[j];
    3510        1386 :       GEN pd = gel(q, i / labs(md)); /* p^{i/d} */
    3511        1386 :       s = md > 0? addii(s, pd): subii(s, pd);
    3512             :     }
    3513        1148 :     t = gc_INT(av2, addii(t, diviuexact(s, i)));
    3514             :   }
    3515         616 :   return gc_INT(av, t);
    3516             : }
    3517             : 
    3518             : GEN
    3519         140 : ffnbirred0(GEN p, long n, long flag)
    3520             : {
    3521         140 :   if (typ(p) != t_INT) pari_err_TYPE("ffnbirred", p);
    3522         140 :   if (n <= 0) pari_err_DOMAIN("ffnbirred", "degree", "<=", gen_0, stoi(n));
    3523         140 :   switch(flag)
    3524             :   {
    3525          70 :     case 0: return ffnbirred(p, n);
    3526          70 :     case 1: return ffsumnbirred(p, n);
    3527             :   }
    3528           0 :   pari_err_FLAG("ffnbirred");
    3529             :   return NULL; /* LCOV_EXCL_LINE */
    3530             : }
    3531             : 
    3532             : static void
    3533        2261 : checkmap(GEN m, const char *s)
    3534             : {
    3535        2261 :   if (typ(m)!=t_VEC || lg(m)!=3 || typ(gel(m,1))!=t_FFELT)
    3536           0 :     pari_err_TYPE(s,m);
    3537        2261 : }
    3538             : 
    3539             : GEN
    3540         189 : ffembed(GEN a, GEN b)
    3541             : {
    3542         189 :   pari_sp av = avma;
    3543         189 :   GEN p, Ta, Tb, g, r = NULL;
    3544         189 :   if (typ(a)!=t_FFELT) pari_err_TYPE("ffembed",a);
    3545         189 :   if (typ(b)!=t_FFELT) pari_err_TYPE("ffembed",b);
    3546         189 :   p = FF_p_i(a); g = FF_gen(a);
    3547         189 :   if (!equalii(p, FF_p_i(b))) pari_err_MODULUS("ffembed",a,b);
    3548         189 :   Ta = FF_mod(a);
    3549         189 :   Tb = FF_mod(b);
    3550         189 :   if (degpol(Tb)%degpol(Ta)!=0)
    3551           7 :     pari_err_DOMAIN("ffembed",GENtostr_raw(a),"is not a subfield of",b,a);
    3552         182 :   r = gel(FFX_roots(Ta, b), 1);
    3553         182 :   return gc_GEN(av, mkvec2(g,r));
    3554             : }
    3555             : 
    3556             : GEN
    3557          91 : ffextend(GEN a, GEN P, long v)
    3558             : {
    3559          91 :   pari_sp av = avma;
    3560             :   long n;
    3561             :   GEN p, T, R, g, m;
    3562          91 :   if (typ(a)!=t_FFELT) pari_err_TYPE("ffextend",a);
    3563          91 :   T = a; p = FF_p_i(a);
    3564          91 :   if (typ(P)!=t_POL || !RgX_is_FpXQX(P,&T,&p)) pari_err_TYPE("ffextend", P);
    3565          49 :   if (!FF_samefield(a, T)) pari_err_MODULUS("ffextend",a,T);
    3566          49 :   if (v < 0) v = varn(P);
    3567          49 :   n = FF_f(T) * degpol(P); R = ffinit(p, n, v); g = ffgen(R, v);
    3568          49 :   m = ffembed(a, g);
    3569          49 :   R = FFX_roots(ffmap(m, P),g);
    3570          49 :   return gc_GEN(av, mkvec2(gel(R,1), m));
    3571             : }
    3572             : 
    3573             : GEN
    3574          42 : fffrobenius(GEN a, long n)
    3575             : {
    3576          42 :   if (typ(a)!=t_FFELT) pari_err_TYPE("fffrobenius",a);
    3577          42 :   retmkvec2(FF_gen(a), FF_Frobenius(a, n));
    3578             : }
    3579             : 
    3580             : GEN
    3581         133 : ffinvmap(GEN m)
    3582             : {
    3583         133 :   pari_sp av = avma;
    3584             :   long i, l;
    3585         133 :   GEN T, F, a, g, r, f = NULL;
    3586         133 :   checkmap(m, "ffinvmap");
    3587         133 :   a = gel(m,1); r = gel(m,2);
    3588         133 :   if (typ(r) != t_FFELT)
    3589           7 :    pari_err_TYPE("ffinvmap", m);
    3590         126 :   g = FF_gen(a);
    3591         126 :   T = FF_mod(r);
    3592         126 :   F = gel(FFX_factor(T, a), 1);
    3593         126 :   l = lg(F);
    3594         490 :   for(i=1; i<l; i++)
    3595             :   {
    3596         490 :     GEN s = FFX_rem(FF_to_FpXQ_i(r), gel(F, i), a);
    3597         490 :     if (degpol(s)==0 && gequal(constant_coeff(s),g)) { f = gel(F, i); break; }
    3598             :   }
    3599         126 :   if (f==NULL) pari_err_TYPE("ffinvmap", m);
    3600         126 :   if (degpol(f)==1) f = FF_neg_i(gel(f,2));
    3601         126 :   return gc_GEN(av, mkvec2(FF_gen(r),f));
    3602             : }
    3603             : 
    3604             : static GEN
    3605        1260 : ffpartmapimage(const char *s, GEN r)
    3606             : {
    3607        1260 :    GEN a = NULL, p = NULL;
    3608        1260 :    if (typ(r)==t_POL && degpol(r) >= 1
    3609        1260 :       && RgX_is_FpXQX(r,&a,&p) && a && typ(a)==t_FFELT) return a;
    3610           0 :    pari_err_TYPE(s, r);
    3611             :    return NULL; /* LCOV_EXCL_LINE */
    3612             : }
    3613             : 
    3614             : static GEN
    3615        2709 : ffeltmap_i(GEN m, GEN x)
    3616             : {
    3617        2709 :    GEN r = gel(m,2);
    3618        2709 :    if (!FF_samefield(x, gel(m,1)))
    3619          84 :      pari_err_DOMAIN("ffmap","m","domain does not contain", x, r);
    3620        2625 :    if (typ(r)==t_FFELT)
    3621        1659 :      return FF_map(r, x);
    3622             :    else
    3623         966 :      return FFX_preimage(x, r, ffpartmapimage("ffmap", r));
    3624             : }
    3625             : 
    3626             : static GEN
    3627        4459 : ffmap_i(GEN m, GEN x)
    3628             : {
    3629             :   GEN y;
    3630        4459 :   long i, lx, tx = typ(x);
    3631        4459 :   switch(tx)
    3632             :   {
    3633        2541 :     case t_FFELT:
    3634        2541 :       return ffeltmap_i(m, x);
    3635        1267 :     case t_POL: case t_RFRAC: case t_SER:
    3636             :     case t_VEC: case t_COL: case t_MAT:
    3637        1267 :       y = cgetg_copy(x, &lx);
    3638        1988 :       for (i = 1; i < lontyp[tx]; i++) y[i] = x[i];
    3639        4564 :       for (; i < lx; i++)
    3640             :       {
    3641        3339 :         GEN yi = ffmap_i(m, gel(x,i));
    3642        3297 :         if (!yi) return NULL;
    3643        3297 :         gel(y,i) = yi;
    3644             :       }
    3645        1225 :       return y;
    3646             :   }
    3647         651 :   return gcopy(x);
    3648             : }
    3649             : 
    3650             : GEN
    3651        1036 : ffmap(GEN m, GEN x)
    3652             : {
    3653        1036 :   pari_sp ltop = avma;
    3654             :   GEN y;
    3655        1036 :   checkmap(m, "ffmap");
    3656        1036 :   y = ffmap_i(m, x);
    3657        1036 :   if (y) return y;
    3658          42 :   retgc_const(ltop, cgetg(1, t_VEC));
    3659             : }
    3660             : 
    3661             : static GEN
    3662         252 : ffeltmaprel_i(GEN m, GEN x)
    3663             : {
    3664         252 :    GEN g = gel(m,1), r = gel(m,2);
    3665         252 :    if (!FF_samefield(x, g))
    3666           0 :      pari_err_DOMAIN("ffmap","m","domain does not contain", x, r);
    3667         252 :    if (typ(r)==t_FFELT)
    3668          84 :      retmkpolmod(FF_map(r, x), pol_x(FF_var(g)));
    3669             :    else
    3670         168 :      retmkpolmod(FFX_preimagerel(x, r, ffpartmapimage("ffmap", r)), gcopy(r));
    3671             : }
    3672             : 
    3673             : static GEN
    3674         252 : ffmaprel_i(GEN m, GEN x)
    3675             : {
    3676         252 :   switch(typ(x))
    3677             :   {
    3678         252 :     case t_FFELT:
    3679         252 :       return ffeltmaprel_i(m, x);
    3680           0 :     case t_POL: pari_APPLY_pol_normalized(ffmaprel_i(m, gel(x,i)));
    3681           0 :     case t_SER: pari_APPLY_ser_normalized(ffmaprel_i(m, gel(x,i)));
    3682           0 :     case t_RFRAC: case t_VEC: case t_COL: case t_MAT:
    3683           0 :       pari_APPLY_same(ffmaprel_i(m, gel(x,i)));
    3684             :   }
    3685           0 :   return gcopy(x);
    3686             : }
    3687             : GEN
    3688         252 : ffmaprel(GEN m, GEN x) { checkmap(m, "ffmaprel"); return ffmaprel_i(m, x); }
    3689             : 
    3690             : static void
    3691          84 : err_compo(GEN m, GEN n)
    3692          84 : { pari_err_DOMAIN("ffcompomap","m","domain does not contain codomain of",n,m); }
    3693             : 
    3694             : GEN
    3695         420 : ffcompomap(GEN m, GEN n)
    3696             : {
    3697         420 :   pari_sp av = avma;
    3698         420 :   GEN g = gel(n,1), r, m2, n2;
    3699         420 :   checkmap(m, "ffcompomap");
    3700         420 :   checkmap(n, "ffcompomap");
    3701         420 :   m2 = gel(m,2); n2 = gel(n,2);
    3702         420 :   switch((typ(m2)==t_POL)|((typ(n2)==t_POL)<<1))
    3703             :   {
    3704          84 :     case 0:
    3705          84 :       if (!FF_samefield(gel(m,1),n2)) err_compo(m,n);
    3706          42 :       r = FF_map(gel(m,2), n2);
    3707          42 :       break;
    3708          84 :     case 2:
    3709          84 :       r = ffmap_i(m, n2);
    3710          42 :       if (lg(r) == 1) err_compo(m,n);
    3711          42 :       break;
    3712         168 :     case 1:
    3713         168 :       r = ffeltmap_i(m, n2);
    3714         126 :       if (!r)
    3715             :       {
    3716             :         GEN a, A, R, M;
    3717             :         long dm, dn;
    3718          42 :         a = ffpartmapimage("ffcompomap",m2);
    3719          42 :         A = FF_to_FpXQ_i(FF_neg(n2));
    3720          42 :         setvarn(A, 1);
    3721          42 :         R = deg1pol(gen_1, A, 0);
    3722          42 :         setvarn(R, 0);
    3723          42 :         M = gcopy(m2);
    3724          42 :         setvarn(M, 1);
    3725          42 :         r = polresultant0(R, M, 1, 0);
    3726          42 :         dm = FF_f(gel(m,1)); dn = FF_f(gel(n,1));
    3727          42 :         if (dm % dn || !FFX_ispower(r, dm/dn, a, &r)) err_compo(m,n);
    3728          42 :         setvarn(r, varn(FF_mod(g)));
    3729             :       }
    3730         126 :       break;
    3731          84 :     case 3:
    3732             :     {
    3733             :       GEN M, R, T, p, a;
    3734          84 :       a = ffpartmapimage("ffcompomap",n2);
    3735          84 :       if (!FF_samefield(a, gel(m,1))) err_compo(m,n);
    3736          42 :       p = FF_p_i(gel(n,1));
    3737          42 :       T = FF_mod(gel(n,1));
    3738          42 :       setvarn(T, 1);
    3739          42 :       R = RgX_to_FpXQX(n2,T,p);
    3740          42 :       setvarn(R, 0);
    3741          42 :       M = gcopy(m2);
    3742          42 :       setvarn(M, 1);
    3743          42 :       r = polresultant0(R, M, 1, 0);
    3744          42 :       setvarn(r, varn(n2));
    3745             :     }
    3746             :   }
    3747         252 :   return gc_GEN(av, mkvec2(g,r));
    3748             : }

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