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 v2.16.1 lcov report (development 28695-49bb1ac00f) Lines: 1744 1943 89.8 %
Date: 2023-09-24 07:47:42 Functions: 184 198 92.9 %
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        1239 : char_update_prime(struct charact *S, GEN p)
      37             : {
      38        1239 :   if (!S->isprime) { S->isprime = 1; S->q = p; }
      39        1239 :   if (!equalii(p, S->q)) pari_err_MODULUS("characteristic", S->q, p);
      40        1232 : }
      41             : static void
      42        6573 : char_update_int(struct charact *S, GEN n)
      43             : {
      44        6573 :   if (S->isprime)
      45             :   {
      46           7 :     if (dvdii(n, S->q)) return;
      47           7 :     pari_err_MODULUS("characteristic", S->q, n);
      48             :   }
      49        6566 :   S->q = gcdii(S->q, n);
      50             : }
      51             : static void
      52      162428 : charact(struct charact *S, GEN x)
      53             : {
      54      162428 :   const long tx = typ(x);
      55             :   long i, l;
      56      162428 :   switch(tx)
      57             :   {
      58        5124 :     case t_INTMOD:char_update_int(S, gel(x,1)); break;
      59        1148 :     case t_FFELT: char_update_prime(S, gel(x,4)); break;
      60       25823 :     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       25823 :       l = lg(x);
      64      172753 :       for (i=lontyp[tx]; i < l; i++) charact(S,gel(x,i));
      65       25809 :       break;
      66           7 :     case t_LIST:
      67           7 :       x = list_data(x);
      68           7 :       if (x) charact(S, x);
      69           7 :       break;
      70             :   }
      71      162400 : }
      72             : static void
      73        4634 : charact_res(struct charact *S, GEN x)
      74             : {
      75        4634 :   const long tx = typ(x);
      76             :   long i, l;
      77        4634 :   switch(tx)
      78             :   {
      79        1449 :     case t_INTMOD:char_update_int(S, gel(x,1)); break;
      80           0 :     case t_FFELT: char_update_prime(S, gel(x,4)); break;
      81          91 :     case t_PADIC: char_update_prime(S, gel(x,2)); break;
      82        1617 :     case t_COMPLEX: case t_QUAD:
      83             :     case t_POLMOD: case t_POL: case t_SER: case t_RFRAC:
      84             :     case t_VEC: case t_COL: case t_MAT:
      85        1617 :       l = lg(x);
      86        5922 :       for (i=lontyp[tx]; i < l; i++) charact_res(S,gel(x,i));
      87        1617 :       break;
      88           0 :     case t_LIST:
      89           0 :       x = list_data(x);
      90           0 :       if (x) charact_res(S, x);
      91           0 :       break;
      92             :   }
      93        4634 : }
      94             : GEN
      95       15484 : characteristic(GEN x)
      96             : {
      97             :   struct charact S;
      98       15484 :   S.q = gen_0; S.isprime = 0;
      99       15484 :   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    66105070 : Rg_is_Fp(GEN x, GEN *pp)
     111             : {
     112             :   GEN mod;
     113    66105070 :   switch(typ(x))
     114             :   {
     115     3196935 :   case t_INTMOD:
     116     3196935 :     mod = gel(x,1);
     117     3196935 :     if (!*pp) *pp = mod;
     118     2948932 :     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     3196935 :     return 1;
     124    54651277 :   case t_INT:
     125    54651277 :     return 1;
     126     8256858 :   default: return 0;
     127             :   }
     128             : }
     129             : 
     130             : int
     131    24834536 : RgX_is_FpX(GEN x, GEN *pp)
     132             : {
     133    24834536 :   long i, lx = lg(x);
     134    82656651 :   for (i=2; i<lx; i++)
     135    66078975 :     if (!Rg_is_Fp(gel(x, i), pp))
     136     8256864 :       return 0;
     137    16577676 :   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       59269 : Rg_is_FpXQ(GEN x, GEN *pT, GEN *pp)
     160             : {
     161             :   GEN pol, mod, p;
     162       59269 :   switch(typ(x))
     163             :   {
     164       26089 :   case t_INTMOD:
     165       26089 :     return Rg_is_Fp(x, pp);
     166        7070 :   case t_INT:
     167        7070 :     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        3199 : RgX_is_FpXQX(GEN x, GEN *pT, GEN *pp)
     202             : {
     203        3199 :   long i, lx = lg(x);
     204       61712 :   for (i = 2; i < lx; i++)
     205       58611 :     if (!Rg_is_FpXQ(gel(x,i), pT, pp)) return 0;
     206        3101 :   return 1;
     207             : }
     208             : 
     209             : /************************************************************************
     210             :  **                                                                    **
     211             :  **                      Ring conversion                               **
     212             :  **                                                                    **
     213             :  ************************************************************************/
     214             : 
     215             : /* p > 0 a t_INT, return lift(x * Mod(1,p)).
     216             :  * If x is an INTMOD, assume modulus is a multiple of p. */
     217             : GEN
     218    34339417 : Rg_to_Fp(GEN x, GEN p)
     219             : {
     220    34339417 :   if (lgefint(p) == 3) return utoi(Rg_to_Fl(x, uel(p,2)));
     221     4543285 :   switch(typ(x))
     222             :   {
     223      274756 :     case t_INT: return modii(x, p);
     224       18790 :     case t_FRAC: {
     225       18790 :       pari_sp av = avma;
     226       18790 :       GEN z = modii(gel(x,1), p);
     227       18790 :       if (z == gen_0) return gen_0;
     228       18785 :       return gerepileuptoint(av, remii(mulii(z, Fp_inv(gel(x,2), p)), p));
     229             :     }
     230          70 :     case t_PADIC: return padic_to_Fp(x, p);
     231     4249680 :     case t_INTMOD: {
     232     4249680 :       GEN q = gel(x,1), a = gel(x,2);
     233     4249680 :       if (equalii(q, p)) return icopy(a);
     234          14 :       if (!dvdii(q,p)) pari_err_MODULUS("Rg_to_Fp", q, p);
     235           0 :       return remii(a, p);
     236             :     }
     237           0 :     default: pari_err_TYPE("Rg_to_Fp",x);
     238             :       return NULL; /* LCOV_EXCL_LINE */
     239             :   }
     240             : }
     241             : /* If x is a POLMOD, assume modulus is a multiple of T. */
     242             : GEN
     243     1290320 : Rg_to_FpXQ(GEN x, GEN T, GEN p)
     244             : {
     245     1290320 :   long ta, tx = typ(x), v = get_FpX_var(T);
     246             :   GEN a, b;
     247     1290320 :   if (is_const_t(tx))
     248             :   {
     249       58531 :     if (tx == t_FFELT)
     250             :     {
     251       17355 :       GEN z = FF_to_FpXQ(x);
     252       17355 :       setvarn(z, v);
     253       17355 :       return z;
     254             :     }
     255       41176 :     return scalar_ZX(degpol(T)? Rg_to_Fp(x, p): gen_0, v);
     256             :   }
     257     1231789 :   switch(tx)
     258             :   {
     259     1229710 :     case t_POLMOD:
     260     1229710 :       b = gel(x,1);
     261     1229710 :       a = gel(x,2); ta = typ(a);
     262     1229710 :       if (is_const_t(ta))
     263        4095 :         return scalar_ZX(degpol(T)? Rg_to_Fp(a, p): gen_0, v);
     264     1225615 :       b = RgX_to_FpX(b, p); if (varn(b) != v) break;
     265     1225615 :       a = RgX_to_FpX(a, p);
     266     1225615 :       if (ZX_equal(b,get_FpX_mod(T)) || signe(FpX_rem(b,T,p))==0)
     267     1225615 :         return FpX_rem(a, T, p);
     268           0 :       break;
     269        2079 :     case t_POL:
     270        2079 :       if (varn(x) != v) break;
     271        2079 :       return FpX_rem(RgX_to_FpX(x,p), T, p);
     272           0 :     case t_RFRAC:
     273           0 :       a = Rg_to_FpXQ(gel(x,1), T,p);
     274           0 :       b = Rg_to_FpXQ(gel(x,2), T,p);
     275           0 :       return FpXQ_div(a,b, T,p);
     276             :   }
     277           0 :   pari_err_TYPE("Rg_to_FpXQ",x);
     278             :   return NULL; /* LCOV_EXCL_LINE */
     279             : }
     280             : GEN
     281     3547500 : RgX_to_FpX(GEN x, GEN p)
     282             : {
     283             :   long i, l;
     284     3547500 :   GEN z = cgetg_copy(x, &l); z[1] = x[1];
     285    15777839 :   for (i = 2; i < l; i++) gel(z,i) = Rg_to_Fp(gel(x,i), p);
     286     3547500 :   return FpX_renormalize(z, l);
     287             : }
     288             : 
     289             : GEN
     290         140 : RgV_to_FpV(GEN x, GEN p)
     291         483 : { pari_APPLY_type(t_VEC, Rg_to_Fp(gel(x,i), p)) }
     292             : 
     293             : GEN
     294      948696 : RgC_to_FpC(GEN x, GEN p)
     295    11932542 : { pari_APPLY_type(t_COL, Rg_to_Fp(gel(x,i), p)) }
     296             : 
     297             : GEN
     298      134233 : RgM_to_FpM(GEN x, GEN p)
     299     1082887 : { pari_APPLY_same(RgC_to_FpC(gel(x,i), p)) }
     300             : 
     301             : GEN
     302      285930 : RgV_to_Flv(GEN x, ulong p)
     303     1172349 : { pari_APPLY_ulong(Rg_to_Fl(gel(x,i), p)) }
     304             : 
     305             : GEN
     306      114124 : RgM_to_Flm(GEN x, ulong p)
     307      392639 : { pari_APPLY_same(RgV_to_Flv(gel(x,i), p)) }
     308             : 
     309             : GEN
     310        5014 : RgX_to_FpXQX(GEN x, GEN T, GEN p)
     311             : {
     312        5014 :   long i, l = lg(x);
     313        5014 :   GEN z = cgetg(l, t_POL); z[1] = x[1];
     314       42911 :   for (i = 2; i < l; i++) gel(z,i) = Rg_to_FpXQ(gel(x,i), T,p);
     315        5014 :   return FpXQX_renormalize(z, l);
     316             : }
     317             : GEN
     318       45437 : RgX_to_FqX(GEN x, GEN T, GEN p)
     319             : {
     320       45437 :   long i, l = lg(x);
     321       45437 :   GEN z = cgetg(l, t_POL); z[1] = x[1];
     322       45437 :   if (T)
     323       10990 :     for (i = 2; i < l; i++) gel(z,i) = Rg_to_FpXQ(gel(x,i), T, p);
     324             :   else
     325      760088 :     for (i = 2; i < l; i++) gel(z,i) = Rg_to_Fp(gel(x,i), p);
     326       45437 :   return FpXQX_renormalize(z, l);
     327             : }
     328             : 
     329             : GEN
     330      219121 : RgC_to_FqC(GEN x, GEN T, GEN p)
     331             : {
     332      219121 :   long i, l = lg(x);
     333      219121 :   GEN z = cgetg(l, t_COL);
     334      219121 :   if (T)
     335     1429127 :     for (i = 1; i < l; i++) gel(z,i) = Rg_to_FpXQ(gel(x,i), T, p);
     336             :   else
     337           0 :     for (i = 1; i < l; i++) gel(z,i) = Rg_to_Fp(gel(x,i), p);
     338      219121 :   return z;
     339             : }
     340             : 
     341             : GEN
     342       52325 : RgM_to_FqM(GEN x, GEN T, GEN p)
     343      271418 : { pari_APPLY_same(RgC_to_FqC(gel(x, i), T, p)) }
     344             : 
     345             : /* lg(V) > 1 */
     346             : GEN
     347      851487 : FpXV_FpC_mul(GEN V, GEN W, GEN p)
     348             : {
     349      851487 :   pari_sp av = avma;
     350      851487 :   long i, l = lg(V);
     351      851487 :   GEN z = ZX_Z_mul(gel(V,1),gel(W,1));
     352     4201029 :   for(i=2; i<l; i++)
     353             :   {
     354     3349542 :     z = ZX_add(z, ZX_Z_mul(gel(V,i),gel(W,i)));
     355     3349542 :     if ((i & 7) == 0) z = gerepileupto(av, z);
     356             :   }
     357      851487 :   return gerepileupto(av, FpX_red(z,p));
     358             : }
     359             : 
     360             : GEN
     361       55832 : FqX_Fq_add(GEN y, GEN x, GEN T, GEN p)
     362             : {
     363       55832 :   long i, lz = lg(y);
     364             :   GEN z;
     365       55832 :   if (!T) return FpX_Fp_add(y, x, p);
     366        8666 :   if (lz == 2) return scalarpol(x, varn(y));
     367        7952 :   z = cgetg(lz,t_POL); z[1] = y[1];
     368        7952 :   gel(z,2) = Fq_add(gel(y,2),x, T, p);
     369        7952 :   if (lz == 3) z = FpXX_renormalize(z,lz);
     370             :   else
     371       33145 :     for(i=3;i<lz;i++) gel(z,i) = gcopy(gel(y,i));
     372        7952 :   return z;
     373             : }
     374             : 
     375             : GEN
     376        1094 : FqX_Fq_sub(GEN y, GEN x, GEN T, GEN p)
     377             : {
     378        1094 :   long i, lz = lg(y);
     379             :   GEN z;
     380        1094 :   if (!T) return FpX_Fp_sub(y, x, p);
     381        1094 :   if (lz == 2) return scalarpol(x, varn(y));
     382        1094 :   z = cgetg(lz,t_POL); z[1] = y[1];
     383        1094 :   gel(z,2) = Fq_sub(gel(y,2), x, T, p);
     384        1094 :   if (lz == 3) z = FpXX_renormalize(z,lz);
     385             :   else
     386       10303 :     for(i=3;i<lz;i++) gel(z,i) = gcopy(gel(y,i));
     387        1094 :   return z;
     388             : }
     389             : 
     390             : GEN
     391      149016 : FqX_Fq_mul_to_monic(GEN P, GEN U, GEN T, GEN p)
     392             : {
     393             :   long i, lP;
     394      149016 :   GEN res = cgetg_copy(P, &lP); res[1] = P[1];
     395      918537 :   for(i=2; i<lP-1; i++) gel(res,i) = Fq_mul(U,gel(P,i), T,p);
     396      149016 :   gel(res,lP-1) = gen_1; return res;
     397             : }
     398             : 
     399             : GEN
     400       38167 : FpXQX_normalize(GEN z, GEN T, GEN p)
     401             : {
     402             :   GEN lc;
     403       38167 :   if (lg(z) == 2) return z;
     404       38153 :   lc = leading_coeff(z);
     405       38153 :   if (typ(lc) == t_POL)
     406             :   {
     407        2159 :     if (lg(lc) > 3) /* nonconstant */
     408        1887 :       return FqX_Fq_mul_to_monic(z, Fq_inv(lc,T,p), T,p);
     409             :     /* constant */
     410         272 :     lc = gel(lc,2);
     411         272 :     z = shallowcopy(z);
     412         272 :     gel(z, lg(z)-1) = lc;
     413             :   }
     414             :   /* lc a t_INT */
     415       36266 :   if (equali1(lc)) return z;
     416          66 :   return FqX_Fq_mul_to_monic(z, Fp_inv(lc,p), T,p);
     417             : }
     418             : 
     419             : GEN
     420      398859 : FqX_eval(GEN x, GEN y, GEN T, GEN p)
     421             : {
     422             :   pari_sp av;
     423             :   GEN p1, r;
     424      398859 :   long j, i=lg(x)-1;
     425      398859 :   if (i<=2)
     426       45957 :     return (i==2)? Fq_red(gel(x,2), T, p): gen_0;
     427      352902 :   av=avma; p1=gel(x,i);
     428             :   /* specific attention to sparse polynomials (see poleval)*/
     429             :   /*You've guessed it! It's a copy-paste(tm)*/
     430     1173802 :   for (i--; i>=2; i=j-1)
     431             :   {
     432      821600 :     for (j=i; !signe(gel(x,j)); j--)
     433         700 :       if (j==2)
     434             :       {
     435         490 :         if (i!=j) y = Fq_pow(y,utoipos(i-j+1), T, p);
     436         490 :         return gerepileupto(av, Fq_mul(p1,y, T, p));
     437             :       }
     438      820900 :     r = (i==j)? y: Fq_pow(y, utoipos(i-j+1), T, p);
     439      820900 :     p1 = Fq_add(Fq_mul(p1,r,T,p), gel(x,j), T, p);
     440             :   }
     441      352412 :   return gerepileupto(av, p1);
     442             : }
     443             : 
     444             : GEN
     445       99679 : FqXY_evalx(GEN Q, GEN x, GEN T, GEN p)
     446             : {
     447       99679 :   long i, lb = lg(Q);
     448             :   GEN z;
     449       99679 :   if (!T) return FpXY_evalx(Q, x, p);
     450       89319 :   z = cgetg(lb, t_POL); z[1] = Q[1];
     451      474735 :   for (i=2; i<lb; i++)
     452             :   {
     453      385416 :     GEN q = gel(Q,i);
     454      385416 :     gel(z,i) = typ(q) == t_INT? modii(q,p): FqX_eval(q, x, T, p);
     455             :   }
     456       89319 :   return FpXQX_renormalize(z, lb);
     457             : }
     458             : 
     459             : /* Q an FpXY, evaluate at (X,Y) = (x,y) */
     460             : GEN
     461       14623 : FqXY_eval(GEN Q, GEN y, GEN x, GEN T, GEN p)
     462             : {
     463       14623 :   pari_sp av = avma;
     464       14623 :   if (!T) return FpXY_eval(Q, y, x, p);
     465         966 :   return gerepileupto(av, FqX_eval(FqXY_evalx(Q, x, T, p), y, T, p));
     466             : }
     467             : 
     468             : /* a X^d */
     469             : GEN
     470    10009376 : monomial(GEN a, long d, long v)
     471             : {
     472             :   long i, n;
     473             :   GEN P;
     474    10009376 :   if (d < 0) {
     475          14 :     if (isrationalzero(a)) return pol_0(v);
     476          14 :     retmkrfrac(a, pol_xn(-d, v));
     477             :   }
     478    10009362 :   if (gequal0(a))
     479             :   {
     480       93275 :     if (isexactzero(a)) return scalarpol_shallow(a,v);
     481           0 :     n = d+2; P = cgetg(n+1, t_POL);
     482           0 :     P[1] = evalsigne(0) | evalvarn(v);
     483             :   }
     484             :   else
     485             :   {
     486     9916089 :     n = d+2; P = cgetg(n+1, t_POL);
     487     9916091 :     P[1] = evalsigne(1) | evalvarn(v);
     488             :   }
     489    29040154 :   for (i = 2; i < n; i++) gel(P,i) = gen_0;
     490     9916091 :   gel(P,i) = a; return P;
     491             : }
     492             : GEN
     493     1863744 : monomialcopy(GEN a, long d, long v)
     494             : {
     495             :   long i, n;
     496             :   GEN P;
     497     1863744 :   if (d < 0) {
     498          14 :     if (isrationalzero(a)) return pol_0(v);
     499          14 :     retmkrfrac(gcopy(a), pol_xn(-d, v));
     500             :   }
     501     1863730 :   if (gequal0(a))
     502             :   {
     503          14 :     if (isexactzero(a)) return scalarpol(a,v);
     504           7 :     n = d+2; P = cgetg(n+1, t_POL);
     505           7 :     P[1] = evalsigne(0) | evalvarn(v);
     506             :   }
     507             :   else
     508             :   {
     509     1863716 :     n = d+2; P = cgetg(n+1, t_POL);
     510     1863716 :     P[1] = evalsigne(1) | evalvarn(v);
     511             :   }
     512     3511270 :   for (i = 2; i < n; i++) gel(P,i) = gen_0;
     513     1863723 :   gel(P,i) = gcopy(a); return P;
     514             : }
     515             : GEN
     516      323515 : pol_x_powers(long N, long v)
     517             : {
     518      323515 :   GEN L = cgetg(N+1,t_VEC);
     519             :   long i;
     520      781248 :   for (i=1; i<=N; i++) gel(L,i) = pol_xn(i-1, v);
     521      323514 :   return L;
     522             : }
     523             : 
     524             : GEN
     525           0 : FqXQ_powers(GEN x, long l, GEN S, GEN T, GEN p)
     526             : {
     527           0 :   return T ? FpXQXQ_powers(x, l, S, T, p): FpXQ_powers(x, l, S, p);
     528             : }
     529             : 
     530             : GEN
     531           0 : FqXQ_matrix_pow(GEN y, long n, long m, GEN S, GEN T, GEN p)
     532             : {
     533           0 :   return T ? FpXQXQ_matrix_pow(y, n, m, S, T, p): FpXQ_matrix_pow(y, n, m, S, p);
     534             : }
     535             : 
     536             : /*******************************************************************/
     537             : /*                                                                 */
     538             : /*                             Fq                                  */
     539             : /*                                                                 */
     540             : /*******************************************************************/
     541             : 
     542             : GEN
     543    11010528 : Fq_add(GEN x, GEN y, GEN T/*unused*/, GEN p)
     544             : {
     545             :   (void)T;
     546    11010528 :   switch((typ(x)==t_POL)|((typ(y)==t_POL)<<1))
     547             :   {
     548      544907 :     case 0: return Fp_add(x,y,p);
     549      764607 :     case 1: return FpX_Fp_add(x,y,p);
     550       92056 :     case 2: return FpX_Fp_add(y,x,p);
     551     9608958 :     case 3: return FpX_add(x,y,p);
     552             :   }
     553             :   return NULL;/*LCOV_EXCL_LINE*/
     554             : }
     555             : 
     556             : GEN
     557     8336935 : Fq_sub(GEN x, GEN y, GEN T/*unused*/, GEN p)
     558             : {
     559             :   (void)T;
     560     8336935 :   switch((typ(x)==t_POL)|((typ(y)==t_POL)<<1))
     561             :   {
     562      243999 :     case 0: return Fp_sub(x,y,p);
     563       24480 :     case 1: return FpX_Fp_sub(x,y,p);
     564       23908 :     case 2: return Fp_FpX_sub(x,y,p);
     565     8044548 :     case 3: return FpX_sub(x,y,p);
     566             :   }
     567             :   return NULL;/*LCOV_EXCL_LINE*/
     568             : }
     569             : 
     570             : GEN
     571      892325 : Fq_neg(GEN x, GEN T/*unused*/, GEN p)
     572             : {
     573             :   (void)T;
     574      892325 :   return (typ(x)==t_POL)? FpX_neg(x,p): Fp_neg(x,p);
     575             : }
     576             : 
     577             : GEN
     578       83614 : Fq_halve(GEN x, GEN T/*unused*/, GEN p)
     579             : {
     580             :   (void)T;
     581       83614 :   return (typ(x)==t_POL)? FpX_halve(x,p): Fp_halve(x,p);
     582             : }
     583             : 
     584             : /* If T==NULL do not reduce*/
     585             : GEN
     586     8008215 : Fq_mul(GEN x, GEN y, GEN T, GEN p)
     587             : {
     588     8008215 :   switch((typ(x)==t_POL)|((typ(y)==t_POL)<<1))
     589             :   {
     590      668961 :     case 0: return Fp_mul(x,y,p);
     591      128947 :     case 1: return FpX_Fp_mul(x,y,p);
     592      402242 :     case 2: return FpX_Fp_mul(y,x,p);
     593     6808067 :     case 3: if (T) return FpXQ_mul(x,y,T,p);
     594     4231198 :             else return FpX_mul(x,y,p);
     595             :   }
     596             :   return NULL;/*LCOV_EXCL_LINE*/
     597             : }
     598             : 
     599             : /* If T==NULL do not reduce*/
     600             : GEN
     601      492741 : Fq_mulu(GEN x, ulong y, /*unused*/GEN T, GEN p)
     602             : {
     603             :   (void) T;
     604      492741 :   return typ(x)==t_POL ? FpX_Fp_mul(x,utoi(y),p): Fp_mulu(x, y, p);
     605             : }
     606             : 
     607             : /* y t_INT */
     608             : GEN
     609       39037 : Fq_Fp_mul(GEN x, GEN y, GEN T/*unused*/, GEN p)
     610             : {
     611             :   (void)T;
     612        4933 :   return (typ(x) == t_POL)? FpX_Fp_mul(x,y,p)
     613       43970 :                           : Fp_mul(x,y,p);
     614             : }
     615             : /* If T==NULL do not reduce*/
     616             : GEN
     617      369591 : Fq_sqr(GEN x, GEN T, GEN p)
     618             : {
     619      369591 :   if (typ(x) == t_POL)
     620             :   {
     621       72844 :     if (T) return FpXQ_sqr(x,T,p);
     622           0 :     else return FpX_sqr(x,p);
     623             :   }
     624             :   else
     625      296747 :     return Fp_sqr(x,p);
     626             : }
     627             : 
     628             : GEN
     629           0 : Fq_neg_inv(GEN x, GEN T, GEN p)
     630             : {
     631           0 :   if (typ(x) == t_INT) return Fp_inv(Fp_neg(x,p),p);
     632           0 :   return FpXQ_inv(FpX_neg(x,p),T,p);
     633             : }
     634             : 
     635             : GEN
     636           0 : Fq_invsafe(GEN x, GEN pol, GEN p)
     637             : {
     638           0 :   if (typ(x) == t_INT) return Fp_invsafe(x,p);
     639           0 :   return FpXQ_invsafe(x,pol,p);
     640             : }
     641             : 
     642             : GEN
     643       89374 : Fq_inv(GEN x, GEN pol, GEN p)
     644             : {
     645       89374 :   if (typ(x) == t_INT) return Fp_inv(x,p);
     646       81608 :   return FpXQ_inv(x,pol,p);
     647             : }
     648             : 
     649             : GEN
     650      308357 : Fq_div(GEN x, GEN y, GEN pol, GEN p)
     651             : {
     652      308357 :   switch((typ(x)==t_POL)|((typ(y)==t_POL)<<1))
     653             :   {
     654      283038 :     case 0: return Fp_div(x,y,p);
     655       16702 :     case 1: return FpX_Fp_div(x,y,p);
     656         406 :     case 2: return FpX_Fp_mul(FpXQ_inv(y,pol,p),x,p);
     657        8211 :     case 3: return FpXQ_div(x,y,pol,p);
     658             :   }
     659             :   return NULL;/*LCOV_EXCL_LINE*/
     660             : }
     661             : 
     662             : GEN
     663      777262 : Fq_pow(GEN x, GEN n, GEN pol, GEN p)
     664             : {
     665      777262 :   if (typ(x) == t_INT) return Fp_pow(x,n,p);
     666      131061 :   return FpXQ_pow(x,n,pol,p);
     667             : }
     668             : 
     669             : GEN
     670       15050 : Fq_powu(GEN x, ulong n, GEN pol, GEN p)
     671             : {
     672       15050 :   if (typ(x) == t_INT) return Fp_powu(x,n,p);
     673        1267 :   return FpXQ_powu(x,n,pol,p);
     674             : }
     675             : 
     676             : GEN
     677      780730 : Fq_sqrt(GEN x, GEN T, GEN p)
     678             : {
     679      780730 :   if (typ(x) == t_INT)
     680             :   {
     681      710597 :     if (!T || odd(get_FpX_degree(T))) return Fp_sqrt(x,p);
     682        9610 :     x = scalarpol_shallow(x, get_FpX_var(T));
     683             :   }
     684       79743 :   return FpXQ_sqrt(x,T,p);
     685             : }
     686             : GEN
     687       60284 : Fq_sqrtn(GEN x, GEN n, GEN T, GEN p, GEN *zeta)
     688             : {
     689       60284 :   if (typ(x) == t_INT)
     690             :   {
     691             :     long d;
     692       59948 :     if (!T) return Fp_sqrtn(x,n,p,zeta);
     693         119 :     d = get_FpX_degree(T);
     694         119 :     if (ugcdiu(n,d) == 1)
     695             :     {
     696          56 :       if (!zeta) return Fp_sqrtn(x,n,p,NULL);
     697             :       /* gcd(n,p-1)=gcd(n,q-1): same number of solutions in Fp and F_q */
     698          21 :       if (equalii(gcdii(subiu(p,1),n), gcdii(subiu(Fp_powu(p,d,n), 1), n)))
     699          14 :         return Fp_sqrtn(x,n,p,zeta);
     700             :     }
     701          70 :     x = scalarpol(x, get_FpX_var(T)); /* left on stack */
     702             :   }
     703         406 :   return FpXQ_sqrtn(x,n,T,p,zeta);
     704             : }
     705             : 
     706             : struct _Fq_field
     707             : {
     708             :   GEN T, p;
     709             : };
     710             : 
     711             : static GEN
     712      302701 : _Fq_red(void *E, GEN x)
     713      302701 : { struct _Fq_field *s = (struct _Fq_field *)E;
     714      302701 :   return Fq_red(x, s->T, s->p);
     715             : }
     716             : 
     717             : static GEN
     718      362523 : _Fq_add(void *E, GEN x, GEN y)
     719             : {
     720             :   (void) E;
     721      362523 :   switch((typ(x)==t_POL)|((typ(y)==t_POL)<<1))
     722             :   {
     723          14 :     case 0: return addii(x,y);
     724           0 :     case 1: return ZX_Z_add(x,y);
     725       15918 :     case 2: return ZX_Z_add(y,x);
     726      346591 :     default: return ZX_add(x,y);
     727             :   }
     728             : }
     729             : 
     730             : static GEN
     731      315028 : _Fq_neg(void *E, GEN x) { (void) E; return typ(x)==t_POL?ZX_neg(x):negi(x); }
     732             : 
     733             : static GEN
     734      242795 : _Fq_mul(void *E, GEN x, GEN y)
     735             : {
     736             :   (void) E;
     737      242795 :   switch((typ(x)==t_POL)|((typ(y)==t_POL)<<1))
     738             :   {
     739         133 :     case 0: return mulii(x,y);
     740        1085 :     case 1: return ZX_Z_mul(x,y);
     741        1043 :     case 2: return ZX_Z_mul(y,x);
     742      240534 :     default: return ZX_mul(x,y);
     743             :   }
     744             : }
     745             : 
     746             : static GEN
     747        9331 : _Fq_inv(void *E, GEN x)
     748        9331 : { struct _Fq_field *s = (struct _Fq_field *)E;
     749        9331 :   return Fq_inv(x,s->T,s->p);
     750             : }
     751             : 
     752             : static int
     753       38388 : _Fq_equal0(GEN x) { return signe(x)==0; }
     754             : 
     755             : static GEN
     756       13965 : _Fq_s(void *E, long x) { (void) E; return stoi(x); }
     757             : 
     758             : static const struct bb_field Fq_field={_Fq_red,_Fq_add,_Fq_mul,_Fq_neg,
     759             :                                        _Fq_inv,_Fq_equal0,_Fq_s};
     760             : 
     761        4179 : const struct bb_field *get_Fq_field(void **E, GEN T, GEN p)
     762             : {
     763        4179 :   if (!T)
     764           0 :     return get_Fp_field(E, p);
     765             :   else
     766             :   {
     767        4179 :     GEN z = new_chunk(sizeof(struct _Fq_field));
     768        4179 :     struct _Fq_field *e = (struct _Fq_field *) z;
     769        4179 :     e->T = T; e->p  = p; *E = (void*)e;
     770        4179 :     return &Fq_field;
     771             :   }
     772             : }
     773             : 
     774             : /*******************************************************************/
     775             : /*                                                                 */
     776             : /*                             Fq[X]                               */
     777             : /*                                                                 */
     778             : /*******************************************************************/
     779             : /* P(X + c) */
     780             : GEN
     781         266 : FpX_translate(GEN P, GEN c, GEN p)
     782             : {
     783         266 :   pari_sp av = avma;
     784             :   GEN Q, *R;
     785             :   long i, k, n;
     786             : 
     787         266 :   if (!signe(P) || !signe(c)) return ZX_copy(P);
     788         266 :   Q = leafcopy(P);
     789         266 :   R = (GEN*)(Q+2); n = degpol(P);
     790        3738 :   for (i=1; i<=n; i++)
     791             :   {
     792      118153 :     for (k=n-i; k<n; k++)
     793      114681 :       R[k] = Fp_add(R[k], Fp_mul(c, R[k+1], p), p);
     794             : 
     795        3472 :     if (gc_needed(av,2))
     796             :     {
     797           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"FpX_translate, i = %ld/%ld", i,n);
     798           0 :       Q = gerepilecopy(av, Q); R = (GEN*)Q+2;
     799             :     }
     800             :   }
     801         266 :   return gerepilecopy(av, FpX_renormalize(Q, lg(Q)));
     802             : }
     803             : /* P(X + c), c an Fq */
     804             : GEN
     805       33880 : FqX_translate(GEN P, GEN c, GEN T, GEN p)
     806             : {
     807       33880 :   pari_sp av = avma;
     808             :   GEN Q, *R;
     809             :   long i, k, n;
     810             : 
     811             :   /* signe works for t_(INT|POL) */
     812       33880 :   if (!signe(P) || !signe(c)) return RgX_copy(P);
     813       33880 :   Q = leafcopy(P);
     814       33880 :   R = (GEN*)(Q+2); n = degpol(P);
     815      150059 :   for (i=1; i<=n; i++)
     816             :   {
     817      433559 :     for (k=n-i; k<n; k++)
     818      317380 :       R[k] = Fq_add(R[k], Fq_mul(c, R[k+1], T, p), T, p);
     819             : 
     820      116179 :     if (gc_needed(av,2))
     821             :     {
     822           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"FqX_translate, i = %ld/%ld", i,n);
     823           0 :       Q = gerepilecopy(av, Q); R = (GEN*)Q+2;
     824             :     }
     825             :   }
     826       33880 :   return gerepilecopy(av, FpXQX_renormalize(Q, lg(Q)));
     827             : }
     828             : 
     829             : GEN
     830       40551 : FqV_roots_to_pol(GEN V, GEN T, GEN p, long v)
     831             : {
     832       40551 :   pari_sp ltop = avma;
     833             :   long k;
     834             :   GEN W;
     835       40551 :   if (lgefint(p) == 3)
     836             :   {
     837       31754 :     ulong pp = p[2];
     838       31754 :     GEN Tl = ZX_to_Flx(T, pp);
     839       31753 :     GEN Vl = ZXC_to_FlxC(V, pp, get_Flx_var(Tl));
     840       31752 :     Tl = FlxqV_roots_to_pol(Vl, Tl, pp, v);
     841       31754 :     return gerepileupto(ltop, FlxX_to_ZXX(Tl));
     842             :   }
     843        8797 :   W = cgetg(lg(V),t_VEC);
     844       78691 :   for(k=1; k < lg(V); k++)
     845       69894 :     gel(W,k) = deg1pol_shallow(gen_1,Fq_neg(gel(V,k),T,p),v);
     846        8797 :   return gerepileupto(ltop, FpXQXV_prod(W, T, p));
     847             : }
     848             : 
     849             : GEN
     850      157171 : FqV_red(GEN x, GEN T, GEN p)
     851     1249142 : { pari_APPLY_same(Fq_red(gel(x,i), T, p)) }
     852             : 
     853             : GEN
     854           0 : FqC_add(GEN x, GEN y, GEN T, GEN p)
     855             : {
     856           0 :   if (!T) return FpC_add(x, y, p);
     857           0 :   pari_APPLY_type(t_COL, Fq_add(gel(x,i), gel(y,i), T, p))
     858             : }
     859             : 
     860             : GEN
     861           0 : FqC_sub(GEN x, GEN y, GEN T, GEN p)
     862             : {
     863           0 :   if (!T) return FpC_sub(x, y, p);
     864           0 :   pari_APPLY_type(t_COL, Fq_sub(gel(x,i), gel(y,i), T, p))
     865             : }
     866             : 
     867             : GEN
     868           0 : FqC_Fq_mul(GEN x, GEN y, GEN T, GEN p)
     869             : {
     870           0 :   if (!T) return FpC_Fp_mul(x, y, p);
     871           0 :   pari_APPLY_type(t_COL, Fq_mul(gel(x,i),y,T,p))
     872             : }
     873             : 
     874             : GEN
     875         105 : FqC_FqV_mul(GEN x, GEN y, GEN T, GEN p)
     876             : {
     877         105 :   long i,j, lx=lg(x), ly=lg(y);
     878             :   GEN z;
     879         105 :   if (ly==1) return cgetg(1,t_MAT);
     880         105 :   z = cgetg(ly,t_MAT);
     881         819 :   for (j=1; j < ly; j++)
     882             :   {
     883         714 :     GEN zj = cgetg(lx,t_COL);
     884        4200 :     for (i=1; i<lx; i++) gel(zj,i) = Fq_mul(gel(x,i),gel(y,j), T, p);
     885         714 :     gel(z, j) = zj;
     886             :   }
     887         105 :   return z;
     888             : }
     889             : 
     890             : GEN
     891        5271 : FpXC_center(GEN x, GEN p, GEN pov2)
     892       40524 : { pari_APPLY_type(t_COL, FpX_center(gel(x,i), p, pov2)) }
     893             : 
     894             : GEN
     895        1730 : FpXM_center(GEN x, GEN p, GEN pov2)
     896        7001 : { pari_APPLY_same(FpXC_center(gel(x,i), p, pov2)) }
     897             : 
     898             : /*******************************************************************/
     899             : /*                                                                 */
     900             : /*                          GENERIC CRT                            */
     901             : /*                                                                 */
     902             : /*******************************************************************/
     903             : static GEN
     904     6005435 : primelist(forprime_t *S, long n, GEN dB)
     905             : {
     906     6005435 :   GEN P = cgetg(n+1, t_VECSMALL);
     907     6005390 :   long i = 1;
     908             :   ulong p;
     909    14901784 :   while (i <= n && (p = u_forprime_next(S)))
     910     8896393 :     if (!dB || umodiu(dB, p)) P[i++] = p;
     911     6005388 :   return P;
     912             : }
     913             : 
     914             : void
     915     5573125 : gen_inccrt_i(const char *str, GEN worker, GEN dB, long n, long mmin,
     916             :              forprime_t *S, GEN *pH, GEN *pmod, GEN crt(GEN, GEN, GEN*),
     917             :              GEN center(GEN, GEN, GEN))
     918             : {
     919     5573125 :   long m = mmin? minss(mmin, n): usqrt(n);
     920             :   GEN  H, P, mod;
     921             :   pari_timer ti;
     922     5573115 :   if (DEBUGLEVEL > 4)
     923             :   {
     924           0 :     timer_start(&ti);
     925           0 :     err_printf("%s: nb primes: %ld\n",str, n);
     926             :   }
     927     5573110 :   if (m == 1)
     928             :   {
     929     5358414 :     GEN P = primelist(S, n, dB);
     930     5358376 :     GEN done = closure_callgen1(worker, P);
     931     5358381 :     H = gel(done,1);
     932     5358381 :     mod = gel(done,2);
     933     5358381 :     if (!*pH && center) H = center(H, mod, shifti(mod,-1));
     934     5358333 :     if (DEBUGLEVEL>4) timer_printf(&ti,"%s: modular", str);
     935             :   }
     936             :   else
     937             :   {
     938      214696 :     long i, s = (n+m-1)/m, r = m - (m*s-n), di = 0;
     939             :     struct pari_mt pt;
     940      214696 :     long pending = 0;
     941      214696 :     H = cgetg(m+1, t_VEC); P = cgetg(m+1, t_VEC);
     942      214696 :     mt_queue_start_lim(&pt, worker, m);
     943      909943 :     for (i=1; i<=m || pending; i++)
     944             :     {
     945             :       GEN done;
     946      695247 :       GEN pr = i <= m ? mkvec(primelist(S, i<=r ? s: s-1, dB)): NULL;
     947      695248 :       mt_queue_submit(&pt, i, pr);
     948      695249 :       done = mt_queue_get(&pt, NULL, &pending);
     949      695249 :       if (done)
     950             :       {
     951      647027 :         di++;
     952      647027 :         gel(H, di) = gel(done,1);
     953      647027 :         gel(P, di) = gel(done,2);
     954      647027 :         if (DEBUGLEVEL>5) err_printf("%ld%% ",100*di/m);
     955             :       }
     956             :     }
     957      214696 :     mt_queue_end(&pt);
     958      214696 :     if (DEBUGLEVEL>5) err_printf("\n");
     959      214696 :     if (DEBUGLEVEL>4) timer_printf(&ti,"%s: modular", str);
     960      214696 :     H = crt(H, P, &mod);
     961      214696 :     if (DEBUGLEVEL>4) timer_printf(&ti,"%s: chinese", str);
     962             :   }
     963     5573029 :   if (*pH) H = crt(mkvec2(*pH, H), mkvec2(*pmod, mod), &mod);
     964     5573029 :   *pH = H; *pmod = mod;
     965     5573029 : }
     966             : void
     967     1990646 : gen_inccrt(const char *str, GEN worker, GEN dB, long n, long mmin,
     968             :            forprime_t *S, GEN *pH, GEN *pmod, GEN crt(GEN, GEN, GEN*),
     969             :            GEN center(GEN, GEN, GEN))
     970             : {
     971     1990646 :   pari_sp av = avma;
     972     1990646 :   gen_inccrt_i(str, worker, dB, n, mmin, S, pH, pmod, crt, center);
     973     1990555 :   gerepileall(av, 2, pH, pmod);
     974     1990693 : }
     975             : 
     976             : GEN
     977     1390292 : gen_crt(const char *str, GEN worker, forprime_t *S, GEN dB, ulong bound, long mmin, GEN *pmod,
     978             :         GEN crt(GEN, GEN, GEN*), GEN center(GEN, GEN, GEN))
     979             : {
     980     1390292 :   GEN mod = gen_1, H = NULL;
     981             :   ulong e;
     982             : 
     983     1390292 :   bound++;
     984     2780647 :   while (bound > (e = expi(mod)))
     985             :   {
     986     1390263 :     long n = (bound - e) / expu(S->p) + 1;
     987     1390284 :     gen_inccrt(str, worker, dB, n, mmin, S, &H, &mod, crt, center);
     988             :   }
     989     1390336 :   if (pmod) *pmod = mod;
     990     1390336 :   return H;
     991             : }
     992             : 
     993             : /*******************************************************************/
     994             : /*                                                                 */
     995             : /*                          MODULAR GCD                            */
     996             : /*                                                                 */
     997             : /*******************************************************************/
     998             : /* return z = a mod q, b mod p (p,q) = 1; qinv = 1/q mod p; a in ]-q,q] */
     999             : static GEN
    1000     5109246 : Fl_chinese_coprime(GEN a, ulong b, GEN q, ulong p, ulong qinv, GEN pq, GEN pq2)
    1001             : {
    1002     5109246 :   ulong d, amod = umodiu(a, p);
    1003     5109245 :   pari_sp av = avma;
    1004             :   GEN ax;
    1005             : 
    1006     5109245 :   if (b == amod) return NULL;
    1007     2104484 :   d = Fl_mul(Fl_sub(b, amod, p), qinv, p); /* != 0 */
    1008     2104951 :   if (d >= 1 + (p>>1))
    1009     1026751 :     ax = subii(a, mului(p-d, q));
    1010             :   else
    1011             :   {
    1012     1078200 :     ax = addii(a, mului(d, q)); /* in ]0, pq[ assuming a in ]-q,q[ */
    1013     1077819 :     if (cmpii(ax,pq2) > 0) ax = subii(ax,pq);
    1014             :   }
    1015     2104390 :   return gerepileuptoint(av, ax);
    1016             : }
    1017             : GEN
    1018         378 : Z_init_CRT(ulong Hp, ulong p) { return stoi(Fl_center(Hp, p, p>>1)); }
    1019             : GEN
    1020       31542 : ZX_init_CRT(GEN Hp, ulong p, long v)
    1021             : {
    1022       31542 :   long i, l = lg(Hp), lim = (long)(p>>1);
    1023       31542 :   GEN H = cgetg(l, t_POL);
    1024       31542 :   H[1] = evalsigne(1) | evalvarn(v);
    1025      794415 :   for (i=2; i<l; i++)
    1026      762873 :     gel(H,i) = stoi(Fl_center(Hp[i], p, lim));
    1027       31542 :   return ZX_renormalize(H,l);
    1028             : }
    1029             : 
    1030             : GEN
    1031        3633 : ZM_init_CRT(GEN Hp, ulong p)
    1032             : {
    1033        3633 :   long i,j, m, l = lg(Hp), lim = (long)(p>>1);
    1034        3633 :   GEN c, cp, H = cgetg(l, t_MAT);
    1035        3633 :   if (l==1) return H;
    1036        3633 :   m = lgcols(Hp);
    1037       12544 :   for (j=1; j<l; j++)
    1038             :   {
    1039        8911 :     cp = gel(Hp,j);
    1040        8911 :     c = cgetg(m, t_COL);
    1041        8911 :     gel(H,j) = c;
    1042       87983 :     for (i=1; i<m; i++) gel(c,i) = stoi(Fl_center(cp[i],p, lim));
    1043             :   }
    1044        3633 :   return H;
    1045             : }
    1046             : 
    1047             : int
    1048        7616 : Z_incremental_CRT(GEN *H, ulong Hp, GEN *ptq, ulong p)
    1049             : {
    1050        7616 :   GEN h, q = *ptq, qp = muliu(q,p);
    1051        7616 :   ulong qinv = Fl_inv(umodiu(q,p), p);
    1052        7616 :   int stable = 1;
    1053        7616 :   h = Fl_chinese_coprime(*H,Hp,q,p,qinv,qp,shifti(qp,-1));
    1054        7616 :   if (h) { *H = h; stable = 0; }
    1055        7616 :   *ptq = qp; return stable;
    1056             : }
    1057             : 
    1058             : static int
    1059      147063 : ZX_incremental_CRT_raw(GEN *ptH, GEN Hp, GEN q, GEN qp, ulong p)
    1060             : {
    1061      147063 :   GEN H = *ptH, h, qp2 = shifti(qp,-1);
    1062      147059 :   ulong qinv = Fl_inv(umodiu(q,p), p);
    1063      147063 :   long i, l = lg(H), lp = lg(Hp);
    1064      147063 :   int stable = 1;
    1065             : 
    1066      147063 :   if (l < lp)
    1067             :   { /* degree increases */
    1068           0 :     GEN x = cgetg(lp, t_POL);
    1069           0 :     for (i=1; i<l; i++)  x[i] = H[i];
    1070           0 :     for (   ; i<lp; i++) gel(x,i) = gen_0;
    1071           0 :     *ptH = H = x;
    1072           0 :     stable = 0;
    1073      147063 :   } else if (l > lp)
    1074             :   { /* degree decreases */
    1075           0 :     GEN x = cgetg(l, t_VECSMALL);
    1076           0 :     for (i=1; i<lp; i++)  x[i] = Hp[i];
    1077           0 :     for (   ; i<l; i++) x[i] = 0;
    1078           0 :     Hp = x; lp = l;
    1079             :   }
    1080     4928808 :   for (i=2; i<lp; i++)
    1081             :   {
    1082     4781818 :     h = Fl_chinese_coprime(gel(H,i),Hp[i],q,p,qinv,qp,qp2);
    1083     4781745 :     if (h) { gel(H,i) = h; stable = 0; }
    1084             :   }
    1085      146990 :   (void)ZX_renormalize(H,lp);
    1086      147065 :   return stable;
    1087             : }
    1088             : 
    1089             : int
    1090           0 : ZX_incremental_CRT(GEN *ptH, GEN Hp, GEN *ptq, ulong p)
    1091             : {
    1092           0 :   GEN q = *ptq, qp = muliu(q,p);
    1093           0 :   int stable = ZX_incremental_CRT_raw(ptH, Hp, q, qp, p);
    1094           0 :   *ptq = qp; return stable;
    1095             : }
    1096             : 
    1097             : int
    1098        5804 : ZM_incremental_CRT(GEN *pH, GEN Hp, GEN *ptq, ulong p)
    1099             : {
    1100        5804 :   GEN h, H = *pH, q = *ptq, qp = muliu(q, p), qp2 = shifti(qp,-1);
    1101        5804 :   ulong qinv = Fl_inv(umodiu(q,p), p);
    1102        5804 :   long i,j, l = lg(H), m = lgcols(H);
    1103        5804 :   int stable = 1;
    1104       20974 :   for (j=1; j<l; j++)
    1105      157241 :     for (i=1; i<m; i++)
    1106             :     {
    1107      142071 :       h = Fl_chinese_coprime(gcoeff(H,i,j), coeff(Hp,i,j),q,p,qinv,qp,qp2);
    1108      142071 :       if (h) { gcoeff(H,i,j) = h; stable = 0; }
    1109             :     }
    1110        5804 :   *ptq = qp; return stable;
    1111             : }
    1112             : 
    1113             : GEN
    1114         623 : ZXM_init_CRT(GEN Hp, long deg, ulong p)
    1115             : {
    1116             :   long i, j, k;
    1117             :   GEN H;
    1118         623 :   long m, l = lg(Hp), lim = (long)(p>>1), n;
    1119         623 :   H = cgetg(l, t_MAT);
    1120         623 :   if (l==1) return H;
    1121         623 :   m = lgcols(Hp);
    1122         623 :   n = deg + 3;
    1123        2114 :   for (j=1; j<l; j++)
    1124             :   {
    1125        1491 :     GEN cp = gel(Hp,j);
    1126        1491 :     GEN c = cgetg(m, t_COL);
    1127        1491 :     gel(H,j) = c;
    1128       23905 :     for (i=1; i<m; i++)
    1129             :     {
    1130       22414 :       GEN dp = gel(cp, i);
    1131       22414 :       long l = lg(dp);
    1132       22414 :       GEN d = cgetg(n, t_POL);
    1133       22414 :       gel(c, i) = d;
    1134       22414 :       d[1] = dp[1] | evalsigne(1);
    1135       45647 :       for (k=2; k<l; k++)
    1136       23233 :         gel(d,k) = stoi(Fl_center(dp[k], p, lim));
    1137       44457 :       for (   ; k<n; k++)
    1138       22043 :         gel(d,k) = gen_0;
    1139             :     }
    1140             :   }
    1141         623 :   return H;
    1142             : }
    1143             : 
    1144             : int
    1145         653 : ZXM_incremental_CRT(GEN *pH, GEN Hp, GEN *ptq, ulong p)
    1146             : {
    1147         653 :   GEN v, H = *pH, q = *ptq, qp = muliu(q, p), qp2 = shifti(qp,-1);
    1148         653 :   ulong qinv = Fl_inv(umodiu(q,p), p);
    1149         653 :   long i,j,k, l = lg(H), m = lgcols(H), n = lg(gmael(H,1,1));
    1150         653 :   int stable = 1;
    1151        2225 :   for (j=1; j<l; j++)
    1152       90418 :     for (i=1; i<m; i++)
    1153             :     {
    1154       88846 :       GEN h = gmael(H,j,i), hp = gmael(Hp,j,i);
    1155       88846 :       long lh = lg(hp);
    1156      246641 :       for (k=2; k<lh; k++)
    1157             :       {
    1158      157795 :         v = Fl_chinese_coprime(gel(h,k),uel(hp,k),q,p,qinv,qp,qp2);
    1159      157795 :         if (v) { gel(h,k) = v; stable = 0; }
    1160             :       }
    1161      108763 :       for (; k<n; k++)
    1162             :       {
    1163       19917 :         v = Fl_chinese_coprime(gel(h,k),0,q,p,qinv,qp,qp2);
    1164       19917 :         if (v) { gel(h,k) = v; stable = 0; }
    1165             :       }
    1166             :     }
    1167         653 :   *ptq = qp; return stable;
    1168             : }
    1169             : 
    1170             : /* record the degrees of Euclidean remainders (make them as large as
    1171             :  * possible : smaller values correspond to a degenerate sequence) */
    1172             : static void
    1173       23261 : Flx_resultant_set_dglist(GEN a, GEN b, GEN dglist, ulong p)
    1174             : {
    1175             :   long da,db,dc, ind;
    1176       23261 :   pari_sp av = avma;
    1177             : 
    1178       23261 :   if (lgpol(a)==0 || lgpol(b)==0) return;
    1179       21994 :   da = degpol(a);
    1180       21994 :   db = degpol(b);
    1181       21994 :   if (db > da)
    1182           0 :   { swapspec(a,b, da,db); }
    1183       21994 :   else if (!da) return;
    1184       21994 :   ind = 0;
    1185      144333 :   while (db)
    1186             :   {
    1187      122340 :     GEN c = Flx_rem(a,b, p);
    1188      122339 :     a = b; b = c; dc = degpol(c);
    1189      122340 :     if (dc < 0) break;
    1190             : 
    1191      122340 :     ind++;
    1192      122340 :     if (dc > dglist[ind]) dglist[ind] = dc;
    1193      122340 :     if (gc_needed(av,2))
    1194             :     {
    1195           0 :       if (DEBUGMEM>1) pari_warn(warnmem,"Flx_resultant_all");
    1196           0 :       gerepileall(av, 2, &a,&b);
    1197             :     }
    1198      122339 :     db = dc; /* = degpol(b) */
    1199             :   }
    1200       21993 :   if (ind+1 > lg(dglist)) setlg(dglist,ind+1);
    1201       21993 :   set_avma(av);
    1202             : }
    1203             : /* assuming the PRS finishes on a degree 1 polynomial C0 + C1X, with
    1204             :  * "generic" degree sequence as given by dglist, set *Ci and return
    1205             :  * resultant(a,b). Modular version of Collins's subresultant */
    1206             : static ulong
    1207     2082176 : Flx_resultant_all(GEN a, GEN b, long *C0, long *C1, GEN dglist, ulong p)
    1208             : {
    1209             :   long da,db,dc, ind;
    1210     2082176 :   ulong lb, res, g = 1UL, h = 1UL, ca = 1UL, cb = 1UL;
    1211     2082176 :   int s = 1;
    1212     2082176 :   pari_sp av = avma;
    1213             : 
    1214     2082176 :   *C0 = 1; *C1 = 0;
    1215     2082176 :   if (lgpol(a)==0 || lgpol(b)==0) return 0;
    1216     2072804 :   da = degpol(a);
    1217     2072805 :   db = degpol(b);
    1218     2072777 :   if (db > da)
    1219             :   {
    1220           0 :     swapspec(a,b, da,db);
    1221           0 :     if (both_odd(da,db)) s = -s;
    1222             :   }
    1223     2072777 :   else if (!da) return 1; /* = a[2] ^ db, since 0 <= db <= da = 0 */
    1224     2072777 :   ind = 0;
    1225    19789582 :   while (db)
    1226             :   { /* sub-resultant algo., applied to ca * a and cb * b, ca,cb scalars,
    1227             :      * da = deg a, db = deg b */
    1228    17721404 :     GEN c = Flx_rem(a,b, p);
    1229    17617082 :     long delta = da - db;
    1230             : 
    1231    17617082 :     if (both_odd(da,db)) s = -s;
    1232    17617477 :     lb = Fl_mul(b[db+2], cb, p);
    1233    17643608 :     a = b; b = c; dc = degpol(c);
    1234    17660283 :     ind++;
    1235    17660283 :     if (dc != dglist[ind]) return gc_ulong(av,0); /* degenerates */
    1236    17655392 :     if (g == h)
    1237             :     { /* frequent */
    1238    17595525 :       ulong cc = Fl_mul(ca, Fl_powu(Fl_div(lb,g,p), delta+1, p), p);
    1239    17660239 :       ca = cb;
    1240    17660239 :       cb = cc;
    1241             :     }
    1242             :     else
    1243             :     {
    1244       59867 :       ulong cc = Fl_mul(ca, Fl_powu(lb, delta+1, p), p);
    1245       59869 :       ulong ghdelta = Fl_mul(g, Fl_powu(h, delta, p), p);
    1246       59869 :       ca = cb;
    1247       59869 :       cb = Fl_div(cc, ghdelta, p);
    1248             :     }
    1249    17717192 :     da = db; /* = degpol(a) */
    1250    17717192 :     db = dc; /* = degpol(b) */
    1251             : 
    1252    17717192 :     g = lb;
    1253    17717192 :     if (delta == 1)
    1254    17617869 :       h = g; /* frequent */
    1255             :     else
    1256       99323 :       h = Fl_mul(h, Fl_powu(Fl_div(g,h,p), delta, p), p);
    1257             : 
    1258    17717500 :     if (gc_needed(av,2))
    1259             :     {
    1260           0 :       if (DEBUGMEM>1) pari_warn(warnmem,"Flx_resultant_all");
    1261           0 :       gerepileall(av, 2, &a,&b);
    1262             :     }
    1263             :   }
    1264     2068178 :   if (da > 1) return 0; /* Failure */
    1265             :   /* last nonconstant polynomial has degree 1 */
    1266     2068178 :   *C0 = Fl_mul(ca, a[2], p);
    1267     2068161 :   *C1 = Fl_mul(ca, a[3], p);
    1268     2068160 :   res = Fl_mul(cb, b[2], p);
    1269     2068185 :   if (s == -1) res = p - res;
    1270     2068185 :   return gc_ulong(av,res);
    1271             : }
    1272             : 
    1273             : /* Q a vector of polynomials representing B in Fp[X][Y], evaluate at X = x,
    1274             :  * Return 0 in case of degree drop. */
    1275             : static GEN
    1276     2105635 : FlxY_evalx_drop(GEN Q, ulong x, ulong p)
    1277             : {
    1278             :   GEN z;
    1279     2105635 :   long i, lb = lg(Q);
    1280     2105635 :   ulong leadz = Flx_eval(leading_coeff(Q), x, p);
    1281     2105226 :   long vs=mael(Q,2,1);
    1282     2105226 :   if (!leadz) return zero_Flx(vs);
    1283             : 
    1284     2094566 :   z = cgetg(lb, t_VECSMALL); z[1] = vs;
    1285    20053536 :   for (i=2; i<lb-1; i++) z[i] = Flx_eval(gel(Q,i), x, p);
    1286     2092561 :   z[i] = leadz; return z;
    1287             : }
    1288             : 
    1289             : GEN
    1290        2072 : FpXY_FpXQ_evaly(GEN Q, GEN y, GEN T, GEN p, long vx)
    1291             : {
    1292        2072 :   pari_sp av = avma;
    1293        2072 :   long i, lb = lg(Q);
    1294             :   GEN z;
    1295        2072 :   if (lb == 2) return pol_0(vx);
    1296        2072 :   z = gel(Q, lb-1);
    1297        2072 :   if (lb == 3 || !signe(y)) return typ(z)==t_INT? scalar_ZX(z, vx): ZX_copy(z);
    1298             : 
    1299        2072 :   if (typ(z) == t_INT) z = scalar_ZX_shallow(z, vx);
    1300       48636 :   for (i=lb-2; i>=2; i--)
    1301             :   {
    1302       46564 :     GEN c = gel(Q,i);
    1303       46564 :     z = FqX_Fq_mul(z, y, T, p);
    1304       46564 :     z = typ(c) == t_INT? FqX_Fq_add(z,c,T,p): FqX_add(z,c,T,p);
    1305             :   }
    1306        2072 :   return gerepileupto(av, z);
    1307             : }
    1308             : 
    1309             : static GEN
    1310      272219 : ZX_norml1(GEN x)
    1311             : {
    1312      272219 :   long i, l = lg(x);
    1313             :   GEN s;
    1314             : 
    1315      272219 :   if (l == 2) return gen_0;
    1316      179665 :   s = gel(x, l-1); /* != 0 */
    1317      657529 :   for (i = l-2; i > 1; i--) {
    1318      477870 :     GEN xi = gel(x,i);
    1319      477870 :     if (!signe(xi)) continue;
    1320      239790 :     s = addii_sign(s,1, xi,1);
    1321             :   }
    1322      179659 :   return s;
    1323             : }
    1324             : /* x >= 0, y != 0, return x + |y| */
    1325             : static GEN
    1326       25584 : addii_abs(GEN x, GEN y)
    1327             : {
    1328       25584 :   if (!signe(x)) return absi_shallow(y);
    1329       16048 :   return addii_sign(x,1, y,1);
    1330             : }
    1331             : 
    1332             : /* x a ZX, return sum_{i >= k} |x[i]| binomial(i, k) */
    1333             : static GEN
    1334       31705 : ZX_norml1_1(GEN x, long k)
    1335             : {
    1336       31705 :   long i, d = degpol(x);
    1337             :   GEN s, C; /* = binomial(i, k) */
    1338             : 
    1339       31704 :   if (!d || k > d) return gen_0;
    1340       31706 :   s = absi_shallow(gel(x, k+2)); /* may be 0 */
    1341       31707 :   C = gen_1;
    1342       68175 :   for (i = k+1; i <= d; i++) {
    1343       36466 :     GEN xi = gel(x,i+2);
    1344       36466 :     if (k) C = diviuexact(muliu(C, i), i-k);
    1345       36471 :     if (signe(xi)) s = addii_abs(s, mulii(C, xi));
    1346             :   }
    1347       31709 :   return s;
    1348             : }
    1349             : /* x has non-negative real coefficients */
    1350             : static GEN
    1351        3255 : RgX_norml1_1(GEN x, long k)
    1352             : {
    1353        3255 :   long i, d = degpol(x);
    1354             :   GEN s, C; /* = binomial(i, k) */
    1355             : 
    1356        3255 :   if (!d || k > d) return gen_0;
    1357        3255 :   s = gel(x, k+2); /* may be 0 */
    1358        3255 :   C = gen_1;
    1359        9128 :   for (i = k+1; i <= d; i++) {
    1360        5873 :     GEN xi = gel(x,i+2);
    1361        5873 :     if (k) C = diviuexact(muliu(C, i), i-k);
    1362        5873 :     if (!gequal0(xi)) s = gadd(s, gmul(C, xi));
    1363             :   }
    1364        3255 :   return s;
    1365             : }
    1366             : 
    1367             : /* N_2(A)^2 */
    1368             : static GEN
    1369        7108 : sqrN2(GEN A, long prec)
    1370             : {
    1371        7108 :   pari_sp av = avma;
    1372        7108 :   long i, l = lg(A);
    1373        7108 :   GEN a = gen_0;
    1374       34823 :   for (i = 2; i < l; i++)
    1375             :   {
    1376       27715 :     a = gadd(a, gabs(gnorm(gel(A,i)), prec));
    1377       27715 :     if (gc_needed(av,1))
    1378             :     {
    1379           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"RgX_RgXY_ResBound i = %ld",i);
    1380           0 :       a = gerepileupto(av, a);
    1381             :     }
    1382             :   }
    1383        7108 :   return a;
    1384             : }
    1385             : /* Interpolate at roots of 1 and use Hadamard bound for univariate resultant:
    1386             :  *   bound = N_2(A)^degpol B N_2(B)^degpol(A),  where
    1387             :  *     N_2(A) = sqrt(sum (N_1(Ai))^2)
    1388             :  * Return e such that Res(A, B) < 2^e */
    1389             : static GEN
    1390        6261 : RgX_RgXY_ResBound(GEN A, GEN B, long prec)
    1391             : {
    1392        6261 :   pari_sp av = avma;
    1393        6261 :   GEN b = gen_0, bnd;
    1394        6261 :   long i, lB = lg(B);
    1395       24712 :   for (i=2; i<lB; i++)
    1396             :   {
    1397       18451 :     GEN t = gel(B,i);
    1398       18451 :     if (typ(t) == t_POL) t = gnorml1(t, prec);
    1399       18451 :     b = gadd(b, gabs(gsqr(t), prec));
    1400       18451 :     if (gc_needed(av,1))
    1401             :     {
    1402           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"RgX_RgXY_ResBound i = %ld",i);
    1403           0 :       b = gerepileupto(av, b);
    1404             :     }
    1405             :   }
    1406        6261 :   bnd = gsqrt(gmul(gpowgs(sqrN2(A,prec), degpol(B)),
    1407             :                    gpowgs(b, degpol(A))), prec);
    1408        6261 :   return gerepileupto(av, bnd);
    1409             : }
    1410             : /* A,B in C[X] return RgX_RgXY_ResBound(A, B(x+y)) */
    1411             : static GEN
    1412         847 : RgX_RgXY_ResBound_1(GEN A, GEN B, long prec)
    1413             : {
    1414         847 :   pari_sp av = avma, av2;
    1415         847 :   GEN b = gen_0, bnd;
    1416         847 :   long i, lB = lg(B);
    1417         847 :   B = shallowcopy(B);
    1418        4102 :   for (i=2; i<lB; i++) gel(B,i) = gabs(gel(B,i), prec);
    1419         847 :   av2 = avma;
    1420        4102 :   for (i=2; i<lB; i++)
    1421             :   {
    1422        3255 :     b = gadd(b, gsqr(RgX_norml1_1(B, i-2)));
    1423        3255 :     if (gc_needed(av2,1))
    1424             :     {
    1425           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"RgX_RgXY_ResBound i = %ld",i);
    1426           0 :       b = gerepileupto(av2, b);
    1427             :     }
    1428             :   }
    1429         847 :   bnd = gsqrt(gmul(gpowgs(sqrN2(A,prec), degpol(B)),
    1430             :                    gpowgs(b, degpol(A))), prec);
    1431         847 :   return gerepileupto(av, bnd);
    1432             : }
    1433             : 
    1434             : /* log2 N_2(A)^2 */
    1435             : static double
    1436      184100 : log2N2(GEN A)
    1437             : {
    1438      184100 :   pari_sp av = avma;
    1439      184100 :   long i, l = lg(A);
    1440      184100 :   GEN a = gen_0;
    1441     1114283 :   for (i=2; i < l; i++)
    1442             :   {
    1443      930200 :     a = addii(a, sqri(gel(A,i)));
    1444      930183 :     if (gc_needed(av,1))
    1445             :     {
    1446           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"ZX_ZXY_ResBound i = %ld",i);
    1447           0 :       a = gerepileupto(av, a);
    1448             :     }
    1449             :   }
    1450      184083 :   return gc_double(av, dbllog2(a));
    1451             : }
    1452             : /* Interpolate at roots of 1 and use Hadamard bound for univariate resultant:
    1453             :  *   bound = N_2(A)^degpol B N_2(B)^degpol(A),  where
    1454             :  *     N_2(A) = sqrt(sum (N_1(Ai))^2)
    1455             :  * Return e such that Res(A, B) < 2^e */
    1456             : ulong
    1457      174001 : ZX_ZXY_ResBound(GEN A, GEN B, GEN dB)
    1458             : {
    1459      174001 :   pari_sp av = avma;
    1460      174001 :   GEN b = gen_0;
    1461      174001 :   long i, lB = lg(B);
    1462             :   double logb;
    1463     1015953 :   for (i=2; i<lB; i++)
    1464             :   {
    1465      841960 :     GEN t = gel(B,i);
    1466      841960 :     if (typ(t) == t_POL) t = ZX_norml1(t);
    1467      841961 :     b = addii(b, sqri(t));
    1468      841951 :     if (gc_needed(av,1))
    1469             :     {
    1470           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"ZX_ZXY_ResBound i = %ld",i);
    1471           0 :       b = gerepileupto(av, b);
    1472             :     }
    1473             :   }
    1474      173993 :   logb = dbllog2(b); if (dB) logb -= 2 * dbllog2(dB);
    1475      173999 :   i = (long)((degpol(B) * log2N2(A) + degpol(A) * logb) / 2);
    1476      173998 :   return gc_ulong(av, (i <= 0)? 1: 1 + (ulong)i);
    1477             : }
    1478             : /* A,B ZX. Return ZX_ZXY_ResBound(A(x), B(x+y)) */
    1479             : static ulong
    1480       10106 : ZX_ZXY_ResBound_1(GEN A, GEN B)
    1481             : {
    1482       10106 :   pari_sp av = avma;
    1483       10106 :   GEN b = gen_0;
    1484       10106 :   long i, lB = lg(B);
    1485       41806 :   for (i=2; i<lB; i++)
    1486             :   {
    1487       31704 :     b = addii(b, sqri(ZX_norml1_1(B, i-2)));
    1488       31699 :     if (gc_needed(av,1))
    1489             :     {
    1490           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"ZX_ZXY_ResBound i = %ld",i);
    1491           0 :       b = gerepileupto(av, b);
    1492             :     }
    1493             :   }
    1494       10102 :   i = (long)((degpol(B) * log2N2(A) + degpol(A) * dbllog2(b)) / 2);
    1495       10104 :   return gc_ulong(av, (i <= 0)? 1: 1 + (ulong)i);
    1496             : }
    1497             : /* special case B = A' */
    1498             : static ulong
    1499     1130682 : ZX_discbound(GEN A)
    1500             : {
    1501     1130682 :   pari_sp av = avma;
    1502     1130682 :   GEN a = gen_0, b = gen_0;
    1503     1130682 :   long i , lA = lg(A), dA = degpol(A);
    1504             :   double loga, logb;
    1505     6744136 :   for (i = 2; i < lA; i++)
    1506             :   {
    1507     5613840 :     GEN c = sqri(gel(A,i));
    1508     5613240 :     a = addii(a, c);
    1509     5613348 :     if (i > 2) b = addii(b, mulii(c, sqru(i-2)));
    1510     5613391 :     if (gc_needed(av,1))
    1511             :     {
    1512           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"ZX_discbound i = %ld",i);
    1513           0 :       gerepileall(av, 2, &a, &b);
    1514             :     }
    1515             :   }
    1516     1130296 :   loga = dbllog2(a);
    1517     1130568 :   logb = dbllog2(b); set_avma(av);
    1518     1130629 :   i = (long)(((dA-1) * loga + dA * logb) / 2);
    1519     1130629 :   return (i <= 0)? 1: 1 + (ulong)i;
    1520             : }
    1521             : 
    1522             : /* return Res(a(Y), b(n,Y)) over Fp. la = leading_coeff(a) [for efficiency] */
    1523             : static ulong
    1524     2254545 : Flx_FlxY_eval_resultant(GEN a, GEN b, ulong n, ulong p, ulong pi, ulong la)
    1525             : {
    1526     2254545 :   GEN ev = FlxY_evalx_pre(b, n, p, pi);
    1527     2254530 :   long drop = lg(b) - lg(ev);
    1528     2254530 :   ulong r = Flx_resultant_pre(a, ev, p, pi);
    1529     2254506 :   if (drop && la != 1) r = Fl_mul(r, Fl_powu_pre(la, drop, p, pi), p);
    1530     2254511 :   return r;
    1531             : }
    1532             : static GEN
    1533         284 : FpX_FpXY_eval_resultant(GEN a, GEN b, GEN n, GEN p, GEN la, long db, long vX)
    1534             : {
    1535         284 :   GEN ev = FpXY_evaly(b, n, p, vX);
    1536         284 :   long drop = db-degpol(ev);
    1537         284 :   GEN r = FpX_resultant(a, ev, p);
    1538         284 :   if (drop && !gequal1(la)) r = Fp_mul(r, Fp_powu(la, drop,p),p);
    1539         284 :   return r;
    1540             : }
    1541             : 
    1542             : /* assume dres := deg(Res_X(a,b), Y) <= deg(a,X) * deg(b,Y) < p */
    1543             : /* Return a Fly */
    1544             : static GEN
    1545      176868 : Flx_FlxY_resultant_polint(GEN a, GEN b, ulong p, ulong pi, long dres, long sx)
    1546             : {
    1547             :   long i;
    1548      176868 :   ulong n, la = Flx_lead(a);
    1549      176867 :   GEN  x = cgetg(dres+2, t_VECSMALL);
    1550      176867 :   GEN  y = cgetg(dres+2, t_VECSMALL);
    1551             :  /* Evaluate at dres+ 1 points: 0 (if dres even) and +/- n, so that P_n(X) =
    1552             :   * P_{-n}(-X), where P_i is Lagrange polynomial: P_i(j) = delta_{i,j} */
    1553     1218730 :   for (i=0,n = 1; i < dres; n++)
    1554             :   {
    1555     1041865 :     x[++i] = n;   y[i] = Flx_FlxY_eval_resultant(a,b, x[i], p,pi,la);
    1556     1041805 :     x[++i] = p-n; y[i] = Flx_FlxY_eval_resultant(a,b, x[i], p,pi,la);
    1557             :   }
    1558      176865 :   if (i == dres)
    1559             :   {
    1560      171439 :     x[++i] = 0;   y[i] = Flx_FlxY_eval_resultant(a,b, x[i], p,pi,la);
    1561             :   }
    1562      176868 :   return Flv_polint(x,y, p, sx);
    1563             : }
    1564             : 
    1565             : static GEN
    1566        8007 : FlxX_pseudorem(GEN x, GEN y, ulong p, ulong pi)
    1567             : {
    1568        8007 :   long vx = varn(x), dx, dy, dz, i, lx, dp;
    1569        8007 :   pari_sp av = avma, av2;
    1570             : 
    1571        8007 :   if (!signe(y)) pari_err_INV("FlxX_pseudorem",y);
    1572        8007 :   (void)new_chunk(2);
    1573        8009 :   dx=degpol(x); x = RgX_recip_i(x)+2;
    1574        8010 :   dy=degpol(y); y = RgX_recip_i(y)+2; dz=dx-dy; dp = dz+1;
    1575        8011 :   av2 = avma;
    1576             :   for (;;)
    1577             :   {
    1578       65389 :     gel(x,0) = Flx_neg(gel(x,0), p); dp--;
    1579      244147 :     for (i=1; i<=dy; i++)
    1580      177356 :       gel(x,i) = Flx_add( Flx_mul_pre(gel(y,0), gel(x,i), p, pi),
    1581      178721 :                           Flx_mul_pre(gel(x,0), gel(y,i), p, pi), p );
    1582     1137195 :     for (   ; i<=dx; i++)
    1583     1072776 :       gel(x,i) = Flx_mul_pre(gel(y,0), gel(x,i), p, pi);
    1584       69458 :     do { x++; dx--; } while (dx >= 0 && lg(gel(x,0))==2);
    1585       64419 :     if (dx < dy) break;
    1586       56415 :     if (gc_needed(av2,1))
    1587             :     {
    1588           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"FlxX_pseudorem dx = %ld >= %ld",dx,dy);
    1589           0 :       gerepilecoeffs(av2,x,dx+1);
    1590             :     }
    1591             :   }
    1592        8004 :   if (dx < 0) return zero_Flx(0);
    1593        8004 :   lx = dx+3; x -= 2;
    1594        8004 :   x[0]=evaltyp(t_POL) | evallg(lx);
    1595        8004 :   x[1]=evalsigne(1) | evalvarn(vx);
    1596        8004 :   x = RgX_recip_i(x);
    1597        8007 :   if (dp)
    1598             :   { /* multiply by y[0]^dp   [beware dummy vars from FpX_FpXY_resultant] */
    1599        2095 :     GEN t = Flx_powu_pre(gel(y,0), dp, p, pi);
    1600        8383 :     for (i=2; i<lx; i++) gel(x,i) = Flx_mul_pre(gel(x,i), t, p, pi);
    1601             :   }
    1602        8011 :   return gerepilecopy(av, x);
    1603             : }
    1604             : 
    1605             : /* return a Flx */
    1606             : GEN
    1607        2679 : FlxX_resultant(GEN u, GEN v, ulong p, long sx)
    1608             : {
    1609        2679 :   pari_sp av = avma, av2;
    1610             :   long degq, dx, dy, du, dv, dr, signh;
    1611             :   ulong pi;
    1612             :   GEN z, g, h, r, p1;
    1613             : 
    1614        2679 :   dx = degpol(u); dy = degpol(v); signh = 1;
    1615        2679 :   if (dx < dy)
    1616             :   {
    1617           7 :     swap(u,v); lswap(dx,dy);
    1618           7 :     if (both_odd(dx, dy)) signh = -signh;
    1619             :   }
    1620        2679 :   if (dy < 0) return zero_Flx(sx);
    1621        2679 :   pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    1622        2679 :   if (dy==0) return gerepileupto(av, Flx_powu_pre(gel(v,2),dx,p,pi));
    1623             : 
    1624        2679 :   g = h = pol1_Flx(sx); av2 = avma;
    1625             :   for(;;)
    1626             :   {
    1627        8007 :     r = FlxX_pseudorem(u,v,p,pi); dr = lg(r);
    1628        8009 :     if (dr == 2) { set_avma(av); return zero_Flx(sx); }
    1629        8009 :     du = degpol(u); dv = degpol(v); degq = du-dv;
    1630        8009 :     u = v; p1 = g; g = leading_coeff(u);
    1631        8010 :     switch(degq)
    1632             :     {
    1633           0 :       case 0: break;
    1634        5901 :       case 1:
    1635        5901 :         p1 = Flx_mul_pre(h,p1, p, pi); h = g; break;
    1636        2109 :       default:
    1637        2109 :         p1 = Flx_mul_pre(Flx_powu_pre(h,degq,p,pi), p1, p, pi);
    1638        2109 :         h = Flx_div_pre(Flx_powu_pre(g,degq,p,pi),
    1639        2107 :                         Flx_powu_pre(h,degq-1,p,pi), p, pi);
    1640             :     }
    1641        8004 :     if (both_odd(du,dv)) signh = -signh;
    1642        8003 :     v = FlxY_Flx_div(r, p1, p);
    1643        8005 :     if (dr==3) break;
    1644        5325 :     if (gc_needed(av2,1))
    1645             :     {
    1646           0 :       if(DEBUGMEM>1) pari_warn(warnmem,"FlxX_resultant, dr = %ld",dr);
    1647           0 :       gerepileall(av2,4, &u, &v, &g, &h);
    1648             :     }
    1649             :   }
    1650        2680 :   z = gel(v,2);
    1651        2680 :   if (dv > 1) z = Flx_div_pre(Flx_powu_pre(z,dv,p,pi),
    1652           0 :                               Flx_powu_pre(h,dv-1,p,pi), p, pi);
    1653        2680 :   if (signh < 0) z = Flx_neg(z,p);
    1654        2680 :   return gerepileupto(av, z);
    1655             : }
    1656             : 
    1657             : /* Warning:
    1658             :  * This function switches between valid and invalid variable ordering*/
    1659             : 
    1660             : static GEN
    1661        6296 : FlxY_to_FlyX(GEN b, long sv)
    1662             : {
    1663        6296 :   long i, n=-1;
    1664        6296 :   long sw = b[1]&VARNBITS;
    1665       21574 :   for(i=2;i<lg(b);i++) n = maxss(n,lgpol(gel(b,i)));
    1666        6296 :   return Flm_to_FlxX(Flm_transpose(FlxX_to_Flm(b,n)),sv,sw);
    1667             : }
    1668             : 
    1669             : /* Return a Fly*/
    1670             : GEN
    1671        6297 : Flx_FlxY_resultant(GEN a, GEN b, ulong p)
    1672             : {
    1673        6297 :   pari_sp ltop=avma;
    1674        6297 :   long dres = degpol(a)*degpol(b);
    1675        6296 :   long sx=a[1], sy=b[1]&VARNBITS;
    1676             :   GEN z;
    1677        6296 :   b = FlxY_to_FlyX(b,sx);
    1678        6293 :   if ((ulong)dres >= p)
    1679        2676 :     z = FlxX_resultant(Fly_to_FlxY(a, sy), b, p, sx);
    1680             :   else
    1681             :   {
    1682        3617 :     ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    1683        3617 :     z = Flx_FlxY_resultant_polint(a, b, p, pi, (ulong)dres, sy);
    1684             :   }
    1685        6297 :   return gerepileupto(ltop,z);
    1686             : }
    1687             : 
    1688             : /* return a t_POL (in variable v >= 0) whose coeffs are the coeffs of b,
    1689             :  * in variable v. This is an incorrect PARI object if initially varn(b) << v.
    1690             :  * We could return a vector of coeffs, but it is convenient to have degpol()
    1691             :  * and friends available. Even in that case, it will behave nicely with all
    1692             :  * functions treating a polynomial as a vector of coeffs (eg poleval).
    1693             :  * FOR INTERNAL USE! */
    1694             : GEN
    1695      125740 : swap_vars(GEN b0, long v)
    1696             : {
    1697      125740 :   long i, n = RgX_degree(b0, v);
    1698             :   GEN b, x;
    1699      125742 :   if (n < 0) return pol_0(v);
    1700      125742 :   b = cgetg(n+3, t_POL); x = b + 2;
    1701      125742 :   b[1] = evalsigne(1) | evalvarn(v);
    1702      639503 :   for (i=0; i<=n; i++) gel(x,i) = polcoef_i(b0, i, v);
    1703      125738 :   return b;
    1704             : }
    1705             : 
    1706             : /* assume varn(b) << varn(a) */
    1707             : /* return a FpY*/
    1708             : GEN
    1709          15 : FpX_FpXY_resultant(GEN a, GEN b, GEN p)
    1710             : {
    1711          15 :   long i,n,dres, db, vY = varn(b), vX = varn(a);
    1712             :   GEN la,x,y;
    1713             : 
    1714          15 :   if (lgefint(p) == 3)
    1715             :   {
    1716           0 :     ulong pp = uel(p,2);
    1717           0 :     b = ZXX_to_FlxX(b, pp, vX);
    1718           0 :     a = ZX_to_Flx(a, pp);
    1719           0 :     x = Flx_FlxY_resultant(a, b, pp);
    1720           0 :     return Flx_to_ZX(x);
    1721             :   }
    1722          15 :   db = RgXY_degreex(b);
    1723          15 :   dres = degpol(a)*degpol(b);
    1724          15 :   la = leading_coeff(a);
    1725          15 :   x = cgetg(dres+2, t_VEC);
    1726          15 :   y = cgetg(dres+2, t_VEC);
    1727             :  /* Evaluate at dres+ 1 points: 0 (if dres even) and +/- n, so that P_n(X) =
    1728             :   * P_{-n}(-X), where P_i is Lagrange polynomial: P_i(j) = delta_{i,j} */
    1729         157 :   for (i=0,n = 1; i < dres; n++)
    1730             :   {
    1731         142 :     gel(x,++i) = utoipos(n);
    1732         142 :     gel(y,i) = FpX_FpXY_eval_resultant(a,b,gel(x,i),p,la,db,vY);
    1733         142 :     gel(x,++i) = subiu(p,n);
    1734         142 :     gel(y,i) = FpX_FpXY_eval_resultant(a,b,gel(x,i),p,la,db,vY);
    1735             :   }
    1736          15 :   if (i == dres)
    1737             :   {
    1738           0 :     gel(x,++i) = gen_0;
    1739           0 :     gel(y,i) = FpX_FpXY_eval_resultant(a,b, gel(x,i), p,la,db,vY);
    1740             :   }
    1741          15 :   return FpV_polint(x,y, p, vY);
    1742             : }
    1743             : 
    1744             : GEN
    1745          79 : FpX_composedsum(GEN P, GEN Q, GEN p)
    1746             : {
    1747          79 :   pari_sp av = avma;
    1748          79 :   if (lgefint(p)==3)
    1749             :   {
    1750           0 :     ulong pp = p[2];
    1751           0 :     GEN z = Flx_composedsum(ZX_to_Flx(P, pp), ZX_to_Flx(Q, pp), pp);
    1752           0 :     return gerepileupto(av, Flx_to_ZX(z));
    1753             :   }
    1754             :   else
    1755             :   {
    1756          79 :     long n = 1+ degpol(P)*degpol(Q);
    1757          79 :     GEN Pl = FpX_invLaplace(FpX_Newton(P,n,p), p);
    1758          79 :     GEN Ql = FpX_invLaplace(FpX_Newton(Q,n,p), p);
    1759          79 :     GEN L = FpX_Laplace(FpXn_mul(Pl, Ql, n, p), p);
    1760          79 :     GEN lead = Fp_mul(Fp_powu(leading_coeff(P),degpol(Q), p),
    1761          79 :         Fp_powu(leading_coeff(Q),degpol(P), p), p);
    1762          79 :     GEN R = FpX_fromNewton(L, p);
    1763          79 :     return gerepileupto(av, FpX_Fp_mul(R, lead, p));
    1764             :   }
    1765             : }
    1766             : 
    1767             : GEN
    1768           0 : FpX_composedprod(GEN P, GEN Q, GEN p)
    1769             : {
    1770           0 :   pari_sp av = avma;
    1771           0 :   if (lgefint(p)==3)
    1772             :   {
    1773           0 :     ulong pp = p[2];
    1774           0 :     GEN z = Flx_composedprod(ZX_to_Flx(P, pp), ZX_to_Flx(Q, pp), pp);
    1775           0 :     return gerepileupto(av, Flx_to_ZX(z));
    1776             :   }
    1777             :   else
    1778             :   {
    1779           0 :     long n = 1+ degpol(P)*degpol(Q);
    1780           0 :     GEN L = FpX_convol(FpX_Newton(P,n,p), FpX_Newton(Q,n,p), p);
    1781           0 :     return gerepileupto(av,FpX_fromNewton(L, p));
    1782             :   }
    1783             : }
    1784             : 
    1785             : static GEN
    1786          79 : _FpX_composedsum(void *E, GEN a, GEN b)
    1787          79 : { return FpX_composedsum(a,b, (GEN)E); }
    1788             : 
    1789             : GEN
    1790        1574 : FpXV_composedsum(GEN V, GEN p)
    1791             : {
    1792        1574 :   if (lgefint(p)==3)
    1793             :   {
    1794           0 :     ulong pp = p[2];
    1795           0 :     return Flx_to_ZX(FlxV_composedsum(ZXV_to_FlxV(V, pp), pp));
    1796             :   }
    1797        1574 :   return gen_product(V, (void *)p, &_FpX_composedsum);
    1798             : }
    1799             : 
    1800             : /* 0, 1, -1, 2, -2, ... */
    1801             : #define next_lambda(a) (a>0 ? -a : 1-a)
    1802             : 
    1803             : /* Assume A in Z[Y], B in Q[Y][X], B squarefree in (Q[Y]/(A))[X] and
    1804             :  * Res_Y(A, B) in Z[X]. Find a small lambda (start from *lambda, use
    1805             :  * next_lambda successively) such that C(X) = Res_Y(A(Y), B(X + lambda Y))
    1806             :  * is squarefree, reset *lambda to the chosen value and return C. Set LERS to
    1807             :  * the Last nonconstant polynomial in the Euclidean Remainder Sequence */
    1808             : static GEN
    1809       20902 : ZX_ZXY_resultant_LERS(GEN A, GEN B0, long *plambda, GEN *LERS)
    1810             : {
    1811             :   ulong bound, dp;
    1812       20902 :   pari_sp av = avma, av2 = 0;
    1813       20902 :   long lambda = *plambda, degA = degpol(A), dres = degA*degpol(B0);
    1814             :   long stable, checksqfree, i,n, cnt, degB;
    1815       20902 :   long v, vX = varn(B0), vY = varn(A); /* vY < vX */
    1816             :   GEN x, y, dglist, B, q, a, b, ev, H, H0, H1, Hp, H0p, H1p, C0, C1;
    1817             :   forprime_t S;
    1818             : 
    1819       20902 :   if (degA == 1)
    1820             :   {
    1821         987 :     GEN a1 = gel(A,3), a0 = gel(A,2);
    1822         987 :     B = lambda? RgX_translate(B0, monomial(stoi(lambda), 1, vY)): B0;
    1823         987 :     H = gsubst(B, vY, gdiv(gneg(a0),a1));
    1824         987 :    if (!equali1(a1)) H = RgX_Rg_mul(H, powiu(a1, poldegree(B,vY)));
    1825         987 :     *LERS = mkvec2(scalarpol_shallow(a0,vX), scalarpol_shallow(a1,vX));
    1826         987 :     return gc_all(av, 2, &H, LERS);
    1827             :   }
    1828             : 
    1829       19915 :   dglist = Hp = H0p = H1p = C0 = C1 = NULL; /* gcc -Wall */
    1830       19915 :   C0 = cgetg(dres+2, t_VECSMALL);
    1831       19915 :   C1 = cgetg(dres+2, t_VECSMALL);
    1832       19915 :   dglist = cgetg(dres+1, t_VECSMALL);
    1833       19915 :   x = cgetg(dres+2, t_VECSMALL);
    1834       19915 :   y = cgetg(dres+2, t_VECSMALL);
    1835       19915 :   B0 = leafcopy(B0);
    1836       19915 :   A = leafcopy(A);
    1837       19914 :   B = B0;
    1838       19914 :   v = fetch_var_higher(); setvarn(A,v);
    1839             :   /* make sure p large enough */
    1840       20558 : INIT:
    1841             :   /* always except the first time */
    1842       20558 :   if (av2) { set_avma(av2); lambda = next_lambda(lambda); }
    1843       20558 :   if (lambda) B = RgX_translate(B0, monomial(stoi(lambda), 1, vY));
    1844       20558 :   B = swap_vars(B, vY); setvarn(B,v);
    1845             :   /* B0(lambda v + x, v) */
    1846       20559 :   if (DEBUGLEVEL>4) err_printf("Trying lambda = %ld\n", lambda);
    1847       20559 :   av2 = avma;
    1848             : 
    1849       20559 :   if (degA <= 3)
    1850             :   { /* sub-resultant faster for small degrees */
    1851        9926 :     H = RgX_resultant_all(A,B,&q);
    1852        9926 :     if (typ(q) != t_POL || degpol(q)!=1) goto INIT;
    1853        9443 :     H0 = gel(q,2);
    1854        9443 :     if (typ(H0) == t_POL) setvarn(H0,vX); else H0 = scalarpol(H0,vX);
    1855        9443 :     H1 = gel(q,3);
    1856        9443 :     if (typ(H1) == t_POL) setvarn(H1,vX); else H1 = scalarpol(H1,vX);
    1857        9443 :     if (!ZX_is_squarefree(H)) goto INIT;
    1858        9401 :     goto END;
    1859             :   }
    1860             : 
    1861       10633 :   H = H0 = H1 = NULL;
    1862       10633 :   degB = degpol(B);
    1863       10633 :   bound = ZX_ZXY_ResBound(A, B, NULL);
    1864       10633 :   if (DEBUGLEVEL>4) err_printf("bound for resultant coeffs: 2^%ld\n",bound);
    1865       10633 :   dp = 1;
    1866       10633 :   init_modular_big(&S);
    1867       10633 :   for(cnt = 0, checksqfree = 1;;)
    1868       49021 :   {
    1869       59654 :     ulong p = u_forprime_next(&S);
    1870             :     GEN Hi;
    1871       59654 :     a = ZX_to_Flx(A, p);
    1872       59655 :     b = ZXX_to_FlxX(B, p, varn(A));
    1873       59655 :     if (degpol(a) < degA || degpol(b) < degB) continue; /* p | lc(A)lc(B) */
    1874       59655 :     if (checksqfree)
    1875             :     { /* find degree list for generic Euclidean Remainder Sequence */
    1876       10633 :       long goal = minss(degpol(a), degpol(b)); /* longest possible */
    1877       72970 :       for (n=1; n <= goal; n++) dglist[n] = 0;
    1878       10633 :       setlg(dglist, 1);
    1879       23662 :       for (n=0; n <= dres; n++)
    1880             :       {
    1881       23262 :         ev = FlxY_evalx_drop(b, n, p);
    1882       23261 :         Flx_resultant_set_dglist(a, ev, dglist, p);
    1883       23262 :         if (lg(dglist)-1 == goal) break;
    1884             :       }
    1885             :       /* last pol in ERS has degree > 1 ? */
    1886       10633 :       goal = lg(dglist)-1;
    1887       10633 :       if (degpol(B) == 1) { if (!goal) goto INIT; }
    1888             :       else
    1889             :       {
    1890       10577 :         if (goal <= 1) goto INIT;
    1891       10520 :         if (dglist[goal] != 0 || dglist[goal-1] != 1) goto INIT;
    1892             :       }
    1893       10576 :       if (DEBUGLEVEL>4)
    1894           0 :         err_printf("Degree list for ERS (trials: %ld) = %Ps\n",n+1,dglist);
    1895             :     }
    1896             : 
    1897     2141992 :     for (i=0,n = 0; i <= dres; n++)
    1898             :     {
    1899     2082407 :       ev = FlxY_evalx_drop(b, n, p);
    1900     2082150 :       x[++i] = n; y[i] = Flx_resultant_all(a, ev, C0+i, C1+i, dglist, p);
    1901     2082394 :       if (!C1[i]) i--; /* C1(i) = 0. No way to recover C0(i) */
    1902             :     }
    1903       59585 :     Hi = Flv_Flm_polint(x, mkvec3(y,C0,C1), p, 0);
    1904       59598 :     Hp = gel(Hi,1); H0p = gel(Hi,2); H1p = gel(Hi,3);
    1905       59598 :     if (!H && degpol(Hp) != dres) continue;
    1906       59598 :     if (dp != 1) Hp = Flx_Fl_mul(Hp, Fl_powu(Fl_inv(dp,p), degA, p), p);
    1907       59598 :     if (checksqfree) {
    1908       10576 :       if (!Flx_is_squarefree(Hp, p)) goto INIT;
    1909       10514 :       if (DEBUGLEVEL>4) err_printf("Final lambda = %ld\n", lambda);
    1910       10514 :       checksqfree = 0;
    1911             :     }
    1912             : 
    1913       59536 :     if (!H)
    1914             :     { /* initialize */
    1915       10514 :       q = utoipos(p); stable = 0;
    1916       10514 :       H = ZX_init_CRT(Hp, p,vX);
    1917       10514 :       H0= ZX_init_CRT(H0p, p,vX);
    1918       10514 :       H1= ZX_init_CRT(H1p, p,vX);
    1919             :     }
    1920             :     else
    1921             :     {
    1922       49022 :       GEN qp = muliu(q,p);
    1923       49020 :       stable  = ZX_incremental_CRT_raw(&H, Hp, q,qp, p)
    1924       49022 :               & ZX_incremental_CRT_raw(&H0,H0p, q,qp, p)
    1925       49022 :               & ZX_incremental_CRT_raw(&H1,H1p, q,qp, p);
    1926       49021 :       q = qp;
    1927             :     }
    1928             :     /* could make it probabilistic for H ? [e.g if stable twice, etc]
    1929             :      * Probabilistic anyway for H0, H1 */
    1930       59535 :     if (DEBUGLEVEL>5 && (stable ||  ++cnt==100))
    1931           0 :     { cnt=0; err_printf("%ld%%%s ",100*expi(q)/bound,stable?"s":""); }
    1932       59535 :     if (stable && (ulong)expi(q) >= bound) break; /* DONE */
    1933       49021 :     if (gc_needed(av,2))
    1934             :     {
    1935           0 :       if (DEBUGMEM>1) pari_warn(warnmem,"ZX_ZXY_rnfequation");
    1936           0 :       gerepileall(av2, 4, &H, &q, &H0, &H1);
    1937             :     }
    1938             :   }
    1939       19915 : END:
    1940       19915 :   if (DEBUGLEVEL>5) err_printf(" done\n");
    1941       19915 :   setvarn(H, vX); (void)delete_var();
    1942       19915 :   *LERS = mkvec2(H0,H1);
    1943       19915 :   *plambda = lambda; return gc_all(av, 2, &H, LERS);
    1944             : }
    1945             : 
    1946             : GEN
    1947       58583 : ZX_ZXY_resultant_all(GEN A, GEN B, long *plambda, GEN *LERS)
    1948             : {
    1949       58583 :   if (LERS)
    1950             :   {
    1951       20902 :     if (!plambda)
    1952           0 :       pari_err_BUG("ZX_ZXY_resultant_all [LERS != NULL needs lambda]");
    1953       20902 :     return ZX_ZXY_resultant_LERS(A, B, plambda, LERS);
    1954             :   }
    1955       37681 :   return ZX_ZXY_rnfequation(A, B, plambda);
    1956             : }
    1957             : 
    1958             : /* If lambda = NULL, return caract(Mod(A, T)), T,A in Z[X].
    1959             :  * Otherwise find a small lambda such that caract (Mod(A + lambda X, T)) is
    1960             :  * squarefree */
    1961             : GEN
    1962        3525 : ZXQ_charpoly_sqf(GEN A, GEN T, long *lambda, long v)
    1963             : {
    1964        3525 :   pari_sp av = avma;
    1965             :   GEN R, a;
    1966             :   long dA;
    1967             :   int delvar;
    1968             : 
    1969        3525 :   if (v < 0) v = 0;
    1970        3525 :   switch (typ(A))
    1971             :   {
    1972        3525 :     case t_POL: dA = degpol(A); if (dA > 0) break;
    1973           0 :       A = constant_coeff(A);
    1974           0 :     default:
    1975           0 :       if (lambda) { A = scalar_ZX_shallow(A,varn(T)); dA = 0; break;}
    1976           0 :       return gerepileupto(av, gpowgs(gsub(pol_x(v), A), degpol(T)));
    1977             :   }
    1978        3525 :   delvar = 0;
    1979        3525 :   if (varn(T) == 0)
    1980             :   {
    1981        3319 :     long v0 = fetch_var(); delvar = 1;
    1982        3319 :     T = leafcopy(T); setvarn(T,v0);
    1983        3319 :     A = leafcopy(A); setvarn(A,v0);
    1984             :   }
    1985        3525 :   R = ZX_ZXY_rnfequation(T, deg1pol_shallow(gen_1, gneg_i(A), 0), lambda);
    1986        3525 :   if (delvar) (void)delete_var();
    1987        3525 :   setvarn(R, v); a = leading_coeff(T);
    1988        3525 :   if (!gequal1(a)) R = gdiv(R, powiu(a, dA));
    1989        3525 :   return gerepileupto(av, R);
    1990             : }
    1991             : 
    1992             : /* charpoly(Mod(A,T)), A may be in Q[X], but assume T and result are integral */
    1993             : GEN
    1994      119224 : ZXQ_charpoly(GEN A, GEN T, long v)
    1995             : {
    1996      119224 :   return (degpol(T) < 16) ? RgXQ_charpoly_i(A,T,v): ZXQ_charpoly_sqf(A,T, NULL, v);
    1997             : }
    1998             : 
    1999             : GEN
    2000        9723 : QXQ_charpoly(GEN A, GEN T, long v)
    2001             : {
    2002        9723 :   pari_sp av = avma;
    2003        9723 :   GEN den, B = Q_remove_denom(A, &den);
    2004        9723 :   GEN P = ZXQ_charpoly(B, T, v);
    2005        9723 :   return gerepilecopy(av, den ? RgX_rescale(P, ginv(den)): P);
    2006             : }
    2007             : 
    2008             : static ulong
    2009     3962775 : ZX_resultant_prime(GEN a, GEN b, GEN dB, long degA, long degB, ulong p)
    2010             : {
    2011     3962775 :   long dropa = degA - degpol(a), dropb = degB - degpol(b);
    2012             :   ulong H, dp;
    2013     3962657 :   if (dropa && dropb) return 0; /* p | lc(A), p | lc(B) */
    2014     3962657 :   H = Flx_resultant(a, b, p);
    2015     3962531 :   if (dropa)
    2016             :   { /* multiply by ((-1)^deg B lc(B))^(deg A - deg a) */
    2017           0 :     ulong c = b[degB+2]; /* lc(B) */
    2018           0 :     if (odd(degB)) c = p - c;
    2019           0 :     c = Fl_powu(c, dropa, p);
    2020           0 :     if (c != 1) H = Fl_mul(H, c, p);
    2021             :   }
    2022     3962531 :   else if (dropb)
    2023             :   { /* multiply by lc(A)^(deg B - deg b) */
    2024           0 :     ulong c = a[degA+2]; /* lc(A) */
    2025           0 :     c = Fl_powu(c, dropb, p);
    2026           0 :     if (c != 1) H = Fl_mul(H, c, p);
    2027             :   }
    2028     3962545 :   dp = dB ? umodiu(dB, p): 1;
    2029     3962545 :   if (dp != 1) H = Fl_mul(H, Fl_powu(Fl_inv(dp,p), degA, p), p);
    2030     3962543 :   return H;
    2031             : }
    2032             : 
    2033             : /* If B=NULL, assume B=A' */
    2034             : static GEN
    2035     1628120 : ZX_resultant_slice(GEN A, GEN B, GEN dB, GEN P, GEN *mod)
    2036             : {
    2037     1628120 :   pari_sp av = avma, av2;
    2038     1628120 :   long degA, degB, i, n = lg(P)-1;
    2039             :   GEN H, T;
    2040             : 
    2041     1628120 :   degA = degpol(A);
    2042     1628118 :   degB = B? degpol(B): degA - 1;
    2043     1628116 :   if (n == 1)
    2044             :   {
    2045      943273 :     ulong Hp, p = uel(P,1);
    2046      943273 :     GEN a = ZX_to_Flx(A, p), b = B? ZX_to_Flx(B, p): Flx_deriv(a, p);
    2047      943233 :     Hp = ZX_resultant_prime(a, b, dB, degA, degB, p);
    2048      943288 :     set_avma(av); *mod = utoipos(p); return utoi(Hp);
    2049             :   }
    2050      684843 :   T = ZV_producttree(P);
    2051      684839 :   A = ZX_nv_mod_tree(A, P, T);
    2052      684842 :   if (B) B = ZX_nv_mod_tree(B, P, T);
    2053      684842 :   H = cgetg(n+1, t_VECSMALL); av2 = avma;
    2054     3704159 :   for(i=1; i <= n; i++, set_avma(av2))
    2055             :   {
    2056     3019324 :     ulong p = P[i];
    2057     3019324 :     GEN a = gel(A,i), b = B? gel(B,i): Flx_deriv(a, p);
    2058     3019561 :     H[i] = ZX_resultant_prime(a, b, dB, degA, degB, p);
    2059             :   }
    2060      684835 :   H = ZV_chinese_tree(H, P, T, ZV_chinesetree(P,T));
    2061      684842 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2062             : }
    2063             : 
    2064             : GEN
    2065     1628161 : ZX_resultant_worker(GEN P, GEN A, GEN B, GEN dB)
    2066             : {
    2067     1628161 :   GEN V = cgetg(3, t_VEC);
    2068     1628120 :   if (typ(B) == t_INT) B = NULL;
    2069     1628120 :   if (!signe(dB)) dB = NULL;
    2070     1628120 :   gel(V,1) = ZX_resultant_slice(A, B, dB, P, &gel(V,2));
    2071     1628149 :   return V;
    2072             : }
    2073             : 
    2074             : /* Compute Res(A, B/dB) in Z, assuming A,B in Z[X], dB in Z or NULL (= 1)
    2075             :  * If B=NULL, take B = A' and assume deg A > 1 and 'bound' is set */
    2076             : GEN
    2077     1297734 : ZX_resultant_all(GEN A, GEN B, GEN dB, ulong bound)
    2078             : {
    2079     1297734 :   pari_sp av = avma;
    2080             :   forprime_t S;
    2081             :   GEN  H, worker;
    2082     1297734 :   if (B)
    2083             :   {
    2084      105109 :     long a = degpol(A), b = degpol(B);
    2085      105109 :     if (a < 0 || b < 0) return gen_0;
    2086      105079 :     if (!a) return powiu(gel(A,2), b);
    2087      105079 :     if (!b) return powiu(gel(B,2), a);
    2088      103362 :     if (!bound) bound = ZX_ZXY_ResBound(A, B, dB);
    2089             :   }
    2090     1295987 :   worker = snm_closure(is_entry("_ZX_resultant_worker"),
    2091             :                        mkvec3(A, B? B: gen_0, dB? dB: gen_0));
    2092     1296062 :   init_modular_big(&S);
    2093     1296016 :   H = gen_crt("ZX_resultant_all", worker, &S, dB, bound, 0, NULL,
    2094             :               ZV_chinese_center, Fp_center);
    2095     1296046 :   return gerepileuptoint(av, H);
    2096             : }
    2097             : 
    2098             : /* A0 and B0 in Q[X] */
    2099             : GEN
    2100          56 : QX_resultant(GEN A0, GEN B0)
    2101             : {
    2102             :   GEN s, a, b, A, B;
    2103          56 :   pari_sp av = avma;
    2104             : 
    2105          56 :   A = Q_primitive_part(A0, &a);
    2106          56 :   B = Q_primitive_part(B0, &b);
    2107          56 :   s = ZX_resultant(A, B);
    2108          56 :   if (!signe(s)) { set_avma(av); return gen_0; }
    2109          56 :   if (a) s = gmul(s, gpowgs(a,degpol(B)));
    2110          56 :   if (b) s = gmul(s, gpowgs(b,degpol(A)));
    2111          56 :   return gerepileupto(av, s);
    2112             : }
    2113             : 
    2114             : GEN
    2115       24353 : ZX_resultant(GEN A, GEN B) { return ZX_resultant_all(A,B,NULL,0); }
    2116             : 
    2117             : GEN
    2118           0 : QXQ_intnorm(GEN A, GEN B)
    2119             : {
    2120             :   GEN c, n, R, lB;
    2121           0 :   long dA = degpol(A), dB = degpol(B);
    2122           0 :   pari_sp av = avma;
    2123           0 :   if (dA < 0) return gen_0;
    2124           0 :   A = Q_primitive_part(A, &c);
    2125           0 :   if (!c || typ(c) == t_INT) {
    2126           0 :     n = c;
    2127           0 :     R = ZX_resultant(B, A);
    2128             :   } else {
    2129           0 :     n = gel(c,1);
    2130           0 :     R = ZX_resultant_all(B, A, gel(c,2), 0);
    2131             :   }
    2132           0 :   if (n && !equali1(n)) R = mulii(R, powiu(n, dB));
    2133           0 :   lB = leading_coeff(B);
    2134           0 :   if (!equali1(lB)) R = diviiexact(R, powiu(lB, dA));
    2135           0 :   return gerepileuptoint(av, R);
    2136             : }
    2137             : 
    2138             : GEN
    2139       18732 : QXQ_norm(GEN A, GEN B)
    2140             : {
    2141             :   GEN c, R, lB;
    2142       18732 :   long dA = degpol(A), dB = degpol(B);
    2143       18732 :   pari_sp av = avma;
    2144       18732 :   if (dA < 0) return gen_0;
    2145       18732 :   A = Q_primitive_part(A, &c);
    2146       18732 :   R = ZX_resultant(B, A);
    2147       18732 :   if (c) R = gmul(R, gpowgs(c, dB));
    2148       18732 :   lB = leading_coeff(B);
    2149       18732 :   if (!equali1(lB)) R = gdiv(R, gpowgs(lB, dA));
    2150       18732 :   return gerepileupto(av, R);
    2151             : }
    2152             : 
    2153             : /* assume x has integral coefficients */
    2154             : GEN
    2155     1195689 : ZX_disc_all(GEN x, ulong bound)
    2156             : {
    2157     1195689 :   pari_sp av = avma;
    2158     1195689 :   long s, d = degpol(x);
    2159             :   GEN l, R;
    2160             : 
    2161     1195692 :   if (d <= 1) return d == 1? gen_1: gen_0;
    2162     1192672 :   s = (d & 2) ? -1: 1;
    2163     1192672 :   l = leading_coeff(x);
    2164     1192679 :   if (!bound) bound = ZX_discbound(x);
    2165     1192594 :   R = ZX_resultant_all(x, NULL, NULL, bound);
    2166     1192655 :   if (is_pm1(l))
    2167     1017406 :   { if (signe(l) < 0) s = -s; }
    2168             :   else
    2169      175245 :     R = diviiexact(R,l);
    2170     1192651 :   if (s == -1) togglesign_safe(&R);
    2171     1192654 :   return gerepileuptoint(av,R);
    2172             : }
    2173             : 
    2174             : GEN
    2175     1133641 : ZX_disc(GEN x) { return ZX_disc_all(x,0); }
    2176             : 
    2177             : static GEN
    2178        7273 : ZXQX_resultant_prime(GEN a, GEN b, GEN dB, long degA, long degB, GEN T, ulong p)
    2179             : {
    2180        7273 :   long dropa = degA - degpol(a), dropb = degB - degpol(b);
    2181             :   GEN H, dp;
    2182        7272 :   if (dropa && dropb) return pol0_Flx(T[1]); /* p | lc(A), p | lc(B) */
    2183        7272 :   H = FlxqX_saferesultant(a, b, T, p);
    2184        7271 :   if (!H) return NULL;
    2185        7271 :   if (dropa)
    2186             :   { /* multiply by ((-1)^deg B lc(B))^(deg A - deg a) */
    2187           0 :     GEN c = gel(b,degB+2); /* lc(B) */
    2188           0 :     if (odd(degB)) c = Flx_neg(c, p);
    2189           0 :     c = Flxq_powu(c, dropa, T, p);
    2190           0 :     if (!Flx_equal1(c)) H = Flxq_mul(H, c, T, p);
    2191             :   }
    2192        7271 :   else if (dropb)
    2193             :   { /* multiply by lc(A)^(deg B - deg b) */
    2194           0 :     GEN c = gel(a,degA+2); /* lc(A) */
    2195           0 :     c = Flxq_powu(c, dropb, T, p);
    2196           0 :     if (!Flx_equal1(c)) H = Flxq_mul(H, c, T, p);
    2197             :   }
    2198        7271 :   dp = dB ? ZX_to_Flx(dB, p): pol1_Flx(T[1]);
    2199        7272 :   if (!Flx_equal1(dp))
    2200             :   {
    2201           0 :     GEN idp = Flxq_invsafe(dp, T, p);
    2202           0 :     if (!idp) return NULL;
    2203           0 :     H = Flxq_mul(H, Flxq_powu(idp, degA, T, p), T, p);
    2204             :   }
    2205        7272 :   return H;
    2206             : }
    2207             : 
    2208             : /* If B=NULL, assume B=A' */
    2209             : static GEN
    2210        3547 : ZXQX_resultant_slice(GEN A, GEN B, GEN U, GEN dB, GEN P, GEN *mod)
    2211             : {
    2212        3547 :   pari_sp av = avma;
    2213        3547 :   long degA, degB, i, n = lg(P)-1;
    2214             :   GEN H, T;
    2215        3547 :   long v = varn(U), redo = 0;
    2216             : 
    2217        3547 :   degA = degpol(A);
    2218        3547 :   degB = B? degpol(B): degA - 1;
    2219        3547 :   if (n == 1)
    2220             :   {
    2221        2307 :     ulong p = uel(P,1);
    2222        2307 :     GEN a = ZXX_to_FlxX(A, p, v), b = B? ZXX_to_FlxX(B, p, v): FlxX_deriv(a, p);
    2223        2307 :     GEN u = ZX_to_Flx(U, p);
    2224        2307 :     GEN Hp = ZXQX_resultant_prime(a, b, dB, degA, degB, u, p);
    2225        2307 :     if (!Hp) { set_avma(av); *mod = gen_1; return pol_0(v); }
    2226        2307 :     Hp = gerepileupto(av, Flx_to_ZX(Hp)); *mod = utoipos(p); return Hp;
    2227             :   }
    2228        1240 :   T = ZV_producttree(P);
    2229        1240 :   A = ZXX_nv_mod_tree(A, P, T, v);
    2230        1240 :   if (B) B = ZXX_nv_mod_tree(B, P, T, v);
    2231        1240 :   U = ZX_nv_mod_tree(U, P, T);
    2232        1240 :   H = cgetg(n+1, t_VEC);
    2233        6204 :   for(i=1; i <= n; i++)
    2234             :   {
    2235        4964 :     ulong p = P[i];
    2236        4964 :     GEN a = gel(A,i), b = B? gel(B,i): FlxX_deriv(a, p), u = gel(U, i);
    2237        4966 :     GEN h = ZXQX_resultant_prime(a, b, dB, degA, degB, u, p);
    2238        4964 :     if (!h)
    2239             :     {
    2240           0 :       gel(H,i) = pol_0(v);
    2241           0 :       P[i] = 1; redo = 1;
    2242             :     }
    2243             :     else
    2244        4964 :       gel(H,i) = h;
    2245             :   }
    2246        1240 :   if (redo) T = ZV_producttree(P);
    2247        1240 :   H = nxV_chinese_center_tree(H, P, T, ZV_chinesetree(P, T));
    2248        1239 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2249             : }
    2250             : 
    2251             : GEN
    2252        3547 : ZXQX_resultant_worker(GEN P, GEN A, GEN B, GEN T, GEN dB)
    2253             : {
    2254        3547 :   GEN V = cgetg(3, t_VEC);
    2255        3547 :   if (isintzero(B)) B = NULL;
    2256        3547 :   if (!signe(dB)) dB = NULL;
    2257        3547 :   gel(V,1) = ZXQX_resultant_slice(A, B, T, dB, P, &gel(V,2));
    2258        3547 :   return V;
    2259             : }
    2260             : 
    2261             : static ulong
    2262        3265 : ZXQX_resultant_bound_i(GEN nf, GEN A, GEN B, GEN (*f)(GEN,GEN,long))
    2263             : {
    2264        3265 :   pari_sp av = avma;
    2265        3265 :   GEN r, M = nf_L2_bound(nf, NULL, &r);
    2266        3265 :   long v = nf_get_varn(nf), i, l = lg(r);
    2267        3265 :   GEN a = cgetg(l, t_COL);
    2268       10373 :   for (i = 1; i < l; i++)
    2269        7108 :     gel(a, i) = f(gsubst(A, v, gel(r,i)), gsubst(B, v, gel(r,i)), DEFAULTPREC);
    2270        3265 :   return gc_ulong(av, (ulong) dbllog2(gmul(M,RgC_fpnorml2(a, DEFAULTPREC))));
    2271             : }
    2272             : static ulong
    2273        2957 : ZXQX_resultant_bound(GEN nf, GEN A, GEN B)
    2274        2957 : { return ZXQX_resultant_bound_i(nf, A, B, &RgX_RgXY_ResBound); }
    2275             : 
    2276             : /* Compute Res(A, B/dB) in Z[X]/T, assuming A,B in Z[X,Y], dB in Z or NULL (= 1)
    2277             :  * If B=NULL, take B = A' and assume deg A > 1 */
    2278             : static GEN
    2279        2954 : ZXQX_resultant_all(GEN A, GEN B, GEN T, GEN dB, ulong bound)
    2280             : {
    2281        2954 :   pari_sp av = avma;
    2282             :   forprime_t S;
    2283             :   GEN  H, worker;
    2284        2954 :   if (B)
    2285             :   {
    2286          70 :     long a = degpol(A), b = degpol(B);
    2287          70 :     if (a < 0 || b < 0) return gen_0;
    2288          70 :     if (!a) return gpowgs(gel(A,2), b);
    2289          70 :     if (!b) return gpowgs(gel(B,2), a);
    2290             :   } else
    2291        2884 :     if (!bound) B = RgX_deriv(A);
    2292        2933 :   if (!bound) bound = ZXQX_resultant_bound(nfinit(T, DEFAULTPREC), A, B);
    2293        2933 :   worker = snm_closure(is_entry("_ZXQX_resultant_worker"),
    2294             :                        mkvec4(A, B? B: gen_0, T, dB? dB: gen_0));
    2295        2933 :   init_modular_big(&S);
    2296        2933 :   H = gen_crt("ZXQX_resultant_all", worker, &S, dB, bound, 0, NULL,
    2297             :               nxV_chinese_center, FpX_center);
    2298        2933 :   if (DEBUGLEVEL)
    2299           0 :     err_printf("ZXQX_resultant_all: a priori bound: %lu, a posteriori: %lu\n",
    2300             :                bound, expi(gsupnorm(H, DEFAULTPREC)));
    2301        2933 :   return gerepileupto(av, H);
    2302             : }
    2303             : 
    2304             : GEN
    2305          70 : nfX_resultant(GEN nf, GEN x, GEN y)
    2306             : {
    2307          70 :   pari_sp av = avma;
    2308          70 :   GEN cx, cy, D, T = nf_get_pol(nf);
    2309             :   ulong bound;
    2310          70 :   long d = degpol(x), v = varn(T);
    2311          70 :   if (d <= 1) return d == 1? pol_1(v): pol_0(v);
    2312          70 :   x = Q_primitive_part(x, &cx);
    2313          70 :   y = Q_primitive_part(y, &cy);
    2314          70 :   bound = ZXQX_resultant_bound(nf, x, y);
    2315          70 :   D = ZXQX_resultant_all(x, y, T, NULL, bound);
    2316          70 :   if (cx) D = gmul(D, gpowgs(cx, degpol(y)));
    2317          70 :   if (cy) D = gmul(D, gpowgs(cy, degpol(x)));
    2318          70 :   return gerepileupto(av, D);
    2319             : }
    2320             : 
    2321             : static GEN
    2322         217 : to_ZX(GEN a, long v) { return typ(a)==t_INT? scalarpol(a,v): a; }
    2323             : 
    2324             : static GEN
    2325        2884 : ZXQX_disc_all(GEN x, GEN T, ulong bound)
    2326             : {
    2327        2884 :   pari_sp av = avma;
    2328        2884 :   long s, d = degpol(x), v = varn(T);
    2329             :   GEN l, R;
    2330             : 
    2331        2884 :   if (d <= 1) return d == 1? pol_1(v): pol_0(v);
    2332        2884 :   s = (d & 2) ? -1: 1;
    2333        2884 :   l = leading_coeff(x);
    2334        2884 :   R = ZXQX_resultant_all(x, NULL, T, NULL, bound);
    2335        2884 :   if (!gequal1(l)) R = QXQ_div(R, to_ZX(l,v), T);
    2336        2884 :   if (s == -1) R = RgX_neg(R);
    2337        2884 :   return gerepileupto(av, R);
    2338             : }
    2339             : 
    2340             : GEN
    2341           7 : QX_disc(GEN x)
    2342             : {
    2343           7 :   pari_sp av = avma;
    2344           7 :   GEN c, d = ZX_disc( Q_primitive_part(x, &c) );
    2345           7 :   if (c) d = gmul(d, gpowgs(c, 2*degpol(x) - 2));
    2346           7 :   return gerepileupto(av, d);
    2347             : }
    2348             : 
    2349             : GEN
    2350        3038 : nfX_disc(GEN nf, GEN x)
    2351             : {
    2352        3038 :   pari_sp av = avma;
    2353        3038 :   GEN c, D, T = nf_get_pol(nf);
    2354             :   ulong bound;
    2355        3038 :   long d = degpol(x), v = varn(T);
    2356        3038 :   if (d <= 1) return d == 1? pol_1(v): pol_0(v);
    2357        2884 :   x = Q_primitive_part(x, &c);
    2358        2884 :   bound = ZXQX_resultant_bound(nf, x, RgX_deriv(x));
    2359        2884 :   D = ZXQX_disc_all(x, T, bound);
    2360        2884 :   if (c) D = gmul(D, gpowgs(c, 2*d - 2));
    2361        2884 :   return gerepileupto(av, D);
    2362             : }
    2363             : 
    2364             : GEN
    2365      559658 : QXQ_mul(GEN x, GEN y, GEN T)
    2366             : {
    2367      559658 :   GEN dx, nx = Q_primitive_part(x, &dx);
    2368      559657 :   GEN dy, ny = Q_primitive_part(y, &dy);
    2369      559659 :   GEN z = ZXQ_mul(nx, ny, T);
    2370      559661 :   if (dx || dy)
    2371             :   {
    2372      556670 :     GEN d = dx ? dy ? gmul(dx, dy): dx : dy;
    2373      556670 :     if (!gequal1(d)) z = ZX_Q_mul(z, d);
    2374             :   }
    2375      559659 :   return z;
    2376             : }
    2377             : 
    2378             : GEN
    2379       92939 : QXQ_sqr(GEN x, GEN T)
    2380             : {
    2381       92939 :   GEN dx, nx = Q_primitive_part(x, &dx);
    2382       92939 :   GEN z = ZXQ_sqr(nx, T);
    2383       92939 :   if (dx)
    2384       91147 :     z = ZX_Q_mul(z, gsqr(dx));
    2385       92939 :   return z;
    2386             : }
    2387             : 
    2388             : static GEN
    2389      101844 : QXQ_inv_slice(GEN A, GEN B, GEN P, GEN *mod)
    2390             : {
    2391      101844 :   pari_sp av = avma;
    2392      101844 :   long i, n = lg(P)-1, v = varn(A), redo = 0;
    2393             :   GEN H, T;
    2394      101844 :   if (n == 1)
    2395             :   {
    2396       56637 :     ulong p = uel(P,1);
    2397       56637 :     GEN a = ZX_to_Flx(A, p), b = ZX_to_Flx(B, p);
    2398       56638 :     GEN U = Flxq_invsafe(a, b, p);
    2399       56637 :     if (!U)
    2400             :     {
    2401          24 :       set_avma(av);
    2402          24 :       *mod = gen_1; return pol_0(v);
    2403             :     }
    2404       56613 :     H = gerepilecopy(av, Flx_to_ZX(U));
    2405       56614 :     *mod = utoipos(p); return H;
    2406             :   }
    2407       45207 :   T = ZV_producttree(P);
    2408       45207 :   A = ZX_nv_mod_tree(A, P, T);
    2409       45207 :   B = ZX_nv_mod_tree(B, P, T);
    2410       45207 :   H = cgetg(n+1, t_VEC);
    2411      224519 :   for(i=1; i <= n; i++)
    2412             :   {
    2413      179313 :     ulong p = P[i];
    2414      179313 :     GEN a = gel(A,i), b = gel(B,i);
    2415      179313 :     GEN U = Flxq_invsafe(a, b, p);
    2416      179309 :     if (!U)
    2417             :     {
    2418         601 :       gel(H,i) = pol_0(v);
    2419         601 :       P[i] = 1; redo = 1;
    2420             :     }
    2421             :     else
    2422      178708 :       gel(H,i) = U;
    2423             :   }
    2424       45206 :   if (redo) T = ZV_producttree(P);
    2425       45206 :   H = nxV_chinese_center_tree(H, P, T, ZV_chinesetree(P, T));
    2426       45207 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2427             : }
    2428             : 
    2429             : GEN
    2430      101844 : QXQ_inv_worker(GEN P, GEN A, GEN B)
    2431             : {
    2432      101844 :   GEN V = cgetg(3, t_VEC);
    2433      101844 :   gel(V,1) = QXQ_inv_slice(A, B, P, &gel(V,2));
    2434      101845 :   return V;
    2435             : }
    2436             : 
    2437             : /* lift(1 / Mod(A,B)). B a ZX, A a scalar or a QX */
    2438             : GEN
    2439       37557 : QXQ_inv(GEN A, GEN B)
    2440             : {
    2441             :   GEN D, Ap, Bp;
    2442             :   ulong pp;
    2443       37557 :   pari_sp av2, av = avma;
    2444             :   forprime_t S;
    2445       37557 :   GEN worker, U, H = NULL, mod = gen_1;
    2446             :   pari_timer ti;
    2447             :   long k, dA, dB;
    2448       37557 :   if (is_scalar_t(typ(A))) return scalarpol(ginv(A), varn(B));
    2449             :   /* A a QX, B a ZX */
    2450       37557 :   A = Q_primitive_part(A, &D);
    2451       37558 :   dA = degpol(A); dB= degpol(B);
    2452             :   /* A, B in Z[X] */
    2453       37558 :   init_modular_small(&S);
    2454             :   do {
    2455       37557 :     pp = u_forprime_next(&S);
    2456       37557 :     Ap = ZX_to_Flx(A, pp);
    2457       37556 :     Bp = ZX_to_Flx(B, pp);
    2458       37556 :   } while (degpol(Ap) != dA || degpol(Bp) != dB);
    2459       37556 :   if (degpol(Flx_gcd(Ap, Bp, pp)) != 0 && degpol(ZX_gcd(A,B))!=0)
    2460          14 :     pari_err_INV("QXQ_inv",mkpolmod(A,B));
    2461       37544 :   worker = snm_closure(is_entry("_QXQ_inv_worker"), mkvec2(A, B));
    2462       37544 :   av2 = avma;
    2463       37544 :   for (k = 1; ;k *= 2)
    2464       41111 :   {
    2465             :     GEN res, b, N, den;
    2466       78655 :     gen_inccrt_i("QXQ_inv", worker, NULL, (k+1)>>1, 0, &S, &H, &mod,
    2467             :                  nxV_chinese_center, FpX_center);
    2468       78655 :     gerepileall(av2, 2, &H, &mod);
    2469       78655 :     b = sqrti(shifti(mod,-1));
    2470       78653 :     if (DEBUGLEVEL>5) timer_start(&ti);
    2471       78653 :     U = FpX_ratlift(H, mod, b, b, NULL);
    2472       78654 :     if (DEBUGLEVEL>5) timer_printf(&ti,"QXQ_inv: ratlift");
    2473       84279 :     if (!U) continue;
    2474       43168 :     N = Q_remove_denom(U, &den); if (!den) den = gen_1;
    2475       43168 :     res = Flx_rem(Flx_Fl_sub(Flx_mul(Ap, ZX_to_Flx(N,pp), pp),
    2476             :                   umodiu(den, pp), pp), Bp, pp);
    2477       43168 :     if (degpol(res) >= 0) continue;
    2478       37544 :     res = ZX_Z_sub(ZX_mul(A, N), den);
    2479       37544 :     res = ZX_is_monic(B) ? ZX_rem(res, B): RgX_pseudorem(res, B);
    2480       37544 :     if (DEBUGLEVEL>5) timer_printf(&ti,"QXQ_inv: final check");
    2481       37544 :     if (degpol(res)<0)
    2482             :     {
    2483       37544 :       if (D) U = RgX_Rg_div(U, D);
    2484       37544 :       return gerepilecopy(av, U);
    2485             :     }
    2486             :   }
    2487             : }
    2488             : 
    2489             : static GEN
    2490      116909 : QXQ_div_slice(GEN A, GEN B, GEN C, GEN P, GEN *mod)
    2491             : {
    2492      116909 :   pari_sp av = avma;
    2493      116909 :   long i, n = lg(P)-1, v = varn(A), redo = 0;
    2494             :   GEN H, T;
    2495      116909 :   if (n == 1)
    2496             :   {
    2497       42725 :     ulong p = uel(P,1);
    2498       42725 :     GEN a = ZX_to_Flx(A, p), b = ZX_to_Flx(B, p), c = ZX_to_Flx(C, p);
    2499       42725 :     GEN bi = Flxq_invsafe(b, c, p), U;
    2500       42725 :     if (!bi)
    2501             :     {
    2502           0 :       set_avma(av);
    2503           0 :       *mod = gen_1; return pol_0(v);
    2504             :     }
    2505       42725 :     U = Flxq_mul(a, bi, c, p);
    2506       42725 :     H = gerepilecopy(av, Flx_to_ZX(U));
    2507       42725 :     *mod = utoipos(p); return H;
    2508             :   }
    2509       74184 :   T = ZV_producttree(P);
    2510       74183 :   A = ZX_nv_mod_tree(A, P, T);
    2511       74184 :   B = ZX_nv_mod_tree(B, P, T);
    2512       74184 :   C = ZX_nv_mod_tree(C, P, T);
    2513       74184 :   H = cgetg(n+1, t_VEC);
    2514      326480 :   for(i=1; i <= n; i++)
    2515             :   {
    2516      252296 :     ulong p = P[i];
    2517      252296 :     GEN a = gel(A,i), b = gel(B,i), c = gel(C, i);
    2518      252296 :     GEN bi = Flxq_invsafe(b, c, p);
    2519      252296 :     if (!bi)
    2520             :     {
    2521           0 :       gel(H,i) = pol_0(v);
    2522           0 :       P[i] = 1; redo = 1;
    2523             :     }
    2524             :     else
    2525      252296 :       gel(H,i) = Flxq_mul(a, bi, c, p);
    2526             :   }
    2527       74184 :   if (redo) T = ZV_producttree(P);
    2528       74184 :   H = nxV_chinese_center_tree(H, P, T, ZV_chinesetree(P, T));
    2529       74184 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2530             : }
    2531             : 
    2532             : GEN
    2533      116909 : QXQ_div_worker(GEN P, GEN A, GEN B, GEN C)
    2534             : {
    2535      116909 :   GEN V = cgetg(3, t_VEC);
    2536      116909 :   gel(V,1) = QXQ_div_slice(A, B, C, P, &gel(V,2));
    2537      116909 :   return V;
    2538             : }
    2539             : 
    2540             : /* lift(Mod(A/B, C)). C a ZX, A, B a scalar or a QX */
    2541             : GEN
    2542       31661 : QXQ_div(GEN A, GEN B, GEN C)
    2543             : {
    2544             :   GEN DA, DB, Ap, Bp, Cp;
    2545             :   ulong pp;
    2546       31661 :   pari_sp av2, av = avma;
    2547             :   forprime_t S;
    2548       31661 :   GEN worker, U, H = NULL, mod = gen_1;
    2549             :   pari_timer ti;
    2550             :   long k, dA, dB, dC;
    2551       31661 :   if (is_scalar_t(typ(A))) return scalarpol(ginv(A), varn(B));
    2552             :   /* A a QX, B a ZX */
    2553       31661 :   A = Q_primitive_part(A, &DA);
    2554       31661 :   B = Q_primitive_part(B, &DB);
    2555       31661 :   dA = degpol(A); dB = degpol(B); dC = degpol(C);
    2556             :   /* A, B in Z[X] */
    2557       31661 :   init_modular_small(&S);
    2558             :   do {
    2559       31661 :     pp = u_forprime_next(&S);
    2560       31661 :     Ap = ZX_to_Flx(A, pp);
    2561       31661 :     Bp = ZX_to_Flx(B, pp);
    2562       31661 :     Cp = ZX_to_Flx(C, pp);
    2563       31661 :   } while (degpol(Ap) != dA || degpol(Bp) != dB || degpol(Cp) != dC);
    2564       31661 :   if (degpol(Flx_gcd(Bp, Cp, pp)) != 0 && degpol(ZX_gcd(B,C))!=0)
    2565           0 :     pari_err_INV("QXQ_div",mkpolmod(B,C));
    2566       31661 :   worker = snm_closure(is_entry("_QXQ_div_worker"), mkvec3(A, B, C));
    2567       31661 :   av2 = avma;
    2568       31661 :   for (k = 1; ;k *= 2)
    2569       45307 :   {
    2570             :     GEN res, b, N, den;
    2571       76968 :     gen_inccrt_i("QXQ_div", worker, NULL, (k+1)>>1, 0, &S, &H, &mod,
    2572             :                  nxV_chinese_center, FpX_center);
    2573       76968 :     gerepileall(av2, 2, &H, &mod);
    2574       76968 :     b = sqrti(shifti(mod,-1));
    2575       76966 :     if (DEBUGLEVEL>5) timer_start(&ti);
    2576       76966 :     U = FpX_ratlift(H, mod, b, b, NULL);
    2577       76968 :     if (DEBUGLEVEL>5) timer_printf(&ti,"QXQ_div: ratlift");
    2578       87578 :     if (!U) continue;
    2579       42271 :     N = Q_remove_denom(U, &den); if (!den) den = gen_1;
    2580       42271 :     res = Flx_rem(Flx_sub(Flx_mul(Bp, ZX_to_Flx(N,pp), pp),
    2581             :                           Flx_Fl_mul(Ap, umodiu(den, pp), pp), pp), Cp, pp);
    2582       42271 :     if (degpol(res) >= 0) continue;
    2583       31661 :     res = ZX_sub(ZX_mul(B, N), ZX_Z_mul(A,den));
    2584       31661 :     res = ZX_is_monic(C) ? ZX_rem(res, C): RgX_pseudorem(res, C);
    2585       31661 :     if (DEBUGLEVEL>5) timer_printf(&ti,"QXQ_div: final check");
    2586       31661 :     if (degpol(res)<0)
    2587             :     {
    2588       31661 :       if (DA && DB) U = RgX_Rg_mul(U, gdiv(DA,DB));
    2589       26929 :       else if (DA) U = RgX_Rg_mul(U, DA);
    2590       15141 :       else if (DB) U = RgX_Rg_div(U, DB);
    2591       31661 :       return gerepilecopy(av, U);
    2592             :     }
    2593             :   }
    2594             : }
    2595             : 
    2596             : /************************************************************************
    2597             :  *                                                                      *
    2598             :  *                           ZXQ_minpoly                                *
    2599             :  *                                                                      *
    2600             :  ************************************************************************/
    2601             : 
    2602             : static GEN
    2603        3523 : ZXQ_minpoly_slice(GEN A, GEN B, long d, GEN P, GEN *mod)
    2604             : {
    2605        3523 :   pari_sp av = avma;
    2606        3523 :   long i, n = lg(P)-1, v = evalvarn(varn(B));
    2607             :   GEN H, T;
    2608        3523 :   if (n == 1)
    2609             :   {
    2610         716 :     ulong p = uel(P,1);
    2611         716 :     GEN a = ZX_to_Flx(A, p), b = ZX_to_Flx(B, p);
    2612         716 :     GEN Hp = Flxq_minpoly(a, b, p);
    2613         716 :     if (degpol(Hp) != d) { p = 1; Hp = pol0_Flx(v); }
    2614         716 :     H = gerepileupto(av, Flx_to_ZX(Hp));
    2615         716 :     *mod = utoipos(p); return H;
    2616             :   }
    2617        2807 :   T = ZV_producttree(P);
    2618        2807 :   A = ZX_nv_mod_tree(A, P, T);
    2619        2807 :   B = ZX_nv_mod_tree(B, P, T);
    2620        2807 :   H = cgetg(n+1, t_VEC);
    2621       16838 :   for(i=1; i <= n; i++)
    2622             :   {
    2623       14031 :     ulong p = P[i];
    2624       14031 :     GEN a = gel(A,i), b = gel(B,i);
    2625       14031 :     GEN m = Flxq_minpoly(a, b, p);
    2626       14031 :     if (degpol(m) != d) { P[i] = 1; m = pol0_Flx(v); }
    2627       14031 :     gel(H, i) = m;
    2628             :   }
    2629        2807 :   H = nxV_chinese_center_tree(H, P, T, ZV_chinesetree(P, T));
    2630        2807 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2631             : }
    2632             : 
    2633             : GEN
    2634        3523 : ZXQ_minpoly_worker(GEN P, GEN A, GEN B, long d)
    2635             : {
    2636        3523 :   GEN V = cgetg(3, t_VEC);
    2637        3523 :   gel(V,1) = ZXQ_minpoly_slice(A, B, d, P, &gel(V,2));
    2638        3523 :   return V;
    2639             : }
    2640             : 
    2641             : GEN
    2642        1701 : ZXQ_minpoly(GEN A, GEN B, long d, ulong bound)
    2643             : {
    2644        1701 :   pari_sp av = avma;
    2645             :   GEN worker, H, dB;
    2646             :   forprime_t S;
    2647        1701 :   B = Q_remove_denom(B, &dB);
    2648        1701 :   worker = strtoclosure("_ZXQ_minpoly_worker", 3, A, B, stoi(d));
    2649        1701 :   init_modular_big(&S);
    2650        1701 :   H = gen_crt("ZXQ_minpoly", worker, &S, dB, bound, 0, NULL,
    2651             :                nxV_chinese_center, FpX_center_i);
    2652        1701 :   return gerepilecopy(av, H);
    2653             : }
    2654             : 
    2655             : /************************************************************************
    2656             :  *                                                                      *
    2657             :  *                   ZX_ZXY_resultant                                   *
    2658             :  *                                                                      *
    2659             :  ************************************************************************/
    2660             : 
    2661             : static GEN
    2662      173253 : ZX_ZXY_resultant_prime(GEN a, GEN b, ulong dp, ulong p,
    2663             :                        long degA, long degB, long dres, long sX)
    2664             : {
    2665      173253 :   long dropa = degA - degpol(a), dropb = degB - degpol(b);
    2666      173252 :   ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
    2667      173251 :   GEN Hp = Flx_FlxY_resultant_polint(a, b, p, pi, dres, sX);
    2668      173256 :   if (dropa && dropb)
    2669           0 :     Hp = zero_Flx(sX);
    2670             :   else {
    2671      173256 :     if (dropa)
    2672             :     { /* multiply by ((-1)^deg B lc(B))^(deg A - deg a) */
    2673           0 :       GEN c = gel(b,degB+2); /* lc(B) */
    2674           0 :       if (odd(degB)) c = Flx_neg(c, p);
    2675           0 :       if (!Flx_equal1(c)) {
    2676           0 :         c = Flx_powu_pre(c, dropa, p, pi);
    2677           0 :         if (!Flx_equal1(c)) Hp = Flx_mul_pre(Hp, c, p, pi);
    2678             :       }
    2679             :     }
    2680      173256 :     else if (dropb)
    2681             :     { /* multiply by lc(A)^(deg B - deg b) */
    2682           0 :       ulong c = uel(a, degA+2); /* lc(A) */
    2683           0 :       c = Fl_powu(c, dropb, p);
    2684           0 :       if (c != 1) Hp = Flx_Fl_mul_pre(Hp, c, p, pi);
    2685             :     }
    2686             :   }
    2687      173256 :   if (dp != 1) Hp = Flx_Fl_mul_pre(Hp, Fl_powu_pre(Fl_inv(dp,p), degA, p, pi), p, pi);
    2688      173256 :   return Hp;
    2689             : }
    2690             : 
    2691             : static GEN
    2692       69272 : ZX_ZXY_resultant_slice(GEN A, GEN B, GEN dB, long degA, long degB, long dres,
    2693             :                        GEN P, GEN *mod, long sX, long vY)
    2694             : {
    2695       69272 :   pari_sp av = avma;
    2696       69272 :   long i, n = lg(P)-1;
    2697             :   GEN H, T, D;
    2698       69272 :   if (n == 1)
    2699             :   {
    2700       39962 :     ulong p = uel(P,1);
    2701       39962 :     ulong dp = dB ? umodiu(dB, p): 1;
    2702       39962 :     GEN a = ZX_to_Flx(A, p), b = ZXX_to_FlxX(B, p, vY);
    2703       39962 :     GEN Hp = ZX_ZXY_resultant_prime(a, b, dp, p, degA, degB, dres, sX);
    2704       39962 :     H = gerepileupto(av, Flx_to_ZX(Hp));
    2705       39961 :     *mod = utoipos(p); return H;
    2706             :   }
    2707       29310 :   T = ZV_producttree(P);
    2708       29310 :   A = ZX_nv_mod_tree(A, P, T);
    2709       29310 :   B = ZXX_nv_mod_tree(B, P, T, vY);
    2710       29310 :   D = dB ? Z_ZV_mod_tree(dB, P, T): NULL;
    2711       29310 :   H = cgetg(n+1, t_VEC);
    2712      117461 :   for(i=1; i <= n; i++)
    2713             :   {
    2714       88150 :     ulong p = P[i];
    2715       88150 :     GEN a = gel(A,i), b = gel(B,i);
    2716       88150 :     ulong dp = D ? uel(D, i): 1;
    2717       88150 :     gel(H,i) = ZX_ZXY_resultant_prime(a, b, dp, p, degA, degB, dres, sX);
    2718             :   }
    2719       29311 :   H = nxV_chinese_center_tree(H, P, T, ZV_chinesetree(P, T));
    2720       29310 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2721             : }
    2722             : 
    2723             : GEN
    2724       69272 : ZX_ZXY_resultant_worker(GEN P, GEN A, GEN B, GEN dB, GEN v)
    2725             : {
    2726       69272 :   GEN V = cgetg(3, t_VEC);
    2727       69272 :   if (isintzero(dB)) dB = NULL;
    2728       69272 :   gel(V,1) = ZX_ZXY_resultant_slice(A, B, dB, v[1], v[2], v[3], P, &gel(V,2), v[4], v[5]);
    2729       69271 :   return V;
    2730             : }
    2731             : 
    2732             : GEN
    2733       60006 : ZX_ZXY_resultant(GEN A, GEN B)
    2734             : {
    2735       60006 :   pari_sp av = avma;
    2736             :   forprime_t S;
    2737             :   ulong bound;
    2738       60006 :   long v = fetch_var_higher();
    2739       60006 :   long degA = degpol(A), degB, dres = degA * degpol(B);
    2740       60006 :   long vX = varn(B), vY = varn(A); /* assume vY has lower priority */
    2741       60006 :   long sX = evalvarn(vX);
    2742             :   GEN worker, H, dB;
    2743       60006 :   B = Q_remove_denom(B, &dB);
    2744       60005 :   if (!dB) B = leafcopy(B);
    2745       60005 :   A = leafcopy(A); setvarn(A,v);
    2746       60005 :   B = swap_vars(B, vY); setvarn(B,v); degB = degpol(B);
    2747       60006 :   bound = ZX_ZXY_ResBound(A, B, dB);
    2748       60004 :   if (DEBUGLEVEL>4) err_printf("bound for resultant coeffs: 2^%ld\n",bound);
    2749      120009 :   worker = snm_closure(is_entry("_ZX_ZXY_resultant_worker"),
    2750       60005 :                        mkvec4(A, B, dB? dB: gen_0,
    2751             :                               mkvecsmall5(degA, degB, dres, sX, vY)));
    2752       60006 :   init_modular_big(&S);
    2753       60006 :   H = gen_crt("ZX_ZXY_resultant_all", worker, &S, dB, bound, 0, NULL,
    2754             :                nxV_chinese_center, FpX_center_i);
    2755       60005 :   setvarn(H, vX); (void)delete_var();
    2756       60005 :   return gerepilecopy(av, H);
    2757             : }
    2758             : 
    2759             : static long
    2760       40402 : ZX_ZXY_rnfequation_lambda(GEN A, GEN B0, long lambda)
    2761             : {
    2762       40402 :   pari_sp av = avma;
    2763       40402 :   long degA = degpol(A), degB, dres = degA*degpol(B0);
    2764       40401 :   long v = fetch_var_higher();
    2765       40401 :   long vX = varn(B0), vY = varn(A); /* assume vY has lower priority */
    2766       40401 :   long sX = evalvarn(vX);
    2767             :   GEN dB, B, a, b, Hp;
    2768             :   forprime_t S;
    2769             : 
    2770       40401 :   B0 = Q_remove_denom(B0, &dB);
    2771       40401 :   if (!dB) B0 = leafcopy(B0);
    2772       40401 :   A = leafcopy(A);
    2773       40401 :   B = B0;
    2774       40401 :   setvarn(A,v);
    2775       45143 : INIT:
    2776       45143 :   if (lambda) B = RgX_translate(B0, monomial(stoi(lambda), 1, vY));
    2777       45143 :   B = swap_vars(B, vY); setvarn(B,v);
    2778             :   /* B0(lambda v + x, v) */
    2779       45143 :   if (DEBUGLEVEL>4) err_printf("Trying lambda = %ld\n", lambda);
    2780             : 
    2781       45143 :   degB = degpol(B);
    2782       45143 :   init_modular_big(&S);
    2783             :   while (1)
    2784           0 :   {
    2785       45143 :     ulong p = u_forprime_next(&S);
    2786       45143 :     ulong dp = dB ? umodiu(dB, p): 1;
    2787       45143 :     if (!dp) continue;
    2788       45143 :     a = ZX_to_Flx(A, p);
    2789       45143 :     b = ZXX_to_FlxX(B, p, v);
    2790       45143 :     Hp = ZX_ZXY_resultant_prime(a, b, dp, p, degA, degB, dres, sX);
    2791       45144 :     if (degpol(Hp) != dres) continue;
    2792       45144 :     if (dp != 1) Hp = Flx_Fl_mul(Hp, Fl_powu(Fl_inv(dp,p), degA, p), p);
    2793       45144 :     if (!Flx_is_squarefree(Hp, p)) { lambda = next_lambda(lambda); goto INIT; }
    2794       40402 :     if (DEBUGLEVEL>4) err_printf("Final lambda = %ld\n", lambda);
    2795       40402 :     (void)delete_var(); return gc_long(av,lambda);
    2796             :   }
    2797             : }
    2798             : 
    2799             : GEN
    2800       41372 : ZX_ZXY_rnfequation(GEN A, GEN B, long *lambda)
    2801             : {
    2802       41372 :   if (lambda)
    2803             :   {
    2804       40402 :     *lambda = ZX_ZXY_rnfequation_lambda(A, B, *lambda);
    2805       40402 :     if (*lambda) B = RgX_translate(B, monomial(stoi(*lambda), 1, varn(A)));
    2806             :   }
    2807       41372 :   return ZX_ZXY_resultant(A,B);
    2808             : }
    2809             : 
    2810             : static GEN
    2811       10371 : ZX_composedsum_slice(GEN A, GEN B, GEN P, GEN *mod)
    2812             : {
    2813       10371 :   pari_sp av = avma;
    2814       10371 :   long i, n = lg(P)-1;
    2815             :   GEN H, T;
    2816       10371 :   if (n == 1)
    2817             :   {
    2818        9869 :     ulong p = uel(P,1);
    2819        9869 :     GEN a = ZX_to_Flx(A, p), b = ZX_to_Flx(B, p);
    2820        9868 :     GEN Hp = Flx_composedsum(a, b, p);
    2821        9866 :     H = gerepileupto(av, Flx_to_ZX(Hp));
    2822        9870 :     *mod = utoipos(p); return H;
    2823             :   }
    2824         502 :   T = ZV_producttree(P);
    2825         502 :   A = ZX_nv_mod_tree(A, P, T);
    2826         502 :   B = ZX_nv_mod_tree(B, P, T);
    2827         502 :   H = cgetg(n+1, t_VEC);
    2828        4526 :   for(i=1; i <= n; i++)
    2829             :   {
    2830        4024 :     ulong p = P[i];
    2831        4024 :     GEN a = gel(A,i), b = gel(B,i);
    2832        4024 :     gel(H,i) = Flx_composedsum(a, b, p);
    2833             :   }
    2834         502 :   H = nxV_chinese_center_tree(H, P, T, ZV_chinesetree(P, T));
    2835         502 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2836             : }
    2837             : 
    2838             : GEN
    2839       10370 : ZX_composedsum_worker(GEN P, GEN A, GEN B)
    2840             : {
    2841       10370 :   GEN V = cgetg(3, t_VEC);
    2842       10371 :   gel(V,1) = ZX_composedsum_slice(A, B, P, &gel(V,2));
    2843       10371 :   return V;
    2844             : }
    2845             : 
    2846             : static GEN
    2847       10105 : ZX_composedsum_i(GEN A, GEN B, GEN lead)
    2848             : {
    2849       10105 :   pari_sp av = avma;
    2850             :   forprime_t S;
    2851             :   ulong bound;
    2852             :   GEN H, worker, mod;
    2853       10105 :   if (degpol(A) < degpol(B)) swap(A, B);
    2854       10106 :   if (!lead) lead  = mulii(leading_coeff(A),leading_coeff(B));
    2855       10106 :   bound = ZX_ZXY_ResBound_1(A, B);
    2856       10103 :   worker = snm_closure(is_entry("_ZX_composedsum_worker"), mkvec2(A,B));
    2857       10107 :   init_modular_big(&S);
    2858       10101 :   H = gen_crt("ZX_composedsum", worker, &S, lead, bound, 0, &mod,
    2859             :               nxV_chinese_center, FpX_center);
    2860       10107 :   return gerepileupto(av, H);
    2861             : }
    2862             : 
    2863             : static long
    2864        9716 : ZX_compositum_lambda(GEN A, GEN B, GEN lead, long lambda)
    2865             : {
    2866        9716 :   pari_sp av = avma;
    2867             :   forprime_t S;
    2868             :   ulong p;
    2869        9716 :   init_modular_big(&S);
    2870        9719 :   p = u_forprime_next(&S);
    2871             :   while (1)
    2872         112 :   {
    2873             :     GEN Hp, a;
    2874        9831 :     if (DEBUGLEVEL>4) err_printf("Trying lambda = %ld\n", lambda);
    2875        9831 :     if (lead && dvdiu(lead,p)) { p = u_forprime_next(&S); continue; }
    2876        9825 :     a = ZX_to_Flx(ZX_rescale(A, stoi(-lambda)), p);
    2877        9820 :     Hp = Flx_composedsum(a, ZX_to_Flx(B, p), p);
    2878        9824 :     if (!Flx_is_squarefree(Hp, p)) { lambda = next_lambda(lambda); continue; }
    2879        9716 :     if (DEBUGLEVEL>4) err_printf("Final lambda = %ld\n", lambda);
    2880        9716 :     return gc_long(av, lambda);
    2881             :   }
    2882             : }
    2883             : 
    2884             : GEN
    2885        9720 : ZX_compositum(GEN A, GEN B, long *lambda)
    2886             : {
    2887        9720 :   GEN lead  = mulii(leading_coeff(A),leading_coeff(B));
    2888        9717 :   if (lambda)
    2889             :   {
    2890        9718 :     *lambda = ZX_compositum_lambda(A, B, lead, *lambda);
    2891        9716 :     A = ZX_rescale(A, stoi(-*lambda));
    2892             :   }
    2893        9720 :   return ZX_composedsum_i(A, B, lead);
    2894             : }
    2895             : 
    2896             : GEN
    2897         385 : ZX_composedsum(GEN A, GEN B)
    2898         385 : { return ZX_composedsum_i(A, B, NULL); }
    2899             : 
    2900             : static GEN
    2901         351 : ZXQX_composedsum_slice(GEN A, GEN B, GEN C, GEN P, GEN *mod)
    2902             : {
    2903         351 :   pari_sp av = avma;
    2904         351 :   long i, n = lg(P)-1, dC = degpol(C), v = varn(C);
    2905             :   GEN H, T;
    2906         351 :   if (n == 1)
    2907             :   {
    2908         174 :     ulong p = uel(P,1);
    2909         174 :     GEN a = ZXX_to_FlxX(A, p, v), b = ZXX_to_FlxX(B, p, v);
    2910         174 :     GEN c = ZX_to_Flx(C, p);
    2911         174 :     GEN Hp = FlxX_to_Flm(FlxqX_composedsum(a, b, c, p), dC);
    2912         174 :     H = gerepileupto(av, Flm_to_ZM(Hp));
    2913         174 :     *mod = utoipos(p); return H;
    2914             :   }
    2915         177 :   T = ZV_producttree(P);
    2916         177 :   A = ZXX_nv_mod_tree(A, P, T, v);
    2917         177 :   B = ZXX_nv_mod_tree(B, P, T, v);
    2918         177 :   C = ZX_nv_mod_tree(C, P, T);
    2919         177 :   H = cgetg(n+1, t_VEC);
    2920         651 :   for(i=1; i <= n; i++)
    2921             :   {
    2922         474 :     ulong p = P[i];
    2923         474 :     GEN a = gel(A,i), b = gel(B,i), c = gel(C,i);
    2924         474 :     gel(H,i) = FlxX_to_Flm(FlxqX_composedsum(a, b, c, p), dC);
    2925             :   }
    2926         177 :   H = nmV_chinese_center_tree_seq(H, P, T, ZV_chinesetree(P, T));
    2927         177 :   *mod = gmael(T, lg(T)-1, 1); return gc_all(av, 2, &H, mod);
    2928             : }
    2929             : 
    2930             : GEN
    2931         351 : ZXQX_composedsum_worker(GEN P, GEN A, GEN B, GEN C)
    2932             : {
    2933         351 :   GEN V = cgetg(3, t_VEC);
    2934         351 :   gel(V,1) = ZXQX_composedsum_slice(A, B, C, P, &gel(V,2));
    2935         351 :   return V;
    2936             : }
    2937             : 
    2938             : static GEN
    2939         308 : ZXQX_composedsum(GEN A, GEN B, GEN T, ulong bound)
    2940             : {
    2941         308 :   pari_sp av = avma;
    2942             :   forprime_t S;
    2943             :   GEN H, worker, mod;
    2944         308 :   GEN lead = mulii(Q_content(leading_coeff(A)), Q_content(leading_coeff(B)));
    2945         308 :   worker = snm_closure(is_entry("_ZXQX_composedsum_worker")
    2946             :                       , mkvec3(A,B,T));
    2947         308 :   init_modular_big(&S);
    2948         308 :   H = gen_crt("ZXQX_composedsum", worker, &S, lead, bound, 0, &mod,
    2949             :               nmV_chinese_center, FpM_center);
    2950         308 :   if (DEBUGLEVEL > 4)
    2951           0 :     err_printf("nfcompositum: a priori bound: %lu, a posteriori: %lu\n",
    2952             :                bound, expi(gsupnorm(H, DEFAULTPREC)));
    2953         308 :   return gerepilecopy(av, RgM_to_RgXX(H, varn(A), varn(T)));
    2954             : }
    2955             : 
    2956             : static long
    2957         308 : ZXQX_composedsum_bound(GEN nf, GEN A, GEN B)
    2958         308 : { return ZXQX_resultant_bound_i(nf, A, B, &RgX_RgXY_ResBound_1); }
    2959             : 
    2960             : GEN
    2961         308 : nf_direct_compositum(GEN nf, GEN A, GEN B)
    2962             : {
    2963         308 :   ulong bnd = ZXQX_composedsum_bound(nf, A, B);
    2964         308 :   return ZXQX_composedsum(A, B, nf_get_pol(nf), bnd);
    2965             : }
    2966             : 
    2967             : /************************************************************************
    2968             :  *                                                                      *
    2969             :  *                   IRREDUCIBLE POLYNOMIAL / Fp                        *
    2970             :  *                                                                      *
    2971             :  ************************************************************************/
    2972             : 
    2973             : /* irreducible (unitary) polynomial of degree n over Fp */
    2974             : GEN
    2975           0 : ffinit_rand(GEN p,long n)
    2976             : {
    2977           0 :   for(;;) {
    2978           0 :     pari_sp av = avma;
    2979           0 :     GEN pol = ZX_add(pol_xn(n, 0), random_FpX(n-1,0, p));
    2980           0 :     if (FpX_is_irred(pol, p)) return pol;
    2981           0 :     set_avma(av);
    2982             :   }
    2983             : }
    2984             : 
    2985             : /* return an extension of degree 2^l of F_2, assume l > 0
    2986             :  * Not stack clean. */
    2987             : static GEN
    2988         634 : ffinit_Artin_Schreier_2(long l)
    2989             : {
    2990             :   GEN Q, T, S;
    2991             :   long i, v;
    2992             : 
    2993         634 :   if (l == 1) return mkvecsmall4(0,1,1,1); /*x^2 + x + 1*/
    2994         585 :   v = fetch_var_higher();
    2995         585 :   S = mkvecsmall5(0, 0, 0, 1, 1); /* y(y^2 + y) */
    2996         585 :   Q = mkpoln(3, pol1_Flx(0), pol1_Flx(0), S); /* x^2 + x + y(y^2+y) */
    2997         585 :   setvarn(Q, v);
    2998             : 
    2999             :   /* x^4+x+1, irred over F_2, minimal polynomial of a root of Q */
    3000         585 :   T = mkvecsmalln(6,evalvarn(v),1UL,1UL,0UL,0UL,1UL);
    3001             :   /* Q = x^2 + x + a(y) irred. over K = F2[y] / (T(y))
    3002             :    * ==> x^2 + x + a(y) b irred. over K for any root b of Q
    3003             :    * ==> x^2 + x + (b^2+b)b */
    3004        3244 :   for (i=2; i<l; i++) T = Flx_FlxY_resultant(T, Q, 2); /* minpoly(b) / F2*/
    3005         585 :   (void)delete_var(); T[1] = 0; return T;
    3006             : }
    3007             : 
    3008             : /* return an extension of degree p^l of F_p, assume l > 0
    3009             :  * Not stack clean. */
    3010             : GEN
    3011         991 : ffinit_Artin_Schreier(ulong p, long l)
    3012             : {
    3013             :   long i, v;
    3014             :   GEN Q, R, S, T, xp;
    3015         991 :   if (p==2) return ffinit_Artin_Schreier_2(l);
    3016         357 :   xp = polxn_Flx(p,0); /* x^p */
    3017         357 :   T = Flx_sub(xp, mkvecsmall3(0,1,1),p); /* x^p - x - 1 */
    3018         357 :   if (l == 1) return T;
    3019             : 
    3020           7 :   v = evalvarn(fetch_var_higher());
    3021           7 :   xp[1] = v;
    3022           7 :   R = Flx_sub(polxn_Flx(2*p-1,0), polxn_Flx(p,0),p);
    3023           7 :   S = Flx_sub(xp, polx_Flx(0), p);
    3024           7 :   Q = FlxX_Flx_sub(Flx_to_FlxX(S, v), R, p); /* x^p - x - (y^(2p-1)-y^p) */
    3025          14 :   for (i = 2; i <= l; ++i) T = Flx_FlxY_resultant(T, Q, p);
    3026           7 :   (void)delete_var(); T[1] = 0; return T;
    3027             : }
    3028             : 
    3029             : static long
    3030      147890 : flinit_check(ulong p, long n, long l)
    3031             : {
    3032             :   ulong q;
    3033      147890 :   if (!uisprime(n)) return 0;
    3034      101180 :   q = p % n; if (!q) return 0;
    3035       98702 :   return ugcd((n-1)/Fl_order(q, n-1, n), l) == 1;
    3036             : }
    3037             : 
    3038             : static GEN
    3039       31713 : flinit(ulong p, long l)
    3040             : {
    3041       31713 :   ulong n = 1+l;
    3042       95767 :   while (!flinit_check(p,n,l)) n += l;
    3043       31713 :   if (DEBUGLEVEL>=4) err_printf("FFInit: using polsubcyclo(%ld, %ld)\n",n,l);
    3044       31713 :   return ZX_to_Flx(polsubcyclo(n,l,0), p);
    3045             : }
    3046             : 
    3047             : static GEN
    3048       28878 : ffinit_fact_Flx(ulong p, long n)
    3049             : {
    3050       28878 :   GEN P, F = factoru_pow(n), Fp = gel(F,1), Fe = gel(F,2), Fm = gel(F,3);
    3051       28878 :   long i, l = lg(Fm);
    3052       28878 :   P = cgetg(l, t_VEC);
    3053       61582 :   for (i = 1; i < l; ++i)
    3054       32704 :     gel(P,i) = p==uel(Fp,i) ?
    3055         991 :                  ffinit_Artin_Schreier(uel(Fp,i), Fe[i])
    3056       32704 :                : flinit(p, uel(Fm,i));
    3057       28878 :   return FlxV_composedsum(P, p);
    3058             : }
    3059             : 
    3060             : static GEN
    3061       52123 : init_Flxq_i(ulong p, long n, long sv)
    3062             : {
    3063             :   GEN P;
    3064       52123 :   if (n == 1) return polx_Flx(sv);
    3065       52123 :   if (flinit_check(p, n+1, n))
    3066             :   {
    3067       23245 :     P = const_vecsmall(n+2,1);
    3068       23245 :     P[1] = sv; return P;
    3069             :   }
    3070       28878 :   P = ffinit_fact_Flx(p,n);
    3071       28878 :   P[1] = sv; return P;
    3072             : }
    3073             : 
    3074             : GEN
    3075           0 : init_Flxq(ulong p, long n, long v)
    3076             : {
    3077           0 :   pari_sp av = avma;
    3078           0 :   return gerepileupto(av, init_Flxq_i(p, n, v));
    3079             : }
    3080             : 
    3081             : /* check if polsubcyclo(n,l,0) is irreducible modulo p */
    3082             : static long
    3083        7185 : fpinit_check(GEN p, long n, long l)
    3084             : {
    3085             :   ulong q;
    3086        7185 :   if (!uisprime(n)) return 0;
    3087        4450 :   q = umodiu(p,n); if (!q) return 0;
    3088        4450 :   return ugcd((n-1)/Fl_order(q, n-1, n), l) == 1;
    3089             : }
    3090             : 
    3091             : /* let k=2 if p%4==1, and k=4 else and assume k*p does not divide l.
    3092             :  * Return an irreducible polynomial of degree l over F_p.
    3093             :  * Variant of Adleman and Lenstra "Finding irreducible polynomials over
    3094             :  * finite fields", ACM, 1986 (5) 350--355.
    3095             :  * Not stack clean */
    3096             : static GEN
    3097        1653 : fpinit(GEN p, long l)
    3098             : {
    3099        1653 :   ulong n = 1+l;
    3100        5202 :   while (!fpinit_check(p,n,l)) n += l;
    3101        1653 :   if (DEBUGLEVEL>=4) err_printf("FFInit: using polsubcyclo(%ld, %ld)\n",n,l);
    3102        1653 :   return FpX_red(polsubcyclo(n,l,0),p);
    3103             : }
    3104             : 
    3105             : static GEN
    3106        1574 : ffinit_fact(GEN p, long n)
    3107             : {
    3108        1574 :   GEN P, F = factoru_pow(n), Fp = gel(F,1), Fe = gel(F,2), Fm = gel(F,3);
    3109        1574 :   long i, l = lg(Fm);
    3110        1574 :   P = cgetg(l, t_VEC);
    3111        3227 :   for (i = 1; i < l; ++i)
    3112        3306 :     gel(P,i) = absequaliu(p, Fp[i]) ?
    3113           0 :                  Flx_to_ZX(ffinit_Artin_Schreier(Fp[i], Fe[i]))
    3114        1653 :                : fpinit(p, Fm[i]);
    3115        1574 :   return FpXV_composedsum(P, p);
    3116             : }
    3117             : 
    3118             : static GEN
    3119       54365 : init_Fq_i(GEN p, long n, long v)
    3120             : {
    3121             :   GEN P;
    3122       54365 :   if (n <= 0) pari_err_DOMAIN("ffinit", "degree", "<=", gen_0, stoi(n));
    3123       54365 :   if (typ(p) != t_INT) pari_err_TYPE("ffinit",p);
    3124       54365 :   if (cmpiu(p, 2) < 0) pari_err_PRIME("ffinit",p);
    3125       54358 :   if (v < 0) v = 0;
    3126       54358 :   if (n == 1) return pol_x(v);
    3127       54106 :   if (lgefint(p) == 3)
    3128       52123 :     return Flx_to_ZX(init_Flxq_i(p[2], n, evalvarn(v)));
    3129        1983 :   if (fpinit_check(p, n+1, n)) return polcyclo(n+1, v);
    3130        1574 :   P = ffinit_fact(p,n);
    3131        1574 :   setvarn(P, v); return P;
    3132             : }
    3133             : GEN
    3134       53812 : init_Fq(GEN p, long n, long v)
    3135             : {
    3136       53812 :   pari_sp av = avma;
    3137       53812 :   return gerepileupto(av, init_Fq_i(p, n, v));
    3138             : }
    3139             : GEN
    3140         553 : ffinit(GEN p, long n, long v)
    3141             : {
    3142         553 :   pari_sp av = avma;
    3143         553 :   return gerepileupto(av, FpX_to_mod(init_Fq_i(p, n, v), p));
    3144             : }
    3145             : 
    3146             : GEN
    3147        3178 : ffnbirred(GEN p, long n)
    3148             : {
    3149        3178 :   pari_sp av = avma;
    3150        3178 :   GEN s = powiu(p,n), F = factoru(n), D = divisorsu_moebius(gel(F, 1));
    3151        3178 :   long j, l = lg(D);
    3152        6797 :   for (j = 2; j < l; j++) /* skip d = 1 */
    3153             :   {
    3154        3619 :     long md = D[j]; /* mu(d) * d, d squarefree */
    3155        3619 :     GEN pd = powiu(p, n / labs(md)); /* p^{n/d} */
    3156        3619 :     s = md > 0? addii(s, pd): subii(s,pd);
    3157             :   }
    3158        3178 :   return gerepileuptoint(av, diviuexact(s, n));
    3159             : }
    3160             : 
    3161             : GEN
    3162         616 : ffsumnbirred(GEN p, long n)
    3163             : {
    3164         616 :   pari_sp av = avma, av2;
    3165         616 :   GEN q, t = p, v = vecfactoru_i(1, n);
    3166             :   long i;
    3167         616 :   q = cgetg(n+1,t_VEC); gel(q,1) = p;
    3168        1764 :   for (i=2; i<=n; i++) gel(q,i) = mulii(gel(q,i-1), p);
    3169         616 :   av2 = avma;
    3170        1764 :   for (i=2; i<=n; i++)
    3171             :   {
    3172        1148 :     GEN s = gel(q,i), F = gel(v,i), D = divisorsu_moebius(gel(F,1));
    3173        1148 :     long j, l = lg(D);
    3174        2534 :     for (j = 2; j < l; j++) /* skip 1 */
    3175             :     {
    3176        1386 :       long md = D[j];
    3177        1386 :       GEN pd = gel(q, i / labs(md)); /* p^{i/d} */
    3178        1386 :       s = md > 0? addii(s, pd): subii(s, pd);
    3179             :     }
    3180        1148 :     t = gerepileuptoint(av2, addii(t, diviuexact(s, i)));
    3181             :   }
    3182         616 :   return gerepileuptoint(av, t);
    3183             : }
    3184             : 
    3185             : GEN
    3186         140 : ffnbirred0(GEN p, long n, long flag)
    3187             : {
    3188         140 :   if (typ(p) != t_INT) pari_err_TYPE("ffnbirred", p);
    3189         140 :   if (n <= 0) pari_err_DOMAIN("ffnbirred", "degree", "<=", gen_0, stoi(n));
    3190         140 :   switch(flag)
    3191             :   {
    3192          70 :     case 0: return ffnbirred(p, n);
    3193          70 :     case 1: return ffsumnbirred(p, n);
    3194             :   }
    3195           0 :   pari_err_FLAG("ffnbirred");
    3196             :   return NULL; /* LCOV_EXCL_LINE */
    3197             : }
    3198             : 
    3199             : static void
    3200        2261 : checkmap(GEN m, const char *s)
    3201             : {
    3202        2261 :   if (typ(m)!=t_VEC || lg(m)!=3 || typ(gel(m,1))!=t_FFELT)
    3203           0 :     pari_err_TYPE(s,m);
    3204        2261 : }
    3205             : 
    3206             : GEN
    3207         189 : ffembed(GEN a, GEN b)
    3208             : {
    3209         189 :   pari_sp av = avma;
    3210         189 :   GEN p, Ta, Tb, g, r = NULL;
    3211         189 :   if (typ(a)!=t_FFELT) pari_err_TYPE("ffembed",a);
    3212         189 :   if (typ(b)!=t_FFELT) pari_err_TYPE("ffembed",b);
    3213         189 :   p = FF_p_i(a); g = FF_gen(a);
    3214         189 :   if (!equalii(p, FF_p_i(b))) pari_err_MODULUS("ffembed",a,b);
    3215         189 :   Ta = FF_mod(a);
    3216         189 :   Tb = FF_mod(b);
    3217         189 :   if (degpol(Tb)%degpol(Ta)!=0)
    3218           7 :     pari_err_DOMAIN("ffembed",GENtostr_raw(a),"is not a subfield of",b,a);
    3219         182 :   r = gel(FFX_roots(Ta, b), 1);
    3220         182 :   return gerepilecopy(av, mkvec2(g,r));
    3221             : }
    3222             : 
    3223             : GEN
    3224          91 : ffextend(GEN a, GEN P, long v)
    3225             : {
    3226          91 :   pari_sp av = avma;
    3227             :   long n;
    3228             :   GEN p, T, R, g, m;
    3229          91 :   if (typ(a)!=t_FFELT) pari_err_TYPE("ffextend",a);
    3230          91 :   T = a; p = FF_p_i(a);
    3231          91 :   if (typ(P)!=t_POL || !RgX_is_FpXQX(P,&T,&p)) pari_err_TYPE("ffextend", P);
    3232          49 :   if (!FF_samefield(a, T)) pari_err_MODULUS("ffextend",a,T);
    3233          49 :   if (v < 0) v = varn(P);
    3234          49 :   n = FF_f(T) * degpol(P); R = ffinit(p, n, v); g = ffgen(R, v);
    3235          49 :   m = ffembed(a, g);
    3236          49 :   R = FFX_roots(ffmap(m, P),g);
    3237          49 :   return gerepilecopy(av, mkvec2(gel(R,1), m));
    3238             : }
    3239             : 
    3240             : GEN
    3241          42 : fffrobenius(GEN a, long n)
    3242             : {
    3243          42 :   if (typ(a)!=t_FFELT) pari_err_TYPE("fffrobenius",a);
    3244          42 :   retmkvec2(FF_gen(a), FF_Frobenius(a, n));
    3245             : }
    3246             : 
    3247             : GEN
    3248         133 : ffinvmap(GEN m)
    3249             : {
    3250         133 :   pari_sp av = avma;
    3251             :   long i, l;
    3252         133 :   GEN T, F, a, g, r, f = NULL;
    3253         133 :   checkmap(m, "ffinvmap");
    3254         133 :   a = gel(m,1); r = gel(m,2);
    3255         133 :   if (typ(r) != t_FFELT)
    3256           7 :    pari_err_TYPE("ffinvmap", m);
    3257         126 :   g = FF_gen(a);
    3258         126 :   T = FF_mod(r);
    3259         126 :   F = gel(FFX_factor(T, a), 1);
    3260         126 :   l = lg(F);
    3261         490 :   for(i=1; i<l; i++)
    3262             :   {
    3263         490 :     GEN s = FFX_rem(FF_to_FpXQ_i(r), gel(F, i), a);
    3264         490 :     if (degpol(s)==0 && gequal(constant_coeff(s),g)) { f = gel(F, i); break; }
    3265             :   }
    3266         126 :   if (f==NULL) pari_err_TYPE("ffinvmap", m);
    3267         126 :   if (degpol(f)==1) f = FF_neg_i(gel(f,2));
    3268         126 :   return gerepilecopy(av, mkvec2(FF_gen(r),f));
    3269             : }
    3270             : 
    3271             : static GEN
    3272        1260 : ffpartmapimage(const char *s, GEN r)
    3273             : {
    3274        1260 :    GEN a = NULL, p = NULL;
    3275        1260 :    if (typ(r)==t_POL && degpol(r) >= 1
    3276        1260 :       && RgX_is_FpXQX(r,&a,&p) && a && typ(a)==t_FFELT) return a;
    3277           0 :    pari_err_TYPE(s, r);
    3278             :    return NULL; /* LCOV_EXCL_LINE */
    3279             : }
    3280             : 
    3281             : static GEN
    3282        2709 : ffeltmap_i(GEN m, GEN x)
    3283             : {
    3284        2709 :    GEN r = gel(m,2);
    3285        2709 :    if (!FF_samefield(x, gel(m,1)))
    3286          84 :      pari_err_DOMAIN("ffmap","m","domain does not contain", x, r);
    3287        2625 :    if (typ(r)==t_FFELT)
    3288        1659 :      return FF_map(r, x);
    3289             :    else
    3290         966 :      return FFX_preimage(x, r, ffpartmapimage("ffmap", r));
    3291             : }
    3292             : 
    3293             : static GEN
    3294        4459 : ffmap_i(GEN m, GEN x)
    3295             : {
    3296             :   GEN y;
    3297        4459 :   long i, lx, tx = typ(x);
    3298        4459 :   switch(tx)
    3299             :   {
    3300        2541 :     case t_FFELT:
    3301        2541 :       return ffeltmap_i(m, x);
    3302        1267 :     case t_POL: case t_RFRAC: case t_SER:
    3303             :     case t_VEC: case t_COL: case t_MAT:
    3304        1267 :       y = cgetg_copy(x, &lx);
    3305        1988 :       for (i=1; i<lontyp[tx]; i++) y[i] = x[1];
    3306        4564 :       for (i=lontyp[tx]; i<lx; i++)
    3307             :       {
    3308        3339 :         GEN yi = ffmap_i(m, gel(x,i));
    3309        3297 :         if (!yi) return NULL;
    3310        3297 :         gel(y,i) = yi;
    3311             :       }
    3312        1225 :       return y;
    3313             :   }
    3314         651 :   return gcopy(x);
    3315             : }
    3316             : 
    3317             : GEN
    3318        1036 : ffmap(GEN m, GEN x)
    3319             : {
    3320        1036 :   pari_sp ltop = avma;
    3321             :   GEN y;
    3322        1036 :   checkmap(m, "ffmap");
    3323        1036 :   y = ffmap_i(m, x);
    3324        1036 :   if (y) return y;
    3325          42 :   set_avma(ltop); return cgetg(1,t_VEC);
    3326             : }
    3327             : 
    3328             : static GEN
    3329         252 : ffeltmaprel_i(GEN m, GEN x)
    3330             : {
    3331         252 :    GEN g = gel(m,1), r = gel(m,2);
    3332         252 :    if (!FF_samefield(x, g))
    3333           0 :      pari_err_DOMAIN("ffmap","m","domain does not contain", x, r);
    3334         252 :    if (typ(r)==t_FFELT)
    3335          84 :      retmkpolmod(FF_map(r, x), pol_x(FF_var(g)));
    3336             :    else
    3337         168 :      retmkpolmod(FFX_preimagerel(x, r, ffpartmapimage("ffmap", r)), gcopy(r));
    3338             : }
    3339             : 
    3340             : static GEN
    3341         252 : ffmaprel_i(GEN m, GEN x)
    3342             : {
    3343             :   GEN y;
    3344         252 :   long i, lx, tx = typ(x);
    3345         252 :   switch(tx)
    3346             :   {
    3347         252 :     case t_FFELT:
    3348         252 :       return ffeltmaprel_i(m, x);
    3349           0 :     case t_POL: case t_RFRAC: case t_SER:
    3350             :     case t_VEC: case t_COL: case t_MAT:
    3351           0 :       y = cgetg_copy(x, &lx);
    3352           0 :       for (i=1; i<lontyp[tx]; i++) y[i] = x[1];
    3353           0 :       for (i=lontyp[tx]; i<lx; i++)
    3354           0 :         gel(y,i) = ffmaprel_i(m, gel(x,i));
    3355           0 :       return y;
    3356             :   }
    3357           0 :   return gcopy(x);
    3358             : }
    3359             : 
    3360             : GEN
    3361         252 : ffmaprel(GEN m, GEN x)
    3362             : {
    3363         252 :   checkmap(m, "ffmaprel");
    3364         252 :   return ffmaprel_i(m, x);
    3365             : }
    3366             : 
    3367             : static void
    3368          84 : err_compo(GEN m, GEN n)
    3369          84 : { pari_err_DOMAIN("ffcompomap","m","domain does not contain codomain of",n,m); }
    3370             : 
    3371             : GEN
    3372         420 : ffcompomap(GEN m, GEN n)
    3373             : {
    3374         420 :   pari_sp av = avma;
    3375         420 :   GEN g = gel(n,1), r, m2, n2;
    3376         420 :   checkmap(m, "ffcompomap");
    3377         420 :   checkmap(n, "ffcompomap");
    3378         420 :   m2 = gel(m,2); n2 = gel(n,2);
    3379         420 :   switch((typ(m2)==t_POL)|((typ(n2)==t_POL)<<1))
    3380             :   {
    3381          84 :     case 0:
    3382          84 :       if (!FF_samefield(gel(m,1),n2)) err_compo(m,n);
    3383          42 :       r = FF_map(gel(m,2), n2);
    3384          42 :       break;
    3385          84 :     case 2:
    3386          84 :       r = ffmap_i(m, n2);
    3387          42 :       if (lg(r) == 1) err_compo(m,n);
    3388          42 :       break;
    3389         168 :     case 1:
    3390         168 :       r = ffeltmap_i(m, n2);
    3391         126 :       if (!r)
    3392             :       {
    3393             :         GEN a, A, R, M;
    3394             :         long dm, dn;
    3395          42 :         a = ffpartmapimage("ffcompomap",m2);
    3396          42 :         A = FF_to_FpXQ_i(FF_neg(n2));
    3397          42 :         setvarn(A, 1);
    3398          42 :         R = deg1pol(gen_1, A, 0);
    3399          42 :         setvarn(R, 0);
    3400          42 :         M = gcopy(m2);
    3401          42 :         setvarn(M, 1);
    3402          42 :         r = polresultant0(R, M, 1, 0);
    3403          42 :         dm = FF_f(gel(m,1)); dn = FF_f(gel(n,1));
    3404          42 :         if (dm % dn || !FFX_ispower(r, dm/dn, a, &r)) err_compo(m,n);
    3405          42 :         setvarn(r, varn(FF_mod(g)));
    3406             :       }
    3407         126 :       break;
    3408          84 :     case 3:
    3409             :     {
    3410             :       GEN M, R, T, p, a;
    3411          84 :       a = ffpartmapimage("ffcompomap",n2);
    3412          84 :       if (!FF_samefield(a, gel(m,1))) err_compo(m,n);
    3413          42 :       p = FF_p_i(gel(n,1));
    3414          42 :       T = FF_mod(gel(n,1));
    3415          42 :       setvarn(T, 1);
    3416          42 :       R = RgX_to_FpXQX(n2,T,p);
    3417          42 :       setvarn(R, 0);
    3418          42 :       M = gcopy(m2);
    3419          42 :       setvarn(M, 1);
    3420          42 :       r = polresultant0(R, M, 1, 0);
    3421          42 :       setvarn(r, varn(n2));
    3422             :     }
    3423             :   }
    3424         252 :   return gerepilecopy(av, mkvec2(g,r));
    3425             : }

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