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Revision 1.2, Fri Sep 28 08:20:28 2018 UTC (4 years, 2 months ago) by noro
Branch: MAIN
CVS Tags: HEAD
Changes since 1.1: +11 -11 lines

Changed macros : QTOS->ZTOS, STOQ->STOZ etc.

/* $OpenXM: OpenXM_contrib2/asir2018/engine/Hgfs.c,v 1.2 2018/09/28 08:20:28 noro Exp $ */

#include "ca.h"
#include "inline.h"

int debug_sfbfctr;

void lnfsf(int n,UM p0,UM p1,struct p_pair *list,UM np0,UM np1);
void extractcoefbm(BM f,int dx,UM r);

int comp_dum(DUM a,DUM b)
{
  if ( DEG(a->f) > DEG(b->f) )
    return -1;
  else if ( DEG(a->f) < DEG(b->f) )
    return 1;
  else
    return 0;
}

void ufctrsf(P p,DCP *dcp)
{
  int n,i,j,k;
  DCP dc,dc0;
  P lc;
  UM mp;
  UM *tl;
  Obj obj;
  struct oDUM *udc,*udc1;

  simp_ff((Obj)p,&obj); p = (P)obj;
  if ( !p ) {
    NEWDC(dc); COEF(dc) = 0; DEG(dc) = ONE; 
    NEXT(dc) = 0; *dcp = dc;
    return;
  }
  mp = W_UMALLOC(UDEG(p));
  ptosfum(p,mp);
  if ( (n = DEG(mp)) < 0 ) {
    *dcp = 0; return;
  } else if ( n == 0 ) {
    NEWDC(dc); COEF(dc) = p; DEG(dc) = ONE; 
    NEXT(dc) = 0; *dcp = dc;
    return;
  }
  lc = COEF(DC(p));
  if ( !_isonesf(COEF(mp)[n]) ) {
    monicsfum(mp);
  }

  W_CALLOC(n+1,struct oDUM,udc);
  gensqfrsfum(mp,udc);

  tl = (UM *)ALLOCA((n+1)*sizeof(UM));
  W_CALLOC(DEG(mp)+1,struct oDUM,udc1);

  for ( i = 0,j = 0; udc[i].f; i++ )
    if ( DEG(udc[i].f) == 1 ) {
      udc1[j].f = udc[i].f; udc1[j].n = udc[i].n; j++;
    } else {
      bzero((char *)tl,(n+1)*sizeof(UM));
      czsfum(udc[i].f,tl);
      for ( k = 0; tl[k]; k++, j++ ) {
        udc1[j].f = tl[k]; udc1[j].n = udc[i].n;
      }
    }
  udc = udc1;
  for ( i = 0; udc[i].f; i++ );
  qsort(udc,i,sizeof(struct oDUM),
    (int (*)(const void *,const void *))comp_dum);

  NEWDC(dc0); COEF(dc0) = lc; DEG(dc0) = ONE; dc = dc0;
  for ( n = 0; udc[n].f; n++ ) {
    NEWDC(NEXT(dc)); dc = NEXT(dc);
    STOZ(udc[n].n,DEG(dc)); sfumtop(VR(p),udc[n].f,&COEF(dc));
  }
  NEXT(dc) = 0; *dcp = dc0;
}

void gensqfrsfum(UM p,struct oDUM *dc)
{
  int n,i,j,d,mod;
  UM t,s,g,f,f1,b;
  GFS u,v;

  if ( (n = DEG(p)) == 1 ) {
    dc[0].f = UMALLOC(DEG(p)); cpyum(p,dc[0].f); dc[0].n = 1;
    return;
  }
  t = W_UMALLOC(n); s = W_UMALLOC(n); g = W_UMALLOC(n);
  f = W_UMALLOC(n); f1 = W_UMALLOC(n); b = W_UMALLOC(n);
  diffsfum(p,t); cpyum(p,s); gcdsfum(t,s,g); 
  if ( !DEG(g) ) {
    dc[0].f = UMALLOC(DEG(p)); cpyum(p,dc[0].f); dc[0].n = 1;
    return;
  }
  cpyum(p,b); cpyum(p,t); divsfum(t,g,f);
  for ( i = 0, d = 0; DEG(f); i++ ) {
    while ( 1 ) {
      cpyum(b,t);
      if ( divsfum(t,f,s) >= 0 )
        break;
      else {
        cpyum(s,b); d++;
      }
    }
    cpyum(b,t); cpyum(f,s); gcdsfum(t,s,f1);
    divsfum(f,f1,s); cpyum(f1,f);
    dc[i].f = UMALLOC(DEG(s)); cpyum(s,dc[i].f); dc[i].n = d;
  }
  mod = characteristic_sf();
  if ( DEG(b) > 0 ) {
    d = 1;
    while ( 1 ) {
      cpyum(b,t);
      for ( j = DEG(t); j >= 0; j-- )
        if ( COEF(t)[j] && (j % mod) )
          break;
      if ( j >= 0 )
        break;
      else {
        DEG(s) = DEG(t)/mod;
        for ( j = 0; j <= DEG(t); j++ ) {
          iftogfs(COEF(t)[j*mod],&u);
          pthrootgfs(u,&v);
          COEF(s)[j] = v?FTOIF(CONT(v)):0;
        }
        cpyum(s,b); d *= mod;
      }
    }
    gensqfrsfum(b,dc+i);
    for ( j = i; dc[j].f; j++ )
      dc[j].n *= d;
  }
}

void randsfum(int d,UM p)
{
  int i;

  for ( i = 0; i < d; i++ )
    COEF(p)[i] = _randomsf();
  for ( i = d-1; i >= 0 && !COEF(p)[i]; i-- );
  p->d = i;
}

void pwrmodsfum(UM p,int e,UM f,UM pr)
{
  UM wt,ws,q;

  if ( e == 0 ) {
    DEG(pr) = 0; COEF(pr)[0] = _onesf();
  } else if ( DEG(p) < 0 ) 
    DEG(pr) = -1;
  else if ( e == 1 ) {
    q = W_UMALLOC(DEG(p)); cpyum(p,pr);
    DEG(pr) = divsfum(pr,f,q);
  } else if ( DEG(p) == 0 ) {
    DEG(pr) = 0; COEF(pr)[0] = _pwrsf(COEF(p)[0],e);
  } else {
    wt = W_UMALLOC(2*DEG(f)); ws = W_UMALLOC(2*DEG(f));
    q = W_UMALLOC(2*DEG(f));
    pwrmodsfum(p,e/2,f,wt);
    if ( !(e%2) )  {
      mulsfum(wt,wt,pr); DEG(pr) = divsfum(pr,f,q);
    } else {
      mulsfum(wt,wt,ws);
      DEG(ws) = divsfum(ws,f,q);
      mulsfum(ws,p,pr);
      DEG(pr) = divsfum(pr,f,q);
    }
  }
}

void spwrsfum(UM m,UM f,Z e,UM r)
{
  UM t,s,q;
  Z e1,rem,two;

  if ( !e ) {
    DEG(r) = 0; COEF(r)[0] = _onesf();
  } else if ( UNIZ(e) )
    cpyum(f,r);
  else {
    STOZ(2,two);
    divqrz(e,two,&e1,&rem);
    t = W_UMALLOC(2*DEG(m)); spwrsfum(m,f,e1,t);
    s = W_UMALLOC(2*DEG(m)); q = W_UMALLOC(2*DEG(m));
    mulsfum(t,t,s); DEG(s) = divsfum(s,m,q);
    if ( rem ) {
      mulsfum(s,f,t); DEG(t) = divsfum(t,m,q); cpyum(t,r);
    } else
      cpyum(s,r);
  }
}

void tracemodsfum(UM m,UM f,int e,UM r)
{
  UM t,s,q,u;
  int i;

  q = W_UMALLOC(2*DEG(m)+DEG(f)); /* XXX */
  t = W_UMALLOC(2*DEG(m));
  s = W_UMALLOC(2*DEG(m));
  u = W_UMALLOC(2*DEG(m));
  DEG(f) = divsfum(f,m,q);
  cpyum(f,s);
  cpyum(f,t);
  for ( i = 1; i < e; i++ ) {
    mulsfum(t,t,u);
    DEG(u) = divsfum(u,m,q); cpyum(u,t);
    addsfum(t,s,u); cpyum(u,s);
  }
  cpyum(s,r);
}

void make_qmatsf(UM p,UM *tab,int ***mp)
{
  int n,i,j;
  int *c;
  UM q,r;
  int **mat;
  int one;

  n = DEG(p);
  *mp = mat = almat(n,n);
  for ( j = 0; j < n; j++ ) {
    r = W_UMALLOC(DEG(tab[j])); q = W_UMALLOC(DEG(tab[j]));  
    cpyum(tab[j],r); DEG(r) = divsfum(r,p,q);
    for ( i = 0, c = COEF(r); i <= DEG(r); i++ )
      mat[i][j] = c[i];
  }
  one = _onesf();
  for ( i = 0; i < n; i++ )
    mat[i][i] = _subsf(mat[i][i],one);
}

void nullsf(int **mat,int n,int *ind)
{
  int i,j,l,s,h,inv;
  int *t,*u;

  bzero((char *)ind,n*sizeof(int));
  ind[0] = 0;
  for ( i = j = 0; j < n; i++, j++ ) {
    for ( ; j < n; j++ ) {
      for ( l = i; l < n; l++ )
        if ( mat[l][j] )
          break;
      if ( l < n ) {
        t = mat[i]; mat[i] = mat[l]; mat[l] = t; break;
      } else
        ind[j] = 1;
    }
    if ( j == n )
      break;
    inv = _invsf(mat[i][j]);
    for ( s = j, t = mat[i]; s < n; s++ )
      t[s] = _mulsf(t[s],inv);
    for ( l = 0; l < n; l++ ) {
      if ( l == i )
        continue;
      u = mat[l]; h = _chsgnsf(u[j]);
      for ( s = j; s < n; s++ )
        u[s] = _addsf(_mulsf(h,t[s]),u[s]);
    }
  }
}

void null_to_solsf(int **mat,int *ind,int n,UM *r)
{
  int i,j,k,l;
  int *c;
  UM w;

  for ( i = 0, l = 0; i < n; i++ ) {
    if ( !ind[i] )
      continue;
    w = UMALLOC(n);
    for ( j = k = 0, c = COEF(w); j < n; j++ )
      if ( ind[j] )
        c[j] = 0;
      else
        c[j] = mat[k++][i];
    c[i] = _chsgnsf(_onesf());
    for ( j = n; j >= 0; j-- )
      if ( c[j] )
        break;
    DEG(w) = j;
    r[l++] = w;
  }
}
/*
make_qmatsf(p,tab,mp)
nullsf(mat,n,ind)
null_to_solsf(ind,n,r)
*/

void czsfum(UM f,UM *r)
{
  int i,j;
  int d,n,ord;
  UM s,t,u,v,w,g,x,m,q;
  UM *base;

  n = DEG(f); base = (UM *)ALLOCA(n*sizeof(UM));
  bzero((char *)base,n*sizeof(UM));

  w = W_UMALLOC(2*n); q = W_UMALLOC(2*n); m = W_UMALLOC(2*n);

  base[0] = W_UMALLOC(0); DEG(base[0]) = 0; COEF(base[0])[0] = _onesf();

  t = W_UMALLOC(1); DEG(t) = 1; COEF(t)[0] = 0; COEF(t)[1] = _onesf();

  ord = field_order_sf();
  pwrmodsfum(t,ord,f,w);
  base[1] = W_UMALLOC(DEG(w));
  cpyum(w,base[1]);

  for ( i = 2; i < n; i++ ) {
    mulsfum(base[i-1],base[1],m);
    DEG(m) = divsfum(m,f,q);
    base[i] = W_UMALLOC(DEG(m)); cpyum(m,base[i]);
  }

  v = W_UMALLOC(n); cpyum(f,v);
  DEG(w) = 1; COEF(w)[0] = 0; COEF(w)[1] = _onesf();
  x = W_UMALLOC(1); DEG(x) = 1; COEF(x)[0] = 0; COEF(x)[1] = _onesf();
  t = W_UMALLOC(n); s = W_UMALLOC(n); u = W_UMALLOC(n); g = W_UMALLOC(n);

  for ( j = 0, d = 1; 2*d <= DEG(v); d++ ) {
    for ( DEG(t) = -1, i = 0; i <= DEG(w); i++ )
      if ( COEF(w)[i] ) {
        mulssfum(base[i],COEF(w)[i],s); 
        addsfum(s,t,u); cpyum(u,t);
      }
    cpyum(t,w); cpyum(v,s); subsfum(w,x,t);
    gcdsfum(s,t,g);
    if ( DEG(g) >= 1 ) {
      berlekampsf(g,d,base,r+j); j += DEG(g)/d;
      divsfum(v,g,q); cpyum(q,v);
      DEG(w) = divsfum(w,v,q);
      for ( i = 0; i < DEG(v); i++ )
        DEG(base[i]) = divsfum(base[i],v,q);
    }
  }
  if ( DEG(v) ) {
    r[j] = UMALLOC(DEG(v)); cpyum(v,r[j]); j++;
  }
  r[j] = 0;
}

int berlekampsf(UM p,int df,UM *tab,UM *r)
{
  int n,i,j,k,nf,d,nr;
  int **mat;
  int *ind;
  UM mp,w,q,gcd,w1,w2;
  UM *u;
  int *root;

  n = DEG(p);
  ind = ALLOCA(n*sizeof(int));
  make_qmatsf(p,tab,&mat);
  nullsf(mat,n,ind);
  for ( i = 0, d = 0; i < n; i++ )
    if ( ind[i] )
      d++;
  if ( d == 1 ) {
    r[0] = UMALLOC(n); cpyum(p,r[0]); return 1;
  }
  u = ALLOCA(d*sizeof(UM *));
  r[0] = UMALLOC(n); cpyum(p,r[0]);
  null_to_solsf(mat,ind,n,u);
  root = ALLOCA(d*sizeof(int));
  w = W_UMALLOC(n); mp = W_UMALLOC(d);
  w1 = W_UMALLOC(n); w2 = W_UMALLOC(n);
  for ( i = 1, nf = 1; i < d; i++ ) {
    minipolysf(u[i],p,mp);
    nr = find_rootsf(mp,root);
    for ( j = 0; j < nf; j++ ) {
      if ( DEG(r[j]) == df )
        continue;
      for ( k = 0; k < nr; k++ ) {
        cpyum(u[i],w1); cpyum(r[j],w2);
        COEF(w1)[0] = _chsgnsf(root[k]);
        gcdsfum(w1,w2,w);
        if ( DEG(w) > 0 && DEG(w) < DEG(r[j]) ) {
          gcd = UMALLOC(DEG(w));
          q = UMALLOC(DEG(r[j])-DEG(w));
          cpyum(w,gcd); divsfum(r[j],w,q);
          r[j] = q; r[nf++] = gcd;
        }
        if ( nf == d )
          return d;
      }
    }
  }
  /* NOT REACHED */
  error("berlekampsf : cannot happen");
  return 0;
}

void minipolysf(UM f,UM p,UM mp)
{
  struct p_pair *list,*l,*l1,*lprev;  
  int n,d;
  UM u,p0,p1,np0,np1,q,w;

  list = (struct p_pair *)MALLOC(sizeof(struct p_pair));
  list->p0 = u = W_UMALLOC(0); DEG(u) = 0; COEF(u)[0] = _onesf();
  list->p1 = W_UMALLOC(0); cpyum(list->p0,list->p1);
  list->next = 0;
  n = DEG(p); w = UMALLOC(2*n);
  p0 = UMALLOC(2*n); cpyum(list->p0,p0);
  p1 = UMALLOC(2*n); cpyum(list->p1,p1);
  q = W_UMALLOC(2*n);
  while ( 1 ) {
    COEF(p0)[DEG(p0)] = 0; DEG(p0)++; COEF(p0)[DEG(p0)] = _onesf();
    mulsfum(f,p1,w); DEG(w) = divsfum(w,p,q); cpyum(w,p1);
    np0 = UMALLOC(n); np1 = UMALLOC(n);
    lnfsf(n,p0,p1,list,np0,np1);
    if ( DEG(np1) < 0 ) {
      cpyum(np0,mp); return;
    } else {
      l1 = (struct p_pair *)MALLOC(sizeof(struct p_pair));
      l1->p0 = np0; l1->p1 = np1;
      for ( l = list, lprev = 0, d = DEG(np1);
        l && (DEG(l->p1) > d); lprev = l, l = l->next );
      if ( lprev ) {
        lprev->next = l1; l1->next = l;
      } else {
        l1->next = list; list = l1;
      }
    }
  }
}

void lnfsf(int n,UM p0,UM p1,struct p_pair *list,UM np0,UM np1)
{
  int h,d1;
  UM t0,t1,s0,s1;
  struct p_pair *l;

  cpyum(p0,np0); cpyum(p1,np1);
  t0 = W_UMALLOC(n); t1 = W_UMALLOC(n);
  s0 = W_UMALLOC(n); s1 = W_UMALLOC(n);
  for ( l = list; l; l = l->next ) {
    d1 = DEG(np1);
    if ( d1 == DEG(l->p1) ) {
      h = _divsf(COEF(np1)[d1],_chsgnsf(COEF(l->p1)[d1]));
      mulssfum(l->p0,h,t0); addsfum(np0,t0,s0); cpyum(s0,np0);
      mulssfum(l->p1,h,t1); addsfum(np1,t1,s1); cpyum(s1,np1);
    }
  }
}

int find_rootsf(UM p,int *root)
{
  UM *r;
  int i,n;

  n = DEG(p);
  r = ALLOCA((DEG(p))*sizeof(UM));
  canzassf(p,1,r);
  for ( i = 0; i < n; i++ )
    root[i] = _chsgnsf(COEF(r[i])[0]);
  return n;
}

void canzassf(UM f,int d,UM *r)
{
  UM t,s,u,w,g,o;
  Z n1,n2,n3,n4,n5,z;
  UM *b;
  int n,q,ed;

  if ( DEG(f) == d ) {
    r[0] = UMALLOC(d); cpyum(f,r[0]);
    return;
  } else {
    n = DEG(f); b = (UM *)ALLOCA(n*sizeof(UM));
    bzero((char *)b,n*sizeof(UM));

    t = W_UMALLOC(2*d);
    s = W_UMALLOC(DEG(f)); u = W_UMALLOC(DEG(f)); 
    w = W_UMALLOC(DEG(f)); g = W_UMALLOC(DEG(f));
    o = W_UMALLOC(0); DEG(o) = 0; COEF(o)[0] = _onesf();
    q = field_order_sf();
    if ( q % 2 ) {
      STOZ(q,n1); STOZ(d,z); pwrz(n1,z,&n2); subz(n2,ONE,&n3);
      STOZ(2,n4); divsz(n3,n4,&n5);
    } else
      ed = d*extdeg_sf();
    while ( 1 ) {
      randsfum(2*d,t);
      if ( q % 2 ) {
        spwrsfum(f,t,n5,s); subsfum(s,o,u);
      } else
        tracemodsfum(f,t,ed,u);
      cpyum(f,w);
      gcdsfum(w,u,g);
      if ( (DEG(g) >= 1) && (DEG(g) < DEG(f)) ) {
        canzassf(g,d,r); 
        cpyum(f,w); divsfum(w,g,s);
        canzassf(s,d,r+DEG(g)/d); 
        return;
      }
    }
  }
}

/* Hensel related functions */

int sfberle(V,V,P,int,GFS *,DCP *);
void sfgcdgen(P,ML,ML *);
void sfhenmain2(BM,UM,UM,int,BM *);
void ptosfbm(int,P,BM);
void sfhensel(int count,P f,V x,V y,int degbound,GFS *evp,P *sfp,ML *listp);

/* f = f(x,y) */

void sfhensel(int count,P f,V x,V y,int degbound,GFS *evp,P *sfp,ML *listp)
{
  int i;
  int fn;
  ML rlist;
  BM fl;
  VL vl,nvl;
  int dx,dy,bound;
  GFS ev;
  P f1,t,c,sf;
  DCP dc,dct,dc0;
  UM q,fm,hm;
  UM *gm;
  struct oEGT tmp0,tmp1,eg_hensel,eg_hensel_t;

  clctv(CO,f,&vl);
  if ( vl->v != x ) {
    reordvar(vl,x,&nvl); reorderp(nvl,vl,f,&f1);
    vl = nvl; f = f1;
  }
  if ( vl->next )
    y = vl->next->v;
  dx = getdeg(x,f);
  dy = getdeg(y,f);
  if ( dx == 1 ) {
    *listp = rlist = MLALLOC(1); rlist->n = 1; rlist->c[0] = 0;
    return;
  }
  fn = sfberle(x,y,f,count,&ev,&dc);
  if ( fn <= 1 ) {
    /* fn == 0 => short of evaluation points */
    *listp = rlist = MLALLOC(1); rlist->n = fn; rlist->c[0] = 0;
    return;
  }
  if ( degbound >= 0 ) {
    /*
     * reconstruct dc so that
     * dc[1],... : factors satisfy degree bound
     * dc[0]     : product of others
     */
    c = dc->c; dc = NEXT(dc);
    dc0 = 0;
    fn = 0;
    while ( dc ) {
      if ( getdeg(x,COEF(dc)) <= degbound ) {
        dct = NEXT(dc); NEXT(dc) = dc0; dc0 = dc; dc = dct;
        fn++;
      } else {
        mulp(vl,COEF(dc),c,&t); c = t;
        dc = NEXT(dc);
      }
    }
    if ( OID(c) == O_P ) {
      NEWDC(dc); COEF(dc) = c; DEG(dc) = ONE; NEXT(dc) = dc0;
      fn++;
    } else {
      mulp(vl,dc0->c,c,&t); dc0->c = t; dc = dc0;
    }
  } else {
    /* pass the the leading coeff. to the first element */
    c = dc->c; dc = NEXT(dc);
    mulp(vl,dc->c,c,&t); dc->c = t;
  }

  /* convert mod y-a factors into UM */
  gm = (UM *)ALLOCA(fn*sizeof(UM));
  for ( i = 0; i < fn; i++, dc = NEXT(dc) ) {
    gm[i] = W_UMALLOC(UDEG(dc->c));
    ptosfum(dc->c,gm[i]);
  }

  /* set bound */
  /* g | f, lc_y(g) = lc_y(f) => deg_y(g) <= deg_y(f) */
  /* so, bound = dy is sufficient, but we use slightly large value */
  bound = dy+2;

  /* f(x,y) -> f(x,y+ev) */
  fl = BMALLOC(dx,bound);
  ptosfbm(bound,f,fl);
  if ( ev ) shiftsfbm(fl,FTOIF(CONT(ev)));

  /* sf = f(x+ev) */
  sfbmtop(fl,x,y,&sf);

  /* fm = fl mod y */
  fm = W_UMALLOC(dx);
  cpyum(COEF(fl)[0],fm);
  hm = W_UMALLOC(dx);

  q = W_UMALLOC(dx);
  rlist = MLALLOC(fn); rlist->n = fn; rlist->bound = bound;
  if ( debug_sfbfctr )
    fprintf(asir_out,"%d candidates\n",fn);
  init_eg(&eg_hensel);
  for ( i = 0; i < fn-1; i++ ) {
    if ( debug_sfbfctr )
      fprintf(asir_out,"deg(fm) = %d, deg(gm[%d]) = %d\n",
      DEG(fm),i,DEG(gm[i]));
    init_eg(&eg_hensel_t);
    get_eg(&tmp0);
    /* fl = gm[i]*hm mod y */
    divsfum(fm,gm[i],hm);
    /* fl is replaced by the cofactor of gk mod y^bound */
    /* rlist->c[i] = gk */
    sfhenmain2(fl,gm[i],hm,bound,(BM *)&rlist->c[i]);
    cpyum(hm,fm);
    get_eg(&tmp1); add_eg(&eg_hensel_t,&tmp0,&tmp1);
    add_eg(&eg_hensel,&tmp0,&tmp1);
    if ( debug_sfbfctr) {
      print_eg("Hensel",&eg_hensel_t);
      fprintf(asir_out,"\n");
    }
  }
  if ( debug_sfbfctr) {
    print_eg("Hensel total",&eg_hensel);
    fprintf(asir_out,"\n");
  }
  /* finally, fl must be the lift of gm[fn-1] */
  rlist->c[i] = fl;

#if 0
  /* y -> y-a */
  mev = _chsgnsf(FTOIF(CONT(ev)));
  for ( i = 0; i < fn; i++ )
    shiftsfbm((BM)(rlist->c[i]),mev);
#endif
  *evp = ev;
  *sfp = sf;
  *listp = rlist;
}

/* main variable of f = x */

int sfberle(V x,V y,P f,int count,GFS *ev,DCP *dcp)
{
  UM wf,wf1,wf2,wfs,gcd;
  int fn,n;
  GFS m,fm;
  DCP dc,dct,dc0;
  VL vl;
  P lc,lc0,f0;
  Obj obj;
  int j,q,index,i;

  NEWVL(vl); vl->v = x;
  NEWVL(NEXT(vl)); NEXT(vl)->v = y;
  NEXT(NEXT(vl)) =0;
  simp_ff((Obj)f,&obj); f = (P)obj;
  n = ZTOS(DEG(DC(f)));
  wf = W_UMALLOC(n); wf1 = W_UMALLOC(n); wf2 = W_UMALLOC(n);
  wfs = W_UMALLOC(n); gcd = W_UMALLOC(n);
  q = field_order_sf();
  lc = DC(f)->c;
  for ( j = 0, fn = n + 1, index = 0; 
    index < q && j < count && fn > 1; index++ ) {
    indextogfs(index,&m);
    substp(vl,lc,y,(P)m,&lc0);
    if ( lc0 ) {
      substp(vl,f,y,(P)m,&f0);
      ptosfum(f0,wf); cpyum(wf,wf1); 
      diffsfum(wf1,wf2); gcdsfum(wf1,wf2,gcd);
      if ( DEG(gcd) == 0 ) {
        ufctrsf(f0,&dc);
        for ( dct = NEXT(dc), i = 0; dct; dct = NEXT(dct), i++ );
        if ( i < fn ) {
          dc0 = dc; fn = i; fm = m;
        }
        j++;
      }
    }
  }
  if ( index == q )
    return 0;
  else if ( fn == 1 )
    return 1;
  else {
    *dcp = dc0;
    *ev = fm;
    return fn;
  }
}

void sfgcdgen(P f,ML blist,ML *clistp)
{
  int i;
  int n,d,np;
  UM wf,wm,wx,wy,wu,wv,wa,wb,wg,q,tum;
  UM *in,*out;
  ML clist;

  n = UDEG(f); np = blist->n;
  d = 2*n;
  q = W_UMALLOC(d); wf = W_UMALLOC(d);
  wm = W_UMALLOC(d); wx = W_UMALLOC(d);
  wy = W_UMALLOC(d); wu = W_UMALLOC(d);
  wv = W_UMALLOC(d); wg = W_UMALLOC(d);
  wa = W_UMALLOC(d); wb = W_UMALLOC(d);
  ptosfum(f,wf); DEG(wg) = 0; COEF(wg)[0] = _onesf();
  *clistp = clist = MLALLOC(np); clist->n = np;
  for ( i = 0, in = (UM *)blist->c, out = (UM *)clist->c; i < np; i++ ) {
    divsfum(wf,in[i],q); tum = wf; wf = q; q = tum;
    cpyum(wf,wx); cpyum(in[i],wy);
    eucsfum(wx,wy,wa,wb); mulsfum(wa,wg,wm);
    DEG(wm) = divsfum(wm,in[i],q); out[i] = UMALLOC(DEG(wm));
    cpyum(wm,out[i]); mulsfum(q,wf,wu);
    mulsfum(wg,wb,wv); addsfum(wu,wv,wg);
  }
}

/* f = g0*h0 mod y -> f = gk*hk mod y^(dy+1), f is replaced by hk */

void sfhenmain2(BM f,UM g0,UM h0,int dy,BM *gp)
{
  int i,k;
  int dx;
  UM wt,wa,wb,q,w1,w2,wh1,wg1,ws;
  UM wc,wd,we,wz;
  BM wb0,wb1;
  int dg,dh;
  BM fk,gk,hk;
  
  if ( DEG(f) < dy )
    error("sfhenmain2 : invalid input");

  dx = degbm(f);
  dg = DEG(g0);
  dh = DEG(h0);

  W_BMALLOC(dx,dy,wb0); W_BMALLOC(dx,dy,wb1);
  wt = W_UMALLOC(dx); ws = W_UMALLOC(dx); q = W_UMALLOC(2*dx);
  wg1 = W_UMALLOC(2*dx); wh1 = W_UMALLOC(2*dx);

  /* fk = gk*hk mod y^k */
  W_BMALLOC(dx,dy,fk);
  cpyum(COEF(f)[0],COEF(fk)[0]);
  gk = BMALLOC(dg,dy);
  cpyum(g0,COEF(gk)[0]);
  W_BMALLOC(dh,dy,hk);
  cpyum(h0,COEF(hk)[0]);

  wc = W_UMALLOC(2*dx); wd = W_UMALLOC(2*dx);
  we = W_UMALLOC(2*dx); wz = W_UMALLOC(2*dx);

  /* compute wa,wb s.t. wa*g0+wb*h0 = 1 mod y */
  w1 = W_UMALLOC(dg); cpyum(g0,w1);
  w2 = W_UMALLOC(dh); cpyum(h0,w2);
  wa = W_UMALLOC(2*dx); wb = W_UMALLOC(2*dx);  /* XXX */
  eucsfum(w1,w2,wa,wb);

  if ( debug_sfbfctr)
    fprintf(stderr,"dy=%d\n",dy);
  for ( k = 1; k <= dy; k++ ) {
    if ( debug_sfbfctr)
      fprintf(stderr,".");

    /* at this point, f = gk*hk mod y^k */

    /* clear wt */
    clearum(wt,dx);

    /* wt = (f-gk*hk)/y^k */
    subsfum(COEF(f)[k],COEF(fk)[k],wt);
    
    /* compute wf1,wg1 s.t. wh1*g0+wg1*h0 = wt */
    mulsfum(wa,wt,wh1); DEG(wh1) = divsfum(wh1,h0,q);
    mulsfum(wh1,g0,wc); subsfum(wt,wc,wd); DEG(wd) = divsfum(wd,h0,wg1);

    /* check */
#if 0
    if ( DEG(wd) >= 0 || DEG(wg1) > ng )
      error("henmain2 : cannot happen(adj)");

    mulsfum(wg1,h0,wc); mulsfum(wh1,g0,wd); addsfum(wc,wd,we);
    subsfum(we,wt,wz);
    if ( DEG(wz) >= 0 )
      error("henmain2 : cannot happen");
#endif

    /* fk += ((wg1*hk+wh1*gk)*y^k+wg1*wh1*y^(2*k) mod y^(dy+1) */
    /* wb0 = wh1*y^k */
    clearbm(dx,wb0);
    cpyum(wh1,COEF(wb0)[k]);

    /* wb1 = gk*wb0 mod y^(dy+1) */
    clearbm(dx,wb1);
    mulsfbm(gk,wb0,wb1);
    /* fk += wb1 */
    addtosfbm(wb1,fk);

    /* wb0 = wg1*y^k */
    clearbm(dx,wb0);
    cpyum(wg1,COEF(wb0)[k]);

    /* wb1 = hk*wb0 mod y^(dy+1) */
    clearbm(dx,wb1);
    mulsfbm(hk,wb0,wb1);
    /* fk += wb1 */
    addtosfbm(wb1,fk);

    /* fk += wg1*wh1*y^(2*k) mod y^(dy+1) */
    if ( 2*k <= dy ) {
      mulsfum(wg1,wh1,wt); addsfum(COEF(fk)[2*k],wt,ws);
      cpyum(ws,COEF(fk)[2*k]);
    }

    /* gk += wg1*y^k, hk += wh1*y^k */
    cpyum(wg1,COEF(gk)[k]);
    cpyum(wh1,COEF(hk)[k]);
  }
  if ( debug_sfbfctr)
    fprintf(stderr,"\n");
  *gp = gk;
  DEG(f) = dy;
  for ( i = 0; i <= dy; i++ )
    cpyum(COEF(hk)[i],COEF(f)[i]);
}

/* a0*g+b0*h = 1 mod y -> a*g+b*h = 1 mod y^(dy+1) */

void sfexgcd_by_hensel(BM g,BM h,int dy,BM *ap,BM *bp)
{
  int i,k;
  int dx;
  UM wt,wa,wb,q,w1,w2,ws;
  UM wc,wd,we,wz,wa1,wb1;
  BM wz0,wz1;
  int dg,dh;
  BM a,b,c;

  dg = degbm(g);
  dh = degbm(h);
  dx = dg+dh;

  a = BMALLOC(dh,dy);
  b = BMALLOC(dg,dy);
  /* c holds a*g+b*h-1 */
  c = BMALLOC(dg+dh,dy);

  W_BMALLOC(dx,dy,wz0); W_BMALLOC(dx,dy,wz1);

  wt = W_UMALLOC(dx); ws = W_UMALLOC(dx); q = W_UMALLOC(2*dx);
  wa1 = W_UMALLOC(2*dx); wb1 = W_UMALLOC(2*dx);
  wc = W_UMALLOC(2*dx); wd = W_UMALLOC(2*dx);
  we = W_UMALLOC(2*dx); wz = W_UMALLOC(2*dx);

  /* compute wa,wb s.t. wa*g0+wb*h0 = 1 mod y */
  w1 = W_UMALLOC(dg); cpyum(COEF(g)[0],w1);
  w2 = W_UMALLOC(dh); cpyum(COEF(h)[0],w2);
  wa = W_UMALLOC(2*dx); wb = W_UMALLOC(2*dx);  /* XXX */
  eucsfum(w1,w2,wa,wb);
  cpyum(wa,COEF(a)[0]); cpyum(wb,COEF(b)[0]);
  
  /* initialize c to a*g+b*h-1 */
  mulsfbm(a,g,c); mulsfbm(b,h,wz0); addtosfbm(wz0,c);
  COEF(COEF(c)[0])[0] = 0;
  
  if ( debug_sfbfctr)
    fprintf(stderr,"dy=%d\n",dy);
  for ( k = 1; k <= dy; k++ ) {
    if ( debug_sfbfctr)
      fprintf(stderr,".");

    /* at this point, a*g+b*h = 1 mod y^k, c = a*g+b*h-1 */

    /* wt = -((a*g+b*h-1)/y^k) */
    cpyum(COEF(c)[k],wt);
    for ( i = DEG(wt); i >= 0; i-- )
      COEF(wt)[i] = _chsgnsf(COEF(wt)[i]);
    
    /* compute wa1,wb1 s.t. wa1*g0+wb1*h0 = wt */
    mulsfum(wa,wt,wa1); DEG(wa1) = divsfum(wa1,COEF(h)[0],q);
    mulsfum(wa1,COEF(g)[0],wc); subsfum(wt,wc,wd); 
    DEG(wd) = divsfum(wd,COEF(h)[0],wb1);

    /* c += ((wa1*g+wb1*h)*y^k mod y^(dy+1) */
    /* wz0 = wa1*y^k */
    clearbm(dx,wz0);
    cpyum(wa1,COEF(wz0)[k]);

    /* wz1 = wz0*g mod y^(dy+1) */
    clearbm(dx,wz1);
    mulsfbm(g,wz0,wz1);
    /* c += wz1 */
    addtosfbm(wz1,c);

    /* wz0 = wb1*y^k */
    clearbm(dx,wz0);
    cpyum(wb1,COEF(wz0)[k]);

    /* wz1 = wz0*h mod y^(dy+1) */
    clearbm(dx,wz1);
    mulsfbm(h,wz0,wz1);
    /* c += wz1 */
    addtosfbm(wz1,c);

    /* a += wa1*y^k, b += wb1*y^k */
    cpyum(wa1,COEF(a)[k]);
    cpyum(wb1,COEF(b)[k]);
  }
  if ( debug_sfbfctr)
    fprintf(stderr,"\n");
  DEG(a) = dy;
  DEG(b) = dy;
  *ap = a;
  *bp = b;
}

/* fl->c[i] = coef_y(f,i) */

void ptosfbm(int dy,P f,BM fl)
{
  DCP dc;
  int d,i,dx;
  UM t;

  dx = ZTOS(DEG(DC(f)));
  if ( DEG(fl) < dy )
    error("ptosfbm : invalid input");
  DEG(fl) = dy;
  clearbm(dx,fl);
  t = UMALLOC(dy);
  for ( dc = DC(f); dc; dc = NEXT(dc) ) {
    d = ZTOS(DEG(dc));
    ptosfum(COEF(dc),t);
    for ( i = 0; i <= DEG(t); i++ )
      COEF(COEF(fl)[i])[d] = COEF(t)[i];
  }
  for ( i = 0; i <= dy; i++ )
    degum(COEF(fl)[i],dx);
}

/* x : main variable */

void sfbmtop(BM f,V x,V y,P *fp)
{
  UM *c;
  int i,j,d,a,dy;
  GFS b;
  DCP dc0,dc,dct;

  dy = DEG(f);
  c = COEF(f);
  d = degbm(f);

  dc0 = 0;
  for ( i = 0; i <= d; i++ ) {
    dc = 0;
    for ( j = 0; j <= dy; j++ ) {
      if ( DEG(c[j]) >= i && (a = COEF(c[j])[i]) ) {
        NEWDC(dct);
        STOZ(j,DEG(dct));
        iftogfs(a,&b);
        COEF(dct) = (P)b;
        NEXT(dct) = dc;
        dc = dct;
      }
    }
    if ( dc ) {
      NEWDC(dct);
      STOZ(i,DEG(dct));
      MKP(y,dc,COEF(dct));
      NEXT(dct) = dc0;
      dc0 = dct;
    }
  }
  if ( dc0 )
    MKP(x,dc0,*fp);
  else
    *fp = 0;
}

void sfsqfr(P f,DCP *dcp)
{
  Obj obj;
  DCP dc;
  VL vl;

  simp_ff((Obj)f,&obj); f = (P)obj;
  clctv(CO,f,&vl);
  if ( !vl ) {
    /* f is a const */
    NEWDC(dc); DEG(dc) = ONE; COEF(dc) = f; NEXT(dc) = 0; *dcp = dc;
  } else if ( !NEXT(vl) )
    sfusqfr(f,dcp);
  else
    sqfrsf(vl,f,dcp);
}

void sfusqfr(P f,DCP *dcp)
{
  DCP dc,dct;
  struct oDUM *udc;
  V x;
  P lc;
  int n,i;
  UM mf;

  x = VR(f);
  n = getdeg(x,f);
  mf = W_UMALLOC(n);
  ptosfum(f,mf);
  lc = COEF(DC(f));
  if ( !_isonesf(COEF(mf)[n]) ) {
    monicsfum(mf);
  }
  W_CALLOC(n+1,struct oDUM,udc);
  gensqfrsfum(mf,udc);
  for ( i = 0, dc = 0; udc[i].f; i++ ) {
    NEWDC(dct); STOZ(udc[i].n,DEG(dct));
    sfumtop(x,udc[i].f,&COEF(dct));
    NEXT(dct) = dc; dc = dct;
  }
  NEWDC(dct); DEG(dct) = ONE; COEF(dct) = (P)lc; NEXT(dct) = dc;
  *dcp = dct;
}

#if 0
void sfbsqfrmain(P f,V x,V y,DCP *dcp)
{
  /* XXX*/
}

/* f is bivariate */

void sfbsqfr(P f,V x,V y,DCP *dcp)
{
  P t,rf,cx,cy;
  VL vl,rvl;
  DCP dcx,dcy,dct,dc;
  struct oVL vl0,vl1;

  /* cy(y) = cont(f,x), f /= cy */
  cont_pp_sfp(vl,f,&cy,&t); f = t;
  /* rvl = [y,x] */
  reordvar(vl,y,&rvl); reorderp(rvl,vl,f,&rf);
  /* cx(x) = cont(rf,y), Rf /= cy */
  cont_pp_sfp(rvl,rf,&cx,&t); rf = t;
  reorderp(vl,rvl,rf,&f);

  /* f -> cx*cy*f */
  sfsqfr(cx,&dcx); dcx = NEXT(dcx);
  sfsqfr(cy,&dcy); dcy = NEXT(dcy);
  if ( dcx ) {
    for ( dct = dcx; NEXT(dct); dct = NEXT(dct) );
    NEXT(dct) = dcy;
  } else
    dcx = dcy;
  if ( OID(f) == O_N )
    *dcp = dcx;
  else {
    /* f must be bivariate */
    sfbsqfrmain(f,x,y,&dc);
    if ( dcx ) {
      for ( dct = dcx; NEXT(dct); dct = NEXT(dct) );
      NEXT(dct) = dc;
    } else
      dcx = dc;
    *dcp = dcx;
  }
}
#endif

void sfdtest(P,ML,V,V,DCP *);

/* if degbound >= 0 find factor s.t. deg_x(factor) <= degbound */

void sfbfctr(P f,V x,V y,int degbound,DCP *dcp)
{
  ML list;
  P sf;
  GFS ev;
  DCP dc,dct;
  BM fl;
  int dx,dy;

  /* sf(x) = f(x+ev) = list->c[0]*list->c[1]*... */
  sfhensel(5,f,x,y,degbound,&ev,&sf,&list);
  if ( list->n == 0 )
    error("sfbfctr : short of evaluation points");
  else if ( list->n == 1 ) {
    /* f is irreducible */
    NEWDC(dc); DEG(dc) = ONE; COEF(dc) = f; NEXT(dc) = 0;
    *dcp = dc;
    return;
  }
  sfdtest(sf,list,x,y,&dc);
  if ( ev ) {
    dx = getdeg(x,sf);
    dy = getdeg(y,sf);
    W_BMALLOC(dx,dy,fl);
    for ( dct = dc; dct; dct = NEXT(dct) ) {
      ptosfbm(dy,COEF(dct),fl);
      shiftsfbm(fl,_chsgnsf(FTOIF(CONT(ev))));
      sfbmtop(fl,x,y,&COEF(dct));
    }
  }
  *dcp = dc;
}

/* returns shifted f, shifted factors and the eval pt */

void sfbfctr_shift(P f,V x,V y,int degbound,GFS *evp,P *sfp,DCP *dcp)
{
  ML list;
  P sf;
  GFS ev;
  DCP dc,dct;
  int dx,dy;

  /* sf(x) = f(x+ev) = list->c[0]*list->c[1]*... */
  sfhensel(5,f,x,y,degbound,&ev,&sf,&list);
  if ( list->n == 0 )
    error("sfbfctr_shift : short of evaluation points");
  else if ( list->n == 1 ) {
    /* f is irreducible */
    NEWDC(dc); DEG(dc) = ONE; COEF(dc) = f; NEXT(dc) = 0;
    *evp = 0;
    *sfp = f;
    *dcp = dc;
  } else {
    sfdtest(sf,list,x,y,dcp);
    *evp = ev;
    *sfp = sf;
  }
}

/* f = f(x,y) = list->c[0]*list->c[1]*... mod y^(list->bound+1) */

void sfdtest(P f,ML list,V x,V y,DCP *dcp)
{
  int np,dx,dy;
  int i,j,k,bound;
  int *win;
  P g,lcg,factor,cofactor,lcyx;
  P csum;
  DCP dcf,dcf0,dc;
  BM *c;
  BM lcy;
  UM lcg0,lcy0,w;
  UM *d1c;
  ML wlist;
  struct oVL vl1,vl0;
  VL vl;
  int z,dt,dtok;

  /* vl = [x,y] */
  vl0.v = x; vl0.next = &vl1; vl1.v = y; vl1.next = 0; vl = &vl0;

  /* setup various structures and arrays */
  dx = getdeg(x,f);
  dy = getdeg(y,f);
  np = list->n;
  win = W_ALLOC(np+1);
  wlist = W_MLALLOC(np);
  wlist->n = list->n;
  bound = wlist->bound = list->bound;
  c = (BM *)COEF(wlist);
  bcopy((char *)COEF(list),(char *)c,(int)(sizeof(BM)*np));

  lcg0 = W_UMALLOC(2*dy);

  /* initialize g by f */
  g = f;

  /* initialize lcg */
  mulp(vl,g,COEF(DC(g)),&lcg);

  /* initialize lcg0 */
  const_term(lcg,lcg0);

  /* initialize csum = lcg(1) */
  sfcsump(vl,lcg,&csum);

  /* initialize lcy by LC(f) */
  W_BMALLOC(0,dy,lcy);
  NEWDC(dc); COEF(dc) = COEF(DC(g)); DEG(dc) = 0; 
  NEWP(lcyx); VR(lcyx) = x; DC(lcyx) = dc;
  ptosfbm(dy,lcyx,lcy);

  /* initialize lcy0 by LC(f) */
  lcy0 = W_UMALLOC(bound);
  ptosfum(COEF(DC(g)),lcy0);

  /* ((d-1 coefs)*lcy0 */
  d1c = (UM *)W_ALLOC(np*sizeof(UM));
  w = W_UMALLOC(2*bound);
  for ( i = 1; i < np; i++ ) {
    extractcoefbm(c[i],degbm(c[i])-1,w);
    d1c[i] = W_UMALLOC(2*bound);
    mulsfum(w,lcy0,d1c[i]);
    /* d1c[i] = d1c[i] mod y^(bound+1) */
    if ( DEG(d1c[i]) > bound ) {
      for ( j = DEG(d1c[i]); j > bound; j-- )
        COEF(d1c[i])[j] = 0;
      degum(d1c[i],bound);
    }
  }

  if ( debug_sfbfctr)
    fprintf(stderr,"np = %d\n",np);
  dtok = 0;
  for ( g = f, k = 1, dcf = dcf0 = 0, win[0] = 1, --np, z = 0; ; z++ ) {
    if ( debug_sfbfctr && !(z % 1000) ) fprintf(stderr,".");
    dt = sfdegtest(dy,bound,d1c,k,win);
    if ( dt )
      dtok++;
    if ( dt && sfdtestmain(vl,lcg,lcg0,lcy,csum,wlist,
        k,win,&factor,&cofactor) ) {
      NEXTDC(dcf0,dcf); DEG(dcf) = ONE; COEF(dcf) = factor;
      g = cofactor;

      /* update lcg */
      mulp(vl,g,COEF(DC(g)),&lcg);

      /* update lcg0 */
      const_term(lcg,lcg0);

      /* update csum */
      sfcsump(vl,lcg,&csum);

      /* update dy */
      dy = getdeg(y,g);

      /* update lcy */
      clearbm(0,lcy);
      COEF(dc) = COEF(DC(g));
      ptosfbm(dy,lcyx,lcy);

      for ( i = 0; i < k - 1; i++ ) 
        for ( j = win[i] + 1; j < win[i + 1]; j++ ) 
          c[j-i-1] = c[j];
      for ( j = win[k-1] + 1; j <= np; j++ )   
          c[j-k] = c[j];
      if ( ( np -= k ) < k ) 
        break;
      if ( np - win[0] + 1 < k ) 
        if ( ++k > np )
          break;
        else
          for ( i = 0; i < k; i++ ) 
            win[i] = i + 1;
      else 
        for ( i = 1; i < k; i++ ) 
          win[i] = win[0] + i;


      /* update lcy0  */
      ptosfum(COEF(DC(g)),lcy0);
    
      /* update d-1 coeffs */
      for ( i = 1; i <= np; i++ ) {
        extractcoefbm(c[i],degbm(c[i])-1,w);
        mulsfum(w,lcy0,d1c[i]);
        /* d1c[i] = d1c[1] mod y^(bound+1) */
        if ( DEG(d1c[i]) > bound ) {
          for ( j = DEG(d1c[i]); j > bound; j-- )
            COEF(d1c[i])[j] = 0;
          degum(d1c[i],bound);
        }
      }
    } else if ( !ncombi(1,np,k,win) ) {
      if ( k == np ) 
        break;
      else
        for ( i = 0, ++k; i < k; i++ ) 
          win[i] = i + 1;
    }
  }
  if ( debug_sfbfctr )
    fprintf(stderr,"total %d, omitted by degtest %d\n",z,z-dtok);
  NEXTDC(dcf0,dcf); COEF(dcf) = g;
  DEG(dcf) = ONE; NEXT(dcf) = 0; *dcp = dcf0;
}

void extractcoefbm(BM f,int dx,UM r)
{
  int j;
  UM fj;

  for ( j = DEG(f); j >= 0; j-- ) {
    fj = COEF(f)[j];
    if ( fj && DEG(fj) >= dx ) {
      COEF(r)[j] = COEF(fj)[dx];
    } else
      COEF(r)[j] = 0;
  }
  degum(r,DEG(f));
}

/* deg_y(prod mod y^(bound+1)) <= dy ? */

int sfdegtest(int dy,int bound,UM *d1c,int k,int *in)
{
  int i,j;
  UM w,w1,wt;
  BM t;

  w = W_UMALLOC(bound);
  w1 = W_UMALLOC(bound);
  clearum(w,bound);
  for ( i = 0; i < k; i++ ) {
    addsfum(w,d1c[in[i]],w1); wt = w; w = w1; w1 = wt;
  }
  return DEG(w) <= dy ? 1 : 0;
}

/* lcy = LC(g), lcg = lcy*g, lcg0 = const part of lcg */

int sfdtestmain(VL vl,P lcg,UM lcg0,BM lcy,P csum,ML list,
  int k,int *in,P *fp,P *cofp)
{
  P fmul,csumg,q,cont;
  V x,y;

  x = vl->v;
  y = vl->next->v;
  if (!sfctest(lcg0,lcy,list,k,in))
    return 0;
  mulsfbmarray(UDEG(lcg),lcy,list,k,in,x,y,&fmul);
  if ( csum ) {
    sfcsump(vl,fmul,&csumg);
    if ( csumg ) {
      if ( !divtp(vl,csum,csumg,&q) )
        return 0;
    } 
  }
  if ( divtp_by_sfbm(vl,lcg,fmul,&q) ) {
    cont_pp_sfp(vl,fmul,&cont,fp);
    cont_pp_sfp(vl,q,&cont,cofp);
    return 1;
  } else
    return 0;
}

void const_term(P f,UM c)
{
  DCP dc;

  for ( dc = DC(f); dc && DEG(dc); dc = NEXT(dc) );
  if ( dc ) 
    ptosfum(COEF(dc),c);
  else 
    DEG(c) = -1;
}

void const_term_sfbm(BM f,UM c)
{
  int i,dy;

  dy = DEG(f);
  for ( i = 0; i <= dy; i++ )
    if ( DEG(COEF(f)[i]) >= 0 )
      COEF(c)[i] = COEF(COEF(f)[i])[0];
    else
      COEF(c)[i] = 0;
  degum(c,dy);
}

/* lcy*(product of const part) | lcg0 ? */

int sfctest(UM lcg0,BM lcy,ML list,int k,int *in)
{
  int dy,i,dr;
  UM t,s,u,w;
  BM *l;

  dy = list->bound;
  t = W_UMALLOC(2*dy);
  s = W_UMALLOC(2*dy);
  u = W_UMALLOC(2*dy);
  const_term_sfbm(lcy,t);
  if ( DEG(t) < 0 )
    return 1;

  l = (BM *)list->c;
  for ( i = 0; i < k; i++ ) {
    const_term_sfbm(l[in[i]],s);
    mulsfum(t,s,u);
    if ( DEG(u) > dy )
      degum(u,dy);
    w = t; t = u; u = w;
  }
  cpyum(lcg0,s);
  dr = divsfum(s,t,u);
  if ( dr >= 0 )
    return 0;
  else
    return 1;
}

/* main var of f is x */

void mulsfbmarray(int dx,BM lcy,ML list,int k,int *in,V x,V y,P *g)
{
  int dy,i;
  BM wb0,wb1,t;
  BM *l;

  dy = list->bound;
  W_BMALLOC(dx,dy,wb0); W_BMALLOC(dx,dy,wb1);
  l = (BM *)list->c;
  clearbm(dx,wb0);
  mulsfbm(lcy,l[in[0]],wb0);
  for ( i = 1; i < k; i++ ) {
    clearbm(dx,wb1);
    mulsfbm(l[in[i]],wb0,wb1);
    t = wb0; wb0 = wb1; wb1 = t;
  }
  sfbmtop(wb0,x,y,g);
}

void sfcsump(VL vl,P f,P *s)
{
  P t,u;
  DCP dc;

  for ( dc = DC(f), t = 0; dc; dc = NEXT(dc) ) {
    addp(vl,COEF(dc),t,&u); t = u;
  }
  *s = t;
}

/* *fp = primitive part of f w.r.t. x */

void cont_pp_sfp(VL vl,P f,P *cp,P *fp)
{
  V x,y;
  int d;
  UM t,s,gcd;
  DCP dc;
  GFS g;

  x = vl->v;
  y = vl->next->v;
  d = getdeg(y,f);
  if ( d == 0 ) {
    itogfs(1,&g);
    *cp = (P)g;
    *fp = f;  /* XXX */
  } else {
    t = W_UMALLOC(2*d);
    s = W_UMALLOC(2*d);
    gcd = W_UMALLOC(2*d);
    dc = DC(f);
    ptosfum(COEF(dc),gcd);
    for ( dc = NEXT(dc); dc; dc = NEXT(dc) ) {
      ptosfum(COEF(dc),t);
      gcdsfum(gcd,t,s);
      cpyum(s,gcd);
    }
    sfumtop(y,gcd,cp);
    divsp(vl,f,*cp,fp);
  }
}

int divtp_by_sfbm(VL vl,P f,P g,P *qp)
{
  V x,y;
  int fx,fy,gx,gy;
  BM fl,gl,ql;
  UM *cf,*cg,*cq;
  UM hg,q,t,s;
  int i,j,dr;

  x = vl->v; y = vl->next->v;
  fx = getdeg(x,f); fy = getdeg(y,f);
  gx = getdeg(x,g); gy = getdeg(y,g);

  if ( fx < gx || fy < gy )
    return 0;
  W_BMALLOC(fx,fy,fl); ptosfbm(fy,f,fl); cf = COEF(fl);
  W_BMALLOC(gx,gy,gl); ptosfbm(gy,g,gl); cg = COEF(gl);
  W_BMALLOC(fx-gx,fy-gy,ql); cq = COEF(ql);

  hg = cg[gy];
  q = W_UMALLOC(fx); t = W_UMALLOC(fx); s = W_UMALLOC(fx);

  for ( i = fy; i >= gy; i-- ) {
    if ( DEG(cf[i]) < 0 )
      continue;
    dr = divsfum(cf[i],hg,q);
    if ( dr >= 0 )
      return 0;
    if ( DEG(q) > fx-gx )
      return 0;
    cpyum(q,cq[i-gy]);
    for ( j = 0; j <= gy; j++ ) {
      mulsfum(cg[j],q,t);
      subsfum(cf[j+i-gy],t,s);
      cpyum(s,cf[j+i-gy]);
    }
  }
  for ( j = gy-1; j >= 0 && DEG(cf[j]) < 0; j-- );
  if ( j >= 0 )
    return 0;
  sfbmtop(ql,x,y,qp);
  return 1;
}

/* XXX generate an irreducible poly of degree n */

extern int current_gfs_q1;
extern int *current_gfs_ntoi;

void generate_defpoly_sfum(int n,UM *dp)
{
  UM r,dr,t,g;
  UM *f;
  int *c,*w;
  int max,i,j;

  *dp = r = UMALLOC(n);
  DEG(r) = n;
  c = COEF(r);
  c[n] = _onesf();
  max = current_gfs_q1;
  w = (int *)ALLOCA(n*sizeof(int));
  bzero(w,n*sizeof(int));

  dr = W_UMALLOC(n); t = W_UMALLOC(n); g = W_UMALLOC(n);
  f = (UM *)ALLOCA((n+1)*sizeof(UM));
  while ( 1 ) {
    for ( i = 0; i < n && w[i] == max; i++ );
    if ( i == n ) {
      /* XXX cannot happen */
      error("generate_defpoly_sfum : cannot happen");
    }
    for ( j = 0; j < i; j++ )
      w[j] = 0;
    w[i]++;
    if ( !current_gfs_ntoi )
      for ( i = 0; i < n; i++ )
        c[i] = w[i]?FTOIF(w[i]):0;
    else
      for ( i = 0; i < n; i++ )
        c[i] = w[i]?FTOIF(w[i]-1):0;
    if ( !c[0] )
      continue;
    diffsfum(r,dr); cpyum(r,t); gcdsfum(t,dr,g);
    if ( DEG(g) > 0 )
      continue;

    czsfum(r,f);
    for ( i = 0; f[i]; i++ );
    if ( i == 1 )
      return;
  }
}